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class="vector-toc-link" href="#Greece"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.2</span> <span>Greece</span> </div> </a> <ul id="toc-Greece-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-China" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#China"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1.3</span> <span>China</span> </div> </a> <ul id="toc-China-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Medieval" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Medieval"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Medieval</span> </div> </a> <ul id="toc-Medieval-sublist" class="vector-toc-list"> <li id="toc-Middle_East" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Middle_East"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Middle East</span> </div> </a> <ul id="toc-Middle_East-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-India" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#India"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>India</span> </div> </a> <ul id="toc-India-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Modern" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Modern"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Modern</span> </div> </a> <ul id="toc-Modern-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Foundations" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Foundations"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Foundations</span> </div> </a> <ul id="toc-Foundations-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Significance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Significance"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Significance</span> </div> </a> <ul id="toc-Significance-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Principles" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Principles"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Principles</span> </div> </a> <button aria-controls="toc-Principles-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Principles subsection</span> </button> <ul id="toc-Principles-sublist" class="vector-toc-list"> <li id="toc-Limits_and_infinitesimals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Limits_and_infinitesimals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Limits and infinitesimals</span> </div> </a> <ul id="toc-Limits_and_infinitesimals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Differential_calculus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Differential_calculus"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Differential calculus</span> </div> </a> <ul id="toc-Differential_calculus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Leibniz_notation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Leibniz_notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Leibniz notation</span> </div> </a> <ul id="toc-Leibniz_notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Integral_calculus" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Integral_calculus"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Integral calculus</span> </div> </a> <ul id="toc-Integral_calculus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fundamental_theorem" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fundamental_theorem"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Fundamental theorem</span> </div> </a> <ul id="toc-Fundamental_theorem-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Applications</span> </div> </a> <ul id="toc-Applications-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Calculus</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 97 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-97" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">97 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%AB%E1%88%8D%E1%8A%A9%E1%88%88%E1%88%B5" title="ካልኩለስ – Amharic" lang="am" hreflang="am" data-title="ካልኩለስ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%81%D8%A7%D8%B6%D9%84_%D9%88%D8%AA%D9%83%D8%A7%D9%85%D9%84" title="تفاضل وتكامل – Arabic" lang="ar" hreflang="ar" data-title="تفاضل وتكامل" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Calculo" title="Calculo – Aragonese" lang="an" hreflang="an" data-title="Calculo" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/C%C3%A1lculu" title="Cálculu – Asturian" lang="ast" hreflang="ast" data-title="Cálculu" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%95%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B2%E0%A6%95%E0%A7%81%E0%A6%B2%E0%A6%BE%E0%A6%B8" title="ক্যালকুলাস – Bangla" lang="bn" hreflang="bn" data-title="ক্যালকুলাস" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/B%C3%AE-chek-hun" title="Bî-chek-hun – Minnan" lang="nan" hreflang="nan" data-title="Bî-chek-hun" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Central Bikol" lang="bcl" hreflang="bcl" data-title="Kalkulus" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-bg badge-Q70894304 mw-list-item" title=""><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%BD%D0%BE_%D0%B8_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D0%BD%D0%BE_%D1%81%D0%BC%D1%8F%D1%82%D0%B0%D0%BD%D0%B5" title="Диференциално и интегрално смятане – Bulgarian" lang="bg" hreflang="bg" data-title="Диференциално и интегрално смятане" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – Bosnian" lang="bs" hreflang="bs" data-title="Infinitezimalni račun" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/C%C3%A0lcul_infinitesimal" title="Càlcul infinitesimal – Catalan" lang="ca" hreflang="ca" data-title="Càlcul infinitesimal" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%C4%83%D0%BB%D0%BB%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математикăлла анализ – Chuvash" lang="cv" hreflang="cv" data-title="Математикăлла анализ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Infinitezim%C3%A1ln%C3%AD_po%C4%8Det" title="Infinitezimální počet – Czech" lang="cs" hreflang="cs" data-title="Infinitezimální počet" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Kakyula" title="Kakyula – Tumbuka" lang="tum" hreflang="tum" data-title="Kakyula" data-language-autonym="ChiTumbuka" data-language-local-name="Tumbuka" class="interlanguage-link-target"><span>ChiTumbuka</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Calcwlws" title="Calcwlws – Welsh" lang="cy" hreflang="cy" data-title="Calcwlws" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Infinitesimalregning" title="Infinitesimalregning – Danish" lang="da" hreflang="da" data-title="Infinitesimalregning" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Infinitesimalrechnung" title="Infinitesimalrechnung – German" lang="de" hreflang="de" data-title="Infinitesimalrechnung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CE%B3%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Λογισμός – Greek" lang="el" hreflang="el" data-title="Λογισμός" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/C%C3%A1lculo_infinitesimal" title="Cálculo infinitesimal – Spanish" lang="es" hreflang="es" data-title="Cálculo infinitesimal" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Infinitezima_kalkulo" title="Infinitezima kalkulo – Esperanto" lang="eo" hreflang="eo" data-title="Infinitezima kalkulo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Kalkulu_infinitesimal" title="Kalkulu infinitesimal – Basque" lang="eu" hreflang="eu" data-title="Kalkulu infinitesimal" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8%D8%A7%D9%86" title="حسابان – Persian" lang="fa" hreflang="fa" data-title="حسابان" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Calculus" title="Calculus – Fiji Hindi" lang="hif" hreflang="hif" data-title="Calculus" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Calcul_infinit%C3%A9simal" title="Calcul infinitésimal – French" lang="fr" hreflang="fr" data-title="Calcul infinitésimal" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Calcalas" title="Calcalas – Irish" lang="ga" hreflang="ga" data-title="Calcalas" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/C%C3%A1lculo_infinitesimal" title="Cálculo infinitesimal – Galician" lang="gl" hreflang="gl" data-title="Cálculo infinitesimal" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分 – Gan" lang="gan" hreflang="gan" data-title="微積分" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%95%E0%AA%B2%E0%AA%A8_%E0%AA%B6%E0%AA%BE%E0%AA%B8%E0%AB%8D%E0%AA%A4%E0%AB%8D%E0%AA%B0" title="કલન શાસ્ત્ર – Gujarati" lang="gu" hreflang="gu" data-title="કલન શાસ્ત્ર" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/M%C3%AC-chit-f%C3%BBn-ho%CC%8Dk" title="Mì-chit-fûn-ho̍k – Hakka Chinese" lang="hak" hreflang="hak" data-title="Mì-chit-fûn-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%AF%B8%EC%A0%81%EB%B6%84%ED%95%99" title="미적분학 – Korean" lang="ko" hreflang="ko" data-title="미적분학" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Calculus" title="Calculus – Hausa" lang="ha" hreflang="ha" data-title="Calculus" data-language-autonym="Hausa" data-language-local-name="Hausa" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%95%E0%A4%B2%E0%A4%A8" title="कलन – Hindi" lang="hi" hreflang="hi" data-title="कलन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – Croatian" lang="hr" hreflang="hr" data-title="Infinitezimalni račun" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Kalkulo" title="Kalkulo – Ido" lang="io" hreflang="io" data-title="Kalkulo" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://id.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Indonesian" lang="id" hreflang="id" data-title="Kalkulus" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Calculo_infinitesimal" title="Calculo infinitesimal – Interlingua" lang="ia" hreflang="ia" data-title="Calculo infinitesimal" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/%C3%96rsm%C3%A6%C3%B0areikningur" title="Örsmæðareikningur – Icelandic" lang="is" hreflang="is" data-title="Örsmæðareikningur" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Calcolo_infinitesimale" title="Calcolo infinitesimale – Italian" lang="it" hreflang="it" data-title="Calcolo infinitesimale" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%A9%D7%91%D7%95%D7%9F_%D7%90%D7%99%D7%A0%D7%A4%D7%99%D7%A0%D7%99%D7%98%D7%A1%D7%99%D7%9E%D7%9C%D7%99" title="חשבון אינפיניטסימלי – Hebrew" lang="he" hreflang="he" data-title="חשבון אינפיניטסימלי" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-jv badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://jv.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Javanese" lang="jv" hreflang="jv" data-title="Kalkulus" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%99%E1%83%90%E1%83%9A%E1%83%99%E1%83%A3%E1%83%9A%E1%83%A3%E1%83%A1%E1%83%98" title="კალკულუსი – Georgian" lang="ka" hreflang="ka" data-title="კალკულუსი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Calculus_infinitesimalis" title="Calculus infinitesimalis – Latin" lang="la" hreflang="la" data-title="Calculus infinitesimalis" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/R%C4%93%C4%B7ini" title="Rēķini – Latvian" lang="lv" hreflang="lv" data-title="Rēķini" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Integralinis_ir_diferencialinis_skai%C4%8Diavimas" title="Integralinis ir diferencialinis skaičiavimas – Lithuanian" lang="lt" hreflang="lt" data-title="Integralinis ir diferencialinis skaičiavimas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Infinitesimaalraekening" title="Infinitesimaalraekening – Limburgish" lang="li" hreflang="li" data-title="Infinitesimaalraekening" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Calculo" title="Calculo – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Calculo" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Madurese" lang="mad" hreflang="mad" data-title="Kalkulus" data-language-autonym="Madhurâ" data-language-local-name="Madurese" class="interlanguage-link-target"><span>Madhurâ</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%98%D0%BD%D1%84%D0%B8%D0%BD%D0%B8%D1%82%D0%B5%D0%B7%D0%B8%D0%BC%D0%B0%D0%BB%D0%BD%D0%BE_%D1%81%D0%BC%D0%B5%D1%82%D0%B0%D1%9A%D0%B5" title="Инфинитезимално сметање – Macedonian" lang="mk" hreflang="mk" data-title="Инфинитезимално сметање" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%95%E0%B4%B2%E0%B4%A8%E0%B4%82" title="കലനം – Malayalam" lang="ml" hreflang="ml" data-title="കലനം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%95%E0%A4%B2%E0%A4%A8" title="कलन – Marathi" lang="mr" hreflang="mr" data-title="कलन" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AA%D9%81%D8%A7%D8%B6%D9%84_%D9%88%D8%AA%D9%83%D8%A7%D9%85%D9%84" title="تفاضل وتكامل – Egyptian Arabic" lang="arz" hreflang="arz" data-title="تفاضل وتكامل" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Malay" lang="ms" hreflang="ms" data-title="Kalkulus" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Minangkabau" lang="min" hreflang="min" data-title="Kalkulus" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB_%D0%B1%D0%B0_%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB" title="Интеграл ба дифференциал тоолол – Mongolian" lang="mn" hreflang="mn" data-title="Интеграл ба дифференциал тоолол" data-language-autonym="Монгол" data-language-local-name="Mongolian" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%80%E1%80%B2%E1%80%80%E1%80%AF%E1%80%9C%E1%80%95%E1%80%BA" title="ကဲကုလပ် – Burmese" lang="my" hreflang="my" data-title="ကဲကုလပ်" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%95%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B2%E0%A5%8D%E0%A4%95%E0%A5%81%E0%A4%B2%E0%A4%B8" title="क्याल्कुलस – Newari" lang="new" hreflang="new" data-title="क्याल्कुलस" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%BE%AE%E5%88%86%E7%A9%8D%E5%88%86%E5%AD%A6" title="微分積分学 – Japanese" lang="ja" hreflang="ja" data-title="微分積分学" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Kalkulus" title="Kalkulus – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Kalkulus" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Calcul_infinitesimal" title="Calcul infinitesimal – Occitan" lang="oc" hreflang="oc" data-title="Calcul infinitesimal" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Kaalkulasii" title="Kaalkulasii – Oromo" lang="om" hreflang="om" data-title="Kaalkulasii" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%95%E0%A9%88%E0%A8%B2%E0%A8%95%E0%A9%82%E0%A8%B2%E0%A8%B8" title="ਕੈਲਕੂਲਸ – Punjabi" lang="pa" hreflang="pa" data-title="ਕੈਲਕੂਲਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%A9%DB%8C%D9%84%DA%A9%D9%88%D9%84%D8%B3" title="کیلکولس – Western Punjabi" lang="pnb" hreflang="pnb" data-title="کیلکولس" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-blk mw-list-item"><a href="https://blk.wikipedia.org/wiki/%E1%80%80%E1%80%B2%E1%80%B8%E1%80%80%E1%80%AF%E1%80%9C%E1%80%90%E1%80%BA%E1%80%9E%E1%80%BA" title="ကဲးကုလတ်သ် – Pa'O" lang="blk" hreflang="blk" data-title="ကဲးကုလတ်သ်" data-language-autonym="ပအိုဝ်ႏဘာႏသာႏ" data-language-local-name="Pa'O" class="interlanguage-link-target"><span>ပအိုဝ်ႏဘာႏသာႏ</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Kialkiulos" title="Kialkiulos – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Kialkiulos" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/C%C3%A1lculo_infinitesimal" title="Cálculo infinitesimal – Portuguese" lang="pt" hreflang="pt" data-title="Cálculo infinitesimal" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Calcul_infinitezimal" title="Calcul infinitezimal – Romanian" lang="ro" hreflang="ro" data-title="Calcul infinitezimal" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Yupaylliy" title="Yupaylliy – Quechua" lang="qu" hreflang="qu" data-title="Yupaylliy" data-language-autonym="Runa Simi" data-language-local-name="Quechua" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математический анализ – Russian" lang="ru" hreflang="ru" data-title="Математический анализ" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математическай анализ – Yakut" lang="sah" hreflang="sah" data-title="Математическай анализ" data-language-autonym="Саха тыла" data-language-local-name="Yakut" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Calculus" title="Calculus – Scots" lang="sco" hreflang="sco" data-title="Calculus" data-language-autonym="Scots" data-language-local-name="Scots" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9A%E0%B6%BD%E0%B6%B1%E0%B6%BA" title="කලනය – Sinhala" lang="si" hreflang="si" data-title="කලනය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Calculus" title="Calculus – Simple English" lang="en-simple" hreflang="en-simple" data-title="Calculus" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-ss mw-list-item"><a href="https://ss.wikipedia.org/wiki/Calculus" title="Calculus – Swati" lang="ss" hreflang="ss" data-title="Calculus" data-language-autonym="SiSwati" data-language-local-name="Swati" class="interlanguage-link-target"><span>SiSwati</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Diferenci%C3%A1lny_a_integr%C3%A1lny_po%C4%8Det" title="Diferenciálny a integrálny počet – Slovak" lang="sk" hreflang="sk" data-title="Diferenciálny a integrálny počet" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – Slovenian" lang="sl" hreflang="sl" data-title="Infinitezimalni račun" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%DB%8C%D8%A7%DA%A9%D8%A7%D8%B1%DB%8C_%D9%88_%D8%AA%DB%95%D9%88%D8%A7%D9%88%DA%A9%D8%A7%D8%B1%DB%8C" title="جیاکاری و تەواوکاری – Central Kurdish" lang="ckb" hreflang="ckb" data-title="جیاکاری و تەواوکاری" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – Serbian" lang="sr" hreflang="sr" data-title="Infinitezimalni račun" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Infinitezimalni_ra%C4%8Dun" title="Infinitezimalni račun – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Infinitezimalni račun" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Differentiaali-_ja_integraalilaskenta" title="Differentiaali- ja integraalilaskenta – Finnish" lang="fi" hreflang="fi" data-title="Differentiaali- ja integraalilaskenta" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Infinitesimalkalkyl" title="Infinitesimalkalkyl – Swedish" lang="sv" hreflang="sv" data-title="Infinitesimalkalkyl" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Calculus" title="Calculus – Tagalog" lang="tl" hreflang="tl" data-title="Calculus" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A8%E0%AF%81%E0%AE%A3%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="நுண்கணிதம் – Tamil" lang="ta" hreflang="ta" data-title="நுண்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%95%E0%B0%B2%E0%B0%A8_%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%AE%E0%B1%81" title="కలన గణితము – Telugu" lang="te" hreflang="te" data-title="కలన గణితము" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%81%E0%B8%84%E0%B8%A5%E0%B8%84%E0%B8%B9%E0%B8%A5%E0%B8%B1%E0%B8%AA" title="แคลคูลัส – Thai" lang="th" hreflang="th" 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.sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1246091330"><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist"><tbody><tr><td class="sidebar-pretitle">Part of a series of articles about</td></tr><tr><th class="sidebar-title-with-pretitle" style="padding-bottom:0.25em;"><a class="mw-selflink selflink">Calculus</a></th></tr><tr><td class="sidebar-image"><big><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17d063dc86a53a2efb1fe86f4a5d47d498652766" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:25.228ex; height:6.343ex;" alt="{\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}"></span></big></td></tr><tr><td class="sidebar-above" style="padding:0.15em 0.25em 0.3em;font-weight:normal;"> <ul><li><a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">Fundamental theorem</a></li></ul> <div class="hlist"> <ul><li><a href="/wiki/Limit_of_a_function" title="Limit of a function">Limits</a></li> <li><a href="/wiki/Continuous_function" title="Continuous function">Continuity</a></li></ul> </div><div class="hlist"> <ul><li><a href="/wiki/Rolle%27s_theorem" title="Rolle's theorem">Rolle's theorem</a></li> <li><a href="/wiki/Mean_value_theorem" title="Mean value theorem">Mean value theorem</a></li> <li><a href="/wiki/Inverse_function_theorem" title="Inverse function theorem">Inverse function theorem</a></li></ul> </div></td></tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base);display:block;margin-top:0.65em;"><span style="font-size:120%"><a href="/wiki/Differential_calculus" title="Differential calculus">Differential</a></span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading"> Definitions</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Derivative" title="Derivative">Derivative</a> (<a href="/wiki/Generalizations_of_the_derivative" title="Generalizations of the derivative">generalizations</a>)</li> <li><a href="/wiki/Differential_(mathematics)" title="Differential (mathematics)">Differential</a> <ul><li><a href="/wiki/Differential_(infinitesimal)" class="mw-redirect" title="Differential (infinitesimal)">infinitesimal</a></li> <li><a href="/wiki/Differential_of_a_function" title="Differential of a function">of a function</a></li> <li><a href="/wiki/Differential_of_a_function#Differentials_in_several_variables" title="Differential of a function">total</a></li></ul></li></ul></td> </tr><tr><th class="sidebar-heading"> Concepts</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Notation_for_differentiation" title="Notation for differentiation">Differentiation notation</a></li> <li><a href="/wiki/Second_derivative" title="Second derivative">Second derivative</a></li> <li><a href="/wiki/Implicit_function" title="Implicit function">Implicit differentiation</a></li> <li><a href="/wiki/Logarithmic_differentiation" title="Logarithmic differentiation">Logarithmic differentiation</a></li> <li><a href="/wiki/Related_rates" title="Related rates">Related rates</a></li> <li><a href="/wiki/Taylor%27s_theorem" title="Taylor's theorem">Taylor's theorem</a></li></ul></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/Differentiation_rules" title="Differentiation rules">Rules and identities</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Sum_rule_in_differentiation" class="mw-redirect" title="Sum rule in differentiation">Sum</a></li> <li><a href="/wiki/Product_rule" title="Product rule">Product</a></li> <li><a href="/wiki/Chain_rule" title="Chain rule">Chain</a></li> <li><a href="/wiki/Power_rule" title="Power rule">Power</a></li> <li><a href="/wiki/Quotient_rule" title="Quotient rule">Quotient</a></li> <li><a href="/wiki/L%27H%C3%B4pital%27s_rule" title="L'Hôpital's rule">L'Hôpital's rule</a></li> <li><a href="/wiki/Inverse_function_rule" title="Inverse function rule">Inverse</a></li> <li><a href="/wiki/General_Leibniz_rule" title="General Leibniz rule">General Leibniz</a></li> <li><a href="/wiki/Fa%C3%A0_di_Bruno%27s_formula" title="Faà di Bruno's formula">Faà di Bruno's formula</a></li> <li><a href="/wiki/Reynolds_transport_theorem" title="Reynolds transport theorem">Reynolds</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><span style="font-size:120%"><a href="/wiki/Integral" title="Integral">Integral</a></span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Lists_of_integrals" title="Lists of integrals">Lists of integrals</a></li> <li><a href="/wiki/Integral_transform" title="Integral transform">Integral transform</a></li> <li><a href="/wiki/Leibniz_integral_rule" title="Leibniz integral rule">Leibniz integral rule</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Definitions</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Antiderivative" title="Antiderivative">Antiderivative</a></li> <li><a href="/wiki/Integral" title="Integral">Integral</a> (<a href="/wiki/Improper_integral" title="Improper integral">improper</a>)</li> <li><a href="/wiki/Riemann_integral" title="Riemann integral">Riemann integral</a></li> <li><a href="/wiki/Lebesgue_integration" class="mw-redirect" title="Lebesgue integration">Lebesgue integration</a></li> <li><a href="/wiki/Contour_integration" title="Contour integration">Contour integration</a></li> <li><a href="/wiki/Integral_of_inverse_functions" title="Integral of inverse functions">Integral of inverse functions</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Integration by</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Integration_by_parts" title="Integration by parts">Parts</a></li> <li><a href="/wiki/Disc_integration" title="Disc integration">Discs</a></li> <li><a href="/wiki/Shell_integration" title="Shell integration">Cylindrical shells</a></li> <li><a href="/wiki/Integration_by_substitution" title="Integration by substitution">Substitution</a> (<a href="/wiki/Trigonometric_substitution" title="Trigonometric substitution">trigonometric</a>, <a href="/wiki/Tangent_half-angle_substitution" title="Tangent half-angle substitution">tangent half-angle</a>, <a href="/wiki/Euler_substitution" title="Euler substitution">Euler</a>)</li> <li><a href="/wiki/Integration_using_Euler%27s_formula" title="Integration using Euler's formula">Euler's formula</a></li> <li><a href="/wiki/Partial_fractions_in_integration" class="mw-redirect" title="Partial fractions in integration">Partial fractions</a> (<a href="/wiki/Heaviside_cover-up_method" title="Heaviside cover-up method">Heaviside's method</a>)</li> <li><a href="/wiki/Order_of_integration_(calculus)" title="Order of integration (calculus)">Changing order</a></li> <li><a href="/wiki/Integration_by_reduction_formulae" title="Integration by reduction formulae">Reduction formulae</a></li> <li><a href="/wiki/Leibniz_integral_rule#Evaluating_definite_integrals" title="Leibniz integral rule">Differentiating under the integral sign</a></li> <li><a href="/wiki/Risch_algorithm" title="Risch algorithm">Risch algorithm</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><span style="font-size:120%"><a href="/wiki/Series_(mathematics)" title="Series (mathematics)">Series</a></span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Geometric_series" title="Geometric series">Geometric</a> (<a href="/wiki/Arithmetico%E2%80%93geometric_sequence" class="mw-redirect" title="Arithmetico–geometric sequence">arithmetico-geometric</a>)</li> <li><a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">Harmonic</a></li> <li><a href="/wiki/Alternating_series" title="Alternating series">Alternating</a></li> <li><a href="/wiki/Power_series" title="Power series">Power</a></li> <li><a href="/wiki/Binomial_series" title="Binomial series">Binomial</a></li> <li><a href="/wiki/Taylor_series" title="Taylor series">Taylor</a></li></ul></td> </tr><tr><th class="sidebar-heading"> <a href="/wiki/Convergence_tests" title="Convergence tests">Convergence tests</a></th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Term_test" class="mw-redirect" title="Term test">Summand limit (term test)</a></li> <li><a href="/wiki/Ratio_test" title="Ratio test">Ratio</a></li> <li><a href="/wiki/Root_test" title="Root test">Root</a></li> <li><a href="/wiki/Integral_test_for_convergence" title="Integral test for convergence">Integral</a></li> <li><a href="/wiki/Direct_comparison_test" title="Direct comparison test">Direct comparison</a></li> <li><br /><a href="/wiki/Limit_comparison_test" title="Limit comparison test">Limit comparison</a></li> <li><a href="/wiki/Alternating_series_test" title="Alternating series test">Alternating series</a></li> <li><a href="/wiki/Cauchy_condensation_test" title="Cauchy condensation test">Cauchy condensation</a></li> <li><a href="/wiki/Dirichlet%27s_test" title="Dirichlet's test">Dirichlet</a></li> <li><a href="/wiki/Abel%27s_test" title="Abel's test">Abel</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><span style="font-size:120%"><a href="/wiki/Vector_calculus" title="Vector calculus">Vector</a></span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Gradient" title="Gradient">Gradient</a></li> <li><a href="/wiki/Divergence" title="Divergence">Divergence</a></li> <li><a href="/wiki/Curl_(mathematics)" title="Curl (mathematics)">Curl</a></li> <li><a href="/wiki/Laplace_operator" title="Laplace operator">Laplacian</a></li> <li><a href="/wiki/Directional_derivative" title="Directional derivative">Directional derivative</a></li> <li><a href="/wiki/Vector_calculus_identities" title="Vector calculus identities">Identities</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Theorems</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Gradient_theorem" title="Gradient theorem">Gradient</a></li> <li><a href="/wiki/Green%27s_theorem" title="Green's theorem">Green's</a></li> <li><a href="/wiki/Stokes%27_theorem" title="Stokes' theorem">Stokes'</a></li> <li><a href="/wiki/Divergence_theorem" title="Divergence theorem">Divergence</a></li> <li><a href="/wiki/Generalized_Stokes_theorem" title="Generalized Stokes theorem">generalized Stokes</a></li> <li><a href="/wiki/Helmholtz_decomposition" title="Helmholtz decomposition">Helmholtz decomposition</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><span style="font-size:120%"><a href="/wiki/Multivariable_calculus" title="Multivariable calculus">Multivariable</a></span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="sidebar-subgroup"><tbody><tr><th class="sidebar-heading"> Formalisms</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Matrix_calculus" title="Matrix calculus">Matrix</a></li> <li><a href="/wiki/Tensor_calculus" class="mw-redirect" title="Tensor calculus">Tensor</a></li> <li><a href="/wiki/Exterior_derivative" title="Exterior derivative">Exterior</a></li> <li><a href="/wiki/Geometric_calculus" title="Geometric calculus">Geometric</a></li></ul></td> </tr><tr><th class="sidebar-heading"> Definitions</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Partial_derivative" title="Partial derivative">Partial derivative</a></li> <li><a href="/wiki/Multiple_integral" title="Multiple integral">Multiple integral</a></li> <li><a href="/wiki/Line_integral" title="Line integral">Line integral</a></li> <li><a href="/wiki/Surface_integral" title="Surface integral">Surface integral</a></li> <li><a href="/wiki/Volume_integral" title="Volume integral">Volume integral</a></li> <li><a href="/wiki/Jacobian_matrix_and_determinant" title="Jacobian matrix and determinant">Jacobian</a></li> <li><a href="/wiki/Hessian_matrix" title="Hessian matrix">Hessian</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content-with-subgroup"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><span style="font-size:120%">Advanced</span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"><table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Calculus_on_Euclidean_space" title="Calculus on Euclidean space">Calculus on Euclidean space</a></li> <li><a href="/wiki/Generalized_function" title="Generalized function">Generalized functions</a></li> <li><a href="/wiki/Limit_of_distributions" title="Limit of distributions">Limit of distributions</a></li></ul></td> </tr></tbody></table></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><span style="font-size:120%">Specialized</span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Fractional_calculus" title="Fractional calculus">Fractional</a></li> <li><a href="/wiki/Malliavin_calculus" title="Malliavin calculus">Malliavin</a></li> <li><a href="/wiki/Stochastic_calculus" title="Stochastic calculus">Stochastic</a></li> <li><a href="/wiki/Calculus_of_variations" title="Calculus of variations">Variations</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;;color: var(--color-base)"><span style="font-size:120%">Miscellanea</span></div><div class="sidebar-list-content mw-collapsible-content" style="border-top:1px solid #aaa;padding-top:0.15em;border-bottom:1px solid #aaa;"> <ul><li><a href="/wiki/Precalculus" title="Precalculus">Precalculus</a></li> <li><a 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title="Mathematics">Mathematics</a></th></tr><tr><td class="sidebar-above" style="padding-bottom:0.35em;"> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History</a></li> <li><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Index</a></li></ul></td></tr><tr><td class="sidebar-content-with-subgroup"> <table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-top:1px solid #aaa;background:#ddddff;text-align:center;;color: var(--color-base)"><a href="/wiki/Areas_of_mathematics" class="mw-redirect" title="Areas of mathematics">Areas</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Number_theory" title="Number theory">Number theory</a></li> <li><a href="/wiki/Geometry" title="Geometry">Geometry</a></li> <li><a href="/wiki/Algebra" title="Algebra">Algebra</a></li> <li><a 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physics">Physics</a></li> <li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Chemistry</a></li> <li><a href="/wiki/Geomathematics" title="Geomathematics">Geosciences</a></li> <li><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computation</a></li> <li><a href="/wiki/Mathematical_and_theoretical_biology" title="Mathematical and theoretical biology">Biology</a></li> <li><a href="/wiki/Computational_linguistics" title="Computational linguistics">Linguistics</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Economics</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy</a></li> <li><a href="/wiki/Mathematics_education" title="Mathematics education">Education</a></li></ul></div></div></td> </tr></tbody></table></td> </tr><tr><th class="sidebar-heading"> <span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/20px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/30px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/40px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics Portal</a></th></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Math_topics_sidebar" title="Template:Math topics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Math_topics_sidebar" title="Template talk:Math topics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Math_topics_sidebar" title="Special:EditPage/Template:Math topics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Calculus</b> is the <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> study of continuous change, in the same way that <a href="/wiki/Geometry" title="Geometry">geometry</a> is the study of shape, and <a href="/wiki/Algebra" title="Algebra">algebra</a> is the study of generalizations of <a href="/wiki/Arithmetic_operations" class="mw-redirect" title="Arithmetic operations">arithmetic operations</a>. </p><p>Originally called <b>infinitesimal calculus</b> or "the calculus of <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimals</a>", it has two major branches, <a href="/wiki/Differential_calculus" title="Differential calculus">differential calculus</a> and <a href="/wiki/Integral_calculus" class="mw-redirect" title="Integral calculus">integral calculus</a>. The former concerns instantaneous <a href="/wiki/Rate_of_change_(mathematics)" class="mw-redirect" title="Rate of change (mathematics)">rates of change</a>, and the <a href="/wiki/Slope" title="Slope">slopes</a> of <a href="/wiki/Curve" title="Curve">curves</a>, while the latter concerns accumulation of quantities, and <a href="/wiki/Area" title="Area">areas</a> under or between curves. These two branches are related to each other by the <a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">fundamental theorem of calculus</a>. They make use of the fundamental notions of <a href="/wiki/Convergence_(mathematics)" class="mw-redirect" title="Convergence (mathematics)">convergence</a> of <a href="/wiki/Infinite_sequence" class="mw-redirect" title="Infinite sequence">infinite sequences</a> and <a href="/wiki/Series_(mathematics)" title="Series (mathematics)">infinite series</a> to a well-defined <a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">limit</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>Infinitesimal calculus was developed independently in the late 17th century by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> and <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Later work, including <a href="/wiki/(%CE%B5,_%CE%B4)-definition_of_limit" class="mw-redirect" title="(ε, δ)-definition of limit">codifying the idea of limits</a>, put these developments on a more solid conceptual footing. Today, calculus has widespread uses in <a href="/wiki/Science" title="Science">science</a>, <a href="/wiki/Engineering" title="Engineering">engineering</a>, and <a href="/wiki/Social_science" title="Social science">social science</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymology">Etymology</h2></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/Special:Search/calculus" class="extiw" title="wiktionary:Special:Search/calculus">calculus</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <p>In <a href="/wiki/Mathematics_education" title="Mathematics education">mathematics education</a>, <i>calculus</i> is an abbreviation of both <a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">infinitesimal calculus</a> and <a href="/wiki/Integral_calculus" class="mw-redirect" title="Integral calculus">integral calculus</a>, which denotes courses of elementary <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">mathematical analysis</a>. </p><p>In <a href="/wiki/Latin" title="Latin">Latin</a>, the word <i>calculus</i> means “small pebble”, (the <a href="/wiki/Diminutive" title="Diminutive">diminutive</a> of <i><a href="https://en.wiktionary.org/wiki/calx" class="extiw" title="wikt:calx">calx</a>,</i> meaning "stone"), a meaning which still <a href="/wiki/Calculus_(medicine)" title="Calculus (medicine)">persists in medicine</a>. Because such pebbles were used for counting out distances,<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> tallying votes, and doing <a href="/wiki/Abacus" title="Abacus">abacus</a> arithmetic, the word came to be the Latin word for <i>calculation</i>. In this sense, it was used in English at least as early as 1672, several years before the publications of Leibniz and Newton, who wrote their mathematical texts in Latin.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>In addition to differential calculus and integral calculus, the term is also used for naming specific methods of computation or theories that imply some sort of computation. Examples of this usage include <a href="/wiki/Propositional_calculus" title="Propositional calculus">propositional calculus</a>, <a href="/wiki/Ricci_calculus" title="Ricci calculus">Ricci calculus</a>, <a href="/wiki/Calculus_of_variations" title="Calculus of variations">calculus of variations</a>, <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>, <a href="/wiki/Sequent_calculus" title="Sequent calculus">sequent calculus</a>, and <a href="/wiki/Process_calculus" title="Process calculus">process calculus</a>. Furthermore, the term "calculus" has variously been applied in ethics and philosophy, for such systems as <a href="/wiki/Jeremy_Bentham" title="Jeremy Bentham">Bentham's</a> <a href="/wiki/Felicific_calculus" title="Felicific calculus">felicific calculus</a>, and the <a href="/wiki/Ethical_calculus" title="Ethical calculus">ethical calculus</a>. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_calculus" title="History of calculus">History of calculus</a></div> <p>Modern calculus was developed in 17th-century Europe by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> and <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a> (independently of each other, first publishing around the same time) but elements of it first appeared in ancient Egypt and later Greece, then in China and the Middle East, and still later again in medieval Europe and India. </p> <div class="mw-heading mw-heading3"><h3 id="Ancient_precursors">Ancient precursors</h3></div> <div class="mw-heading mw-heading4"><h4 id="Egypt">Egypt</h4></div> <p>Calculations of <a href="/wiki/Volume" title="Volume">volume</a> and <a href="/wiki/Area" title="Area">area</a>, one goal of integral calculus, can be found in the <a href="/wiki/Egyptian_mathematics" class="mw-redirect" title="Egyptian mathematics">Egyptian</a> <a href="/wiki/Moscow_Mathematical_Papyrus" title="Moscow Mathematical Papyrus">Moscow papyrus</a> (<abbr title="circa">c.</abbr><span style="white-space:nowrap;"> 1820<span class="nowrap"> </span>BC</span>), but the formulae are simple instructions, with no indication as to how they were obtained.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Greece">Greece</h4></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Greek_mathematics" title="Greek mathematics">Greek mathematics</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Parabolic_segment_and_inscribed_triangle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Parabolic_segment_and_inscribed_triangle.svg/170px-Parabolic_segment_and_inscribed_triangle.svg.png" decoding="async" width="170" height="280" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Parabolic_segment_and_inscribed_triangle.svg/255px-Parabolic_segment_and_inscribed_triangle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Parabolic_segment_and_inscribed_triangle.svg/340px-Parabolic_segment_and_inscribed_triangle.svg.png 2x" data-file-width="243" data-file-height="400" /></a><figcaption>Archimedes used the <a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">method of exhaustion</a> to calculate the area under a parabola in his work <i><a href="/wiki/Quadrature_of_the_Parabola" title="Quadrature of the Parabola">Quadrature of the Parabola</a></i>.</figcaption></figure> <p>Laying the foundations for integral calculus and foreshadowing the concept of the limit, ancient Greek mathematician <a href="/wiki/Eudoxus_of_Cnidus" title="Eudoxus of Cnidus">Eudoxus of Cnidus</a> (<span title="circa">c.</span><span style="white-space:nowrap;"> 390–337<span class="nowrap"> </span>BC</span>) developed the <a href="/wiki/Method_of_exhaustion" title="Method of exhaustion">method of exhaustion</a> to prove the formulas for cone and pyramid volumes. </p><p>During the <a href="/wiki/Hellenistic_period" title="Hellenistic period">Hellenistic period</a>, this method was further developed by <a href="/wiki/Archimedes" title="Archimedes">Archimedes</a> (<span title="circa">c.</span><span style="white-space:nowrap;"> 287</span> – c.<span style="white-space:nowrap;"> 212</span><span class="nowrap"> </span>BC), who combined it with a concept of the <a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">indivisibles</a>—a precursor to <a href="/wiki/Archimedes_use_of_infinitesimals" class="mw-redirect" title="Archimedes use of infinitesimals">infinitesimals</a>—allowing him to solve several problems now treated by integral calculus. In <i><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></i> he describes, for example, calculating the <a href="/wiki/Center_of_gravity" class="mw-redirect" title="Center of gravity">center of gravity</a> of a solid <a href="/wiki/Sphere" title="Sphere">hemisphere</a>, the center of gravity of a <a href="/wiki/Frustum" title="Frustum">frustum</a> of a circular <a href="/wiki/Paraboloid" title="Paraboloid">paraboloid</a>, and the area of a region bounded by a <a href="/wiki/Parabola" title="Parabola">parabola</a> and one of its <a href="/wiki/Secant_line" title="Secant line">secant lines</a>.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="China">China</h4></div> <p>The method of exhaustion was later discovered independently in <a href="/wiki/Chinese_mathematics" title="Chinese mathematics">China</a> by <a href="/wiki/Liu_Hui" title="Liu Hui">Liu Hui</a> in the 3rd century AD to find the area of a circle.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:0_11-0" class="reference"><a href="#cite_note-:0-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> In the 5th century AD, <a href="/wiki/Zu_Gengzhi" title="Zu Gengzhi">Zu Gengzhi</a>, son of <a href="/wiki/Zu_Chongzhi" title="Zu Chongzhi">Zu Chongzhi</a>, established a method<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> that would later be called <a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">Cavalieri's principle</a> to find the volume of a <a href="/wiki/Sphere" title="Sphere">sphere</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Medieval">Medieval</h3></div> <style data-mw-deduplicate="TemplateStyles:r1237032888/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner img{background-color:white}}</style><div class="thumb tmulti tleft"><div class="thumbinner multiimageinner" style="width:322px;max-width:322px"><div class="trow"><div class="tsingle" style="width:107px;max-width:107px"><div class="thumbimage" style="height:139px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Hazan_(cropped).png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Hazan_%28cropped%29.png/105px-Hazan_%28cropped%29.png" decoding="async" width="105" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Hazan_%28cropped%29.png/158px-Hazan_%28cropped%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d4/Hazan_%28cropped%29.png 2x" data-file-width="180" data-file-height="240" /></a></span></div><div class="thumbcaption"><a href="/wiki/Ibn_al-Haytham" title="Ibn al-Haytham">Ibn al-Haytham</a>, 11th-century Arab mathematician and physicist</div></div><div class="tsingle" style="width:211px;max-width:211px"><div class="thumbimage" style="height:139px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:%E0%A4%AD%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A4%B0%E0%A4%BE%E0%A4%9A%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%AF.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/%E0%A4%AD%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A4%B0%E0%A4%BE%E0%A4%9A%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%AF.jpg/209px-%E0%A4%AD%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A4%B0%E0%A4%BE%E0%A4%9A%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%AF.jpg" decoding="async" width="209" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/7b/%E0%A4%AD%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%95%E0%A4%B0%E0%A4%BE%E0%A4%9A%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%AF.jpg 1.5x" data-file-width="300" data-file-height="200" /></a></span></div><div class="thumbcaption">Indian mathematician and astronomer <a href="/wiki/Bh%C4%81skara_II" title="Bhāskara II">Bhāskara II</a></div></div></div></div></div> <div class="mw-heading mw-heading4"><h4 id="Middle_East">Middle East</h4></div> <p>In the Middle East, <a href="/wiki/Ibn_al-Haytham" title="Ibn al-Haytham">Hasan Ibn al-Haytham</a>, Latinized as Alhazen (<span title="circa">c.</span><span style="white-space:nowrap;"> 965</span> – c.<span style="white-space:nowrap;"> 1040</span><span class="nowrap"> </span>AD) derived a formula for the sum of <a href="/wiki/Fourth_power" title="Fourth power">fourth powers</a>. He used the results to carry out what would now be called an <a href="/wiki/Integral" title="Integral">integration</a> of this function, where the formulae for the sums of integral squares and fourth powers allowed him to calculate the volume of a <a href="/wiki/Paraboloid" title="Paraboloid">paraboloid</a>.<sup id="cite_ref-katz_14-0" class="reference"><a href="#cite_note-katz-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="India">India</h4></div> <p><a href="/wiki/Bh%C4%81skara_II" title="Bhāskara II">Bhāskara II</a> (<span title="circa">c.</span><span style="white-space:nowrap;"> 1114–1185</span>) was acquainted with some ideas of differential calculus and suggested that the "differential coefficient" vanishes at an extremum value of the function.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> In his astronomical work, he gave a procedure that looked like a precursor to infinitesimal methods. Namely, if <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x\approx y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>≈</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\approx y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aad656b6c009dbc111be61d5ab821ff8e8927e93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.584ex; height:2.009ex;" alt="{\displaystyle x\approx y}"></span> then <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin(y)-\sin(x)\approx (y-x)\cos(y).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>≈</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo>−</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(y)-\sin(x)\approx (y-x)\cos(y).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8dd0adb4808892ab22bcbe974beddeaf27e6f642" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.999ex; height:2.843ex;" alt="{\displaystyle \sin(y)-\sin(x)\approx (y-x)\cos(y).}"></span> This can be interpreted as the discovery that <a href="/wiki/Cosine" class="mw-redirect" title="Cosine">cosine</a> is the derivative of <a href="/wiki/Sine" class="mw-redirect" title="Sine">sine</a>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> In the 14th century, Indian mathematicians gave a non-rigorous method, resembling differentiation, applicable to some trigonometric functions. <a href="/wiki/Madhava_of_Sangamagrama" title="Madhava of Sangamagrama">Madhava of Sangamagrama</a> and the <a href="/wiki/Kerala_School_of_Astronomy_and_Mathematics" class="mw-redirect" title="Kerala School of Astronomy and Mathematics">Kerala School of Astronomy and Mathematics</a> stated components of calculus, but according to <a href="/wiki/Victor_J._Katz" title="Victor J. Katz">Victor J. Katz</a> they were not able to "combine many differing ideas under the two unifying themes of the <a href="/wiki/Derivative" title="Derivative">derivative</a> and the <a href="/wiki/Integral" title="Integral">integral</a>, show the connection between the two, and turn calculus into the great problem-solving tool we have today".<sup id="cite_ref-katz_14-1" class="reference"><a href="#cite_note-katz-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Modern">Modern</h3></div> <p><a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a>'s work <i>Stereometria Doliorum</i> (1615) formed the basis of integral calculus.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> Kepler developed a method to calculate the area of an ellipse by adding up the lengths of many radii drawn from a focus of the ellipse.<sup id="cite_ref-EB1911_18-0" class="reference"><a href="#cite_note-EB1911-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>Significant work was a treatise, the origin being Kepler's methods,<sup id="cite_ref-EB1911_18-1" class="reference"><a href="#cite_note-EB1911-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> written by <a href="/wiki/Bonaventura_Cavalieri" title="Bonaventura Cavalieri">Bonaventura Cavalieri</a>, who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimally thin cross-sections. The ideas were similar to Archimedes' in <i><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method</a></i>, but this treatise is believed to have been lost in the 13th century and was only rediscovered in the early 20th century, and so would have been unknown to Cavalieri. Cavalieri's work was not well respected since his methods could lead to erroneous results, and the infinitesimal quantities he introduced were disreputable at first. </p><p>The formal study of calculus brought together Cavalieri's infinitesimals with the <a href="/wiki/Calculus_of_finite_differences" class="mw-redirect" title="Calculus of finite differences">calculus of finite differences</a> developed in Europe at around the same time. <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a>, claiming that he borrowed from <a href="/wiki/Diophantus" title="Diophantus">Diophantus</a>, introduced the concept of <a href="/wiki/Adequality" title="Adequality">adequality</a>, which represented equality up to an infinitesimal error term.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> The combination was achieved by <a href="/wiki/John_Wallis" title="John Wallis">John Wallis</a>, <a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a>, and <a href="/wiki/James_Gregory_(astronomer_and_mathematician)" class="mw-redirect" title="James Gregory (astronomer and mathematician)">James Gregory</a>, the latter two proving predecessors to the <a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">second fundamental theorem of calculus</a> around 1670.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>The <a href="/wiki/Product_rule" title="Product rule">product rule</a> and <a href="/wiki/Chain_rule" title="Chain rule">chain rule</a>,<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> the notions of <a href="/wiki/Higher_derivative" class="mw-redirect" title="Higher derivative">higher derivatives</a> and <a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a>,<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> and of <a href="/wiki/Analytic_function" title="Analytic function">analytic functions</a><sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> were used by <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> in an idiosyncratic notation which he applied to solve problems of <a href="/wiki/Mathematical_physics" title="Mathematical physics">mathematical physics</a>. In his works, Newton rephrased his ideas to suit the mathematical idiom of the time, replacing calculations with infinitesimals by equivalent geometrical arguments which were considered beyond reproach. He used the methods of calculus to solve the problem of planetary motion, the shape of the surface of a rotating fluid, the oblateness of the earth, the motion of a weight sliding on a <a href="/wiki/Cycloid" title="Cycloid">cycloid</a>, and many other problems discussed in his <i><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia Mathematica</a></i> (1687). In other work, he developed series expansions for functions, including fractional and irrational powers, and it was clear that he understood the principles of the <a href="/wiki/Taylor_series" title="Taylor series">Taylor series</a>. He did not publish all these discoveries, and at this time infinitesimal methods were still considered disreputable.<sup id="cite_ref-:1_25-0" class="reference"><a href="#cite_note-:1-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:322px;max-width:322px"><div class="trow"><div class="tsingle" style="width:169px;max-width:169px"><div class="thumbimage" style="height:206px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Gottfried_Wilhelm_Leibniz,_Bernhard_Christoph_Francke.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg/167px-Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg" decoding="async" width="167" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg/251px-Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg/334px-Gottfried_Wilhelm_Leibniz%2C_Bernhard_Christoph_Francke.jpg 2x" data-file-width="4486" data-file-height="5538" /></a></span></div><div class="thumbcaption"><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a> was the first to state clearly the rules of calculus.</div></div><div class="tsingle" style="width:149px;max-width:149px"><div class="thumbimage" style="height:206px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:GodfreyKneller-IsaacNewton-1689.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/GodfreyKneller-IsaacNewton-1689.jpg/147px-GodfreyKneller-IsaacNewton-1689.jpg" decoding="async" width="147" height="206" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/GodfreyKneller-IsaacNewton-1689.jpg/221px-GodfreyKneller-IsaacNewton-1689.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/GodfreyKneller-IsaacNewton-1689.jpg/294px-GodfreyKneller-IsaacNewton-1689.jpg 2x" data-file-width="1364" data-file-height="1916" /></a></span></div><div class="thumbcaption"><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> developed the use of calculus in his <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">laws of motion</a> and <a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">universal gravitation</a>.</div></div></div></div></div> <p>These ideas were arranged into a true calculus of infinitesimals by <a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a>, who was originally accused of <a href="/wiki/Plagiarism" title="Plagiarism">plagiarism</a> by Newton.<sup id="cite_ref-leib_26-0" class="reference"><a href="#cite_note-leib-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> He is now regarded as an <a href="/wiki/Multiple_discovery" title="Multiple discovery">independent inventor</a> of and contributor to calculus. His contribution was to provide a clear set of rules for working with infinitesimal quantities, allowing the computation of second and higher derivatives, and providing the <a href="/wiki/Product_rule" title="Product rule">product rule</a> and <a href="/wiki/Chain_rule" title="Chain rule">chain rule</a>, in their differential and integral forms. Unlike Newton, Leibniz put painstaking effort into his choices of notation.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>Today, Leibniz and Newton are usually both given credit for independently inventing and developing calculus. Newton was the first to apply calculus to general <a href="/wiki/Physics" title="Physics">physics</a>. Leibniz developed much of the notation used in calculus today.<sup id="cite_ref-TMU_28-0" class="reference"><a href="#cite_note-TMU-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 51–52">: 51–52 </span></sup> The basic insights that both Newton and Leibniz provided were the laws of differentiation and integration, emphasizing that differentiation and integration are inverse processes, second and higher derivatives, and the notion of an approximating polynomial series. </p><p>When Newton and Leibniz first published their results, there was <a href="/wiki/Newton_v._Leibniz_calculus_controversy" class="mw-redirect" title="Newton v. Leibniz calculus controversy">great controversy</a> over which mathematician (and therefore which country) deserved credit. Newton derived his results first (later to be published in his <i><a href="/wiki/Method_of_Fluxions" title="Method of Fluxions">Method of Fluxions</a></i>), but Leibniz published his "<a href="/wiki/Nova_Methodus_pro_Maximis_et_Minimis" title="Nova Methodus pro Maximis et Minimis">Nova Methodus pro Maximis et Minimis</a>" first. Newton claimed Leibniz stole ideas from his unpublished notes, which Newton had shared with a few members of the <a href="/wiki/Royal_Society" title="Royal Society">Royal Society</a>. This controversy divided English-speaking mathematicians from continental European mathematicians for many years, to the detriment of English mathematics.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> A careful examination of the papers of Leibniz and Newton shows that they arrived at their results independently, with Leibniz starting first with integration and Newton with differentiation. It is Leibniz, however, who gave the new discipline its name. Newton called his calculus "<a href="/wiki/Method_of_fluxions" class="mw-redirect" title="Method of fluxions">the science of fluxions</a>", a term that endured in English schools into the 19th century.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 100">: 100 </span></sup> The first complete treatise on calculus to be written in English and use the Leibniz notation was not published until 1815.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Maria_Gaetana_Agnesi.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Maria_Gaetana_Agnesi.jpg/170px-Maria_Gaetana_Agnesi.jpg" decoding="async" width="170" height="198" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/57/Maria_Gaetana_Agnesi.jpg/255px-Maria_Gaetana_Agnesi.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/57/Maria_Gaetana_Agnesi.jpg/340px-Maria_Gaetana_Agnesi.jpg 2x" data-file-width="344" data-file-height="400" /></a><figcaption><a href="/wiki/Maria_Gaetana_Agnesi" title="Maria Gaetana Agnesi">Maria Gaetana Agnesi</a></figcaption></figure> <p>Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. One of the first and most complete works on both infinitesimal and <a href="/wiki/Integral_calculus" class="mw-redirect" title="Integral calculus">integral calculus</a> was written in 1748 by <a href="/wiki/Maria_Gaetana_Agnesi" title="Maria Gaetana Agnesi">Maria Gaetana Agnesi</a>.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Foundations">Foundations</h3></div> <p>In calculus, <i>foundations</i> refers to the <a href="/wiki/Rigorous#Mathematical_rigor" class="mw-redirect" title="Rigorous">rigorous</a> development of the subject from <a href="/wiki/Axiom" title="Axiom">axioms</a> and definitions. In early calculus, the use of <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimal</a> quantities was thought unrigorous and was fiercely criticized by several authors, most notably <a href="/wiki/Michel_Rolle" title="Michel Rolle">Michel Rolle</a> and <a href="/wiki/George_Berkeley" title="George Berkeley">Bishop Berkeley</a>. Berkeley famously described infinitesimals as the <a href="/wiki/Ghosts_of_departed_quantities" class="mw-redirect" title="Ghosts of departed quantities">ghosts of departed quantities</a> in his book <i><a href="/wiki/The_Analyst" title="The Analyst">The Analyst</a></i> in 1734. Working out a rigorous foundation for calculus occupied mathematicians for much of the century following Newton and Leibniz, and is still to some extent an active area of research today.<sup id="cite_ref-Bell-SEP_34-0" class="reference"><a href="#cite_note-Bell-SEP-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>Several mathematicians, including <a href="/wiki/Colin_Maclaurin" title="Colin Maclaurin">Maclaurin</a>, tried to prove the soundness of using infinitesimals, but it would not be until 150 years later when, due to the work of <a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Cauchy</a> and <a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Weierstrass</a>, a way was finally found to avoid mere "notions" of infinitely small quantities.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> The foundations of differential and integral calculus had been laid. In Cauchy's <i><a href="/wiki/Cours_d%27Analyse" title="Cours d'Analyse">Cours d'Analyse</a></i>, we find a broad range of foundational approaches, including a definition of <a href="/wiki/Continuous_function" title="Continuous function">continuity</a> in terms of infinitesimals, and a (somewhat imprecise) prototype of an <a href="/wiki/(%CE%B5,_%CE%B4)-definition_of_limit" class="mw-redirect" title="(ε, δ)-definition of limit">(ε, δ)-definition of limit</a> in the definition of differentiation.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> In his work, Weierstrass formalized the concept of <a href="/wiki/Limit_of_a_function" title="Limit of a function">limit</a> and eliminated infinitesimals (although his definition can validate <a href="/wiki/Nilsquare" class="mw-redirect" title="Nilsquare">nilsquare</a> infinitesimals). Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities, though the subject is still occasionally called "infinitesimal calculus". <a href="/wiki/Bernhard_Riemann" title="Bernhard Riemann">Bernhard Riemann</a> used these ideas to give a precise definition of the integral.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> It was also during this period that the ideas of calculus were generalized to the <a href="/wiki/Complex_plane" title="Complex plane">complex plane</a> with the development of <a href="/wiki/Complex_analysis" title="Complex analysis">complex analysis</a>.<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p><p>In modern mathematics, the foundations of calculus are included in the field of <a href="/wiki/Real_analysis" title="Real analysis">real analysis</a>, which contains full definitions and <a href="/wiki/Mathematical_proof" title="Mathematical proof">proofs</a> of the theorems of calculus. The reach of calculus has also been greatly extended. <a href="/wiki/Henri_Lebesgue" title="Henri Lebesgue">Henri Lebesgue</a> invented <a href="/wiki/Measure_theory" class="mw-redirect" title="Measure theory">measure theory</a>, based on earlier developments by <a href="/wiki/%C3%89mile_Borel" title="Émile Borel">Émile Borel</a>, and used it to define integrals of all but the most <a href="/wiki/Pathological_(mathematics)" title="Pathological (mathematics)">pathological</a> functions.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Laurent_Schwartz" title="Laurent Schwartz">Laurent Schwartz</a> introduced <a href="/wiki/Distribution_(mathematics)" title="Distribution (mathematics)">distributions</a>, which can be used to take the derivative of any function whatsoever.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p><p>Limits are not the only rigorous approach to the foundation of calculus. Another way is to use <a href="/wiki/Abraham_Robinson" title="Abraham Robinson">Abraham Robinson</a>'s <a href="/wiki/Non-standard_analysis" class="mw-redirect" title="Non-standard analysis">non-standard analysis</a>. Robinson's approach, developed in the 1960s, uses technical machinery from <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a> to augment the real number system with <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimal</a> and <a href="/wiki/Infinity" title="Infinity">infinite</a> numbers, as in the original Newton-Leibniz conception. The resulting numbers are called <a href="/wiki/Hyperreal_number" title="Hyperreal number">hyperreal numbers</a>, and they can be used to give a Leibniz-like development of the usual rules of calculus.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> There is also <a href="/wiki/Smooth_infinitesimal_analysis" title="Smooth infinitesimal analysis">smooth infinitesimal analysis</a>, which differs from non-standard analysis in that it mandates neglecting higher-power infinitesimals during derivations.<sup id="cite_ref-Bell-SEP_34-1" class="reference"><a href="#cite_note-Bell-SEP-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> Based on the ideas of <a href="/wiki/F._W._Lawvere" class="mw-redirect" title="F. W. Lawvere">F. W. Lawvere</a> and employing the methods of <a href="/wiki/Category_theory" title="Category theory">category theory</a>, smooth infinitesimal analysis views all functions as being <a href="/wiki/Continuous_function" title="Continuous function">continuous</a> and incapable of being expressed in terms of <a href="/wiki/Discrete_mathematics" title="Discrete mathematics">discrete</a> entities. One aspect of this formulation is that the <a href="/wiki/Law_of_excluded_middle" title="Law of excluded middle">law of excluded middle</a> does not hold.<sup id="cite_ref-Bell-SEP_34-2" class="reference"><a href="#cite_note-Bell-SEP-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> The law of excluded middle is also rejected in <a href="/wiki/Constructive_mathematics" class="mw-redirect" title="Constructive mathematics">constructive mathematics</a>, a branch of mathematics that insists that proofs of the existence of a number, function, or other mathematical object should give a construction of the object. Reformulations of calculus in a constructive framework are generally part of the subject of <a href="/wiki/Constructive_analysis" title="Constructive analysis">constructive analysis</a>.<sup id="cite_ref-Bell-SEP_34-3" class="reference"><a href="#cite_note-Bell-SEP-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Significance">Significance</h3></div> <p>While many of the ideas of calculus had been developed earlier in <a href="/wiki/Greek_mathematics" title="Greek mathematics">Greece</a>, <a href="/wiki/Chinese_mathematics" title="Chinese mathematics">China</a>, <a href="/wiki/Indian_mathematics" title="Indian mathematics">India</a>, <a href="/wiki/Islamic_mathematics" class="mw-redirect" title="Islamic mathematics">Iraq, Persia</a>, and <a href="/wiki/Japanese_mathematics" title="Japanese mathematics">Japan</a>, the use of calculus began in Europe, during the 17th century, when Newton and Leibniz built on the work of earlier mathematicians to introduce its basic principles.<sup id="cite_ref-:0_11-1" class="reference"><a href="#cite_note-:0-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_25-1" class="reference"><a href="#cite_note-:1-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> The Hungarian polymath <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a> wrote of this work, </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics, and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>Applications of differential calculus include computations involving <a href="/wiki/Velocity" title="Velocity">velocity</a> and <a href="/wiki/Acceleration" title="Acceleration">acceleration</a>, the <a href="/wiki/Slope" title="Slope">slope</a> of a curve, and <a href="/wiki/Mathematical_optimization" title="Mathematical optimization">optimization</a>.<sup id="cite_ref-:5_44-0" class="reference"><a href="#cite_note-:5-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 341–453">: 341–453 </span></sup> Applications of integral calculus include computations involving area, <a href="/wiki/Volume" title="Volume">volume</a>, <a href="/wiki/Arc_length" title="Arc length">arc length</a>, <a href="/wiki/Center_of_mass" title="Center of mass">center of mass</a>, <a href="/wiki/Work_(physics)" title="Work (physics)">work</a>, and <a href="/wiki/Pressure" title="Pressure">pressure</a>.<sup id="cite_ref-:5_44-1" class="reference"><a href="#cite_note-:5-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 685–700">: 685–700 </span></sup> More advanced applications include <a href="/wiki/Power_series" title="Power series">power series</a> and <a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a>. </p><p>Calculus is also used to gain a more precise understanding of the nature of space, time, and motion. For centuries, mathematicians and philosophers wrestled with paradoxes involving <a href="/wiki/Division_by_zero" title="Division by zero">division by zero</a> or sums of infinitely many numbers. These questions arise in the study of <a href="/wiki/Motion_(physics)" class="mw-redirect" title="Motion (physics)">motion</a> and area. The <a href="/wiki/Ancient_Greek" title="Ancient Greek">ancient Greek</a> philosopher <a href="/wiki/Zeno_of_Elea" title="Zeno of Elea">Zeno of Elea</a> gave several famous examples of such <a href="/wiki/Zeno%27s_paradoxes" title="Zeno's paradoxes">paradoxes</a>. Calculus provides tools, especially the <a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">limit</a> and the <a href="/wiki/Infinite_series" class="mw-redirect" title="Infinite series">infinite series</a>, that resolve the paradoxes.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Principles">Principles</h2></div> <div class="mw-heading mw-heading3"><h3 id="Limits_and_infinitesimals">Limits and infinitesimals</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Limit_of_a_function" title="Limit of a function">Limit of a function</a> and <a href="/wiki/Infinitesimal" title="Infinitesimal">Infinitesimal</a></div> <p>Calculus is usually developed by working with very small quantities. Historically, the first method of doing so was by <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimals</a>. These are objects which can be treated like real numbers but which are, in some sense, "infinitely small". For example, an infinitesimal number could be greater than 0, but less than any number in the sequence 1, 1/2, 1/3, ... and thus less than any positive <a href="/wiki/Real_number" title="Real number">real number</a>. From this point of view, calculus is a collection of techniques for manipulating infinitesimals. The symbols <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/845c817e348381a13f3fad5184169ce0e021c685" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.546ex; height:2.176ex;" alt="{\displaystyle dx}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dy}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dy}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c5eda9ec854eb0076d43c147eb8956637a1003f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.371ex; height:2.509ex;" alt="{\displaystyle dy}"></span> were taken to be infinitesimal, and the derivative <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle dy/dx}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>d</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dy/dx}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add69069028cada9be6b945dd4b9895e3ff2fd23" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.079ex; height:2.843ex;" alt="{\displaystyle dy/dx}"></span> was their ratio.<sup id="cite_ref-Bell-SEP_34-4" class="reference"><a href="#cite_note-Bell-SEP-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p><p>The infinitesimal approach fell out of favor in the 19th century because it was difficult to make the notion of an infinitesimal precise. In the late 19th century, infinitesimals were replaced within academia by the <a href="/wiki/Epsilon,_delta" class="mw-redirect" title="Epsilon, delta">epsilon, delta</a> approach to <a href="/wiki/Limit_of_a_function" title="Limit of a function">limits</a>. Limits describe the behavior of a <a href="/wiki/Function_(mathematics)" title="Function (mathematics)">function</a> at a certain input in terms of its values at nearby inputs. They capture small-scale behavior using the intrinsic structure of the <a href="/wiki/Real_number" title="Real number">real number system</a> (as a <a href="/wiki/Metric_space" title="Metric space">metric space</a> with the <a href="/wiki/Least-upper-bound_property" title="Least-upper-bound property">least-upper-bound property</a>). In this treatment, calculus is a collection of techniques for manipulating certain limits. Infinitesimals get replaced by sequences of smaller and smaller numbers, and the infinitely small behavior of a function is found by taking the limiting behavior for these sequences. Limits were thought to provide a more rigorous foundation for calculus, and for this reason, they became the standard approach during the 20th century. However, the infinitesimal concept was revived in the 20th century with the introduction of <a href="/wiki/Non-standard_analysis" class="mw-redirect" title="Non-standard analysis">non-standard analysis</a> and <a href="/wiki/Smooth_infinitesimal_analysis" title="Smooth infinitesimal analysis">smooth infinitesimal analysis</a>, which provided solid foundations for the manipulation of infinitesimals.<sup id="cite_ref-Bell-SEP_34-5" class="reference"><a href="#cite_note-Bell-SEP-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Differential_calculus">Differential calculus</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Differential_calculus" title="Differential calculus">Differential calculus</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Tangent_line_to_a_curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Tangent_line_to_a_curve.svg/300px-Tangent_line_to_a_curve.svg.png" decoding="async" width="300" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Tangent_line_to_a_curve.svg/450px-Tangent_line_to_a_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Tangent_line_to_a_curve.svg/600px-Tangent_line_to_a_curve.svg.png 2x" data-file-width="319" data-file-height="222" /></a><figcaption>Tangent line at <span class="texhtml">(<i>x</i><sub>0</sub>, <i>f</i>(<i>x</i><sub>0</sub>))</span>. The derivative <span class="texhtml"><i>f′</i>(<i>x</i>)</span> of a curve at a point is the slope (rise over run) of the line tangent to that curve at that point.</figcaption></figure> <p>Differential calculus is the study of the definition, properties, and applications of the <a href="/wiki/Derivative" title="Derivative">derivative</a> of a function. The process of finding the derivative is called <i>differentiation</i>. Given a function and a point in the domain, the derivative at that point is a way of encoding the small-scale behavior of the function near that point. By finding the derivative of a function at every point in its domain, it is possible to produce a new function, called the <i>derivative function</i> or just the <i>derivative</i> of the original function. In formal terms, the derivative is a <a href="/wiki/Linear_operator" class="mw-redirect" title="Linear operator">linear operator</a> which takes a function as its input and produces a second function as its output. This is more abstract than many of the processes studied in elementary algebra, where functions usually input a number and output another number. For example, if the doubling function is given the input three, then it outputs six, and if the squaring function is given the input three, then it outputs nine. The derivative, however, can take the squaring function as an input. This means that the derivative takes all the information of the squaring function—such as that two is sent to four, three is sent to nine, four is sent to sixteen, and so on—and uses this information to produce another function. The function produced by differentiating the squaring function turns out to be the doubling function.<sup id="cite_ref-TMU_28-1" class="reference"><a href="#cite_note-TMU-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 32">: 32 </span></sup> </p><p>In more explicit terms the "doubling function" may be denoted by <span class="texhtml"><i>g</i>(<i>x</i>) = 2<i>x</i></span> and the "squaring function" by <span class="texhtml"><i>f</i>(<i>x</i>) = <i>x</i><sup>2</sup></span>. The "derivative" now takes the function <span class="texhtml"><i>f</i>(<i>x</i>)</span>, defined by the expression "<span class="texhtml"><i>x</i><sup>2</sup></span>", as an input, that is all the information—such as that two is sent to four, three is sent to nine, four is sent to sixteen, and so on—and uses this information to output another function, the function <span class="texhtml"><i>g</i>(<i>x</i>) = 2<i>x</i></span>, as will turn out. </p><p>In <a href="/wiki/Lagrange%27s_notation" class="mw-redirect" title="Lagrange's notation">Lagrange's notation</a>, the symbol for a derivative is an <a href="/wiki/Apostrophe" title="Apostrophe">apostrophe</a>-like mark called a <a href="/wiki/Prime_(symbol)" title="Prime (symbol)">prime</a>. Thus, the derivative of a function called <span class="texhtml"><i>f</i></span> is denoted by <span class="texhtml"><i>f′</i></span>, pronounced "f prime" or "f dash". For instance, if <span class="texhtml"><i>f</i>(<i>x</i>) = <i>x</i><sup>2</sup></span> is the squaring function, then <span class="texhtml"><i>f′</i>(<i>x</i>) = 2<i>x</i></span> is its derivative (the doubling function <span class="texhtml"><i>g</i></span> from above). </p><p>If the input of the function represents time, then the derivative represents change concerning time. For example, if <span class="texhtml"><i>f</i></span> is a function that takes time as input and gives the position of a ball at that time as output, then the derivative of <span class="texhtml"><i>f</i></span> is how the position is changing in time, that is, it is the <a href="/wiki/Velocity" title="Velocity">velocity</a> of the ball.<sup id="cite_ref-TMU_28-2" class="reference"><a href="#cite_note-TMU-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 18–20">: 18–20 </span></sup> </p><p>If a function is <a href="/wiki/Linear_function" title="Linear function">linear</a> (that is if the <a href="/wiki/Graph_of_a_function" title="Graph of a function">graph</a> of the function is a straight line), then the function can be written as <span class="texhtml"><i>y</i> = <i>mx</i> + <i>b</i></span>, where <span class="texhtml"><i>x</i></span> is the independent variable, <span class="texhtml"><i>y</i></span> is the dependent variable, <span class="texhtml"><i>b</i></span> is the <i>y</i>-intercept, and: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {\text{rise}}{\text{run}}}={\frac {{\text{change in }}y}{{\text{change in }}x}}={\frac {\Delta y}{\Delta x}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>rise</mtext> <mtext>run</mtext> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>change in </mtext> </mrow> <mi>y</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>change in </mtext> </mrow> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {\text{rise}}{\text{run}}}={\frac {{\text{change in }}y}{{\text{change in }}x}}={\frac {\Delta y}{\Delta x}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/313c6a18c1b2ec00c8ae723e70d431b0037382aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:32.669ex; height:6.009ex;" alt="{\displaystyle m={\frac {\text{rise}}{\text{run}}}={\frac {{\text{change in }}y}{{\text{change in }}x}}={\frac {\Delta y}{\Delta x}}.}"></span></dd></dl> <p>This gives an exact value for the slope of a straight line.<sup id="cite_ref-:4_46-0" class="reference"><a href="#cite_note-:4-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 6">: 6 </span></sup> If the graph of the function is not a straight line, however, then the change in <span class="texhtml"><i>y</i></span> divided by the change in <span class="texhtml"><i>x</i></span> varies. Derivatives give an exact meaning to the notion of change in output concerning change in input. To be concrete, let <span class="texhtml"><i>f</i></span> be a function, and fix a point <span class="texhtml"><i>a</i></span> in the domain of <span class="texhtml"><i>f</i></span>. <span class="texhtml">(<i>a</i>, <i>f</i>(<i>a</i>))</span> is a point on the graph of the function. If <span class="texhtml"><i>h</i></span> is a number close to zero, then <span class="texhtml"><i>a</i> + <i>h</i></span> is a number close to <span class="texhtml"><i>a</i></span>. Therefore, <span class="texhtml">(<i>a</i> + <i>h</i>, <i>f</i>(<i>a</i> + <i>h</i>))</span> is close to <span class="texhtml">(<i>a</i>, <i>f</i>(<i>a</i>))</span>. The slope between these two points is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {f(a+h)-f(a)}{(a+h)-a}}={\frac {f(a+h)-f(a)}{h}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> <mi>h</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {f(a+h)-f(a)}{(a+h)-a}}={\frac {f(a+h)-f(a)}{h}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2017cd12adcbfa0f07bcc1090006133781fff8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:41.867ex; height:6.509ex;" alt="{\displaystyle m={\frac {f(a+h)-f(a)}{(a+h)-a}}={\frac {f(a+h)-f(a)}{h}}.}"></span></dd></dl> <p>This expression is called a <i><a href="/wiki/Difference_quotient" title="Difference quotient">difference quotient</a></i>. A line through two points on a curve is called a <i>secant line</i>, so <span class="texhtml"><i>m</i></span> is the slope of the secant line between <span class="texhtml">(<i>a</i>, <i>f</i>(<i>a</i>))</span> and <span class="texhtml">(<i>a</i> + <i>h</i>, <i>f</i>(<i>a</i> + <i>h</i>))</span>. The second line is only an approximation to the behavior of the function at the point <span class="texhtml"><i> a</i></span> because it does not account for what happens between <span class="texhtml"><i> a</i></span> and <span class="texhtml"><i> a</i> + <i>h</i></span>. It is not possible to discover the behavior at <span class="texhtml"><i> a</i></span> by setting <span class="texhtml"><i>h</i></span> to zero because this would require <a href="/wiki/Dividing_by_zero" class="mw-redirect" title="Dividing by zero">dividing by zero</a>, which is undefined. The derivative is defined by taking the <a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">limit</a> as <span class="texhtml"><i>h</i></span> tends to zero, meaning that it considers the behavior of <span class="texhtml"><i>f</i></span> for all small values of <span class="texhtml"><i>h</i></span> and extracts a consistent value for the case when <span class="texhtml"><i>h</i></span> equals zero: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b3d79e9ff8acf531bb7596a6e0687fbb8027ffb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.937ex; height:5.843ex;" alt="{\displaystyle \lim _{h\to 0}{f(a+h)-f(a) \over {h}}.}"></span></dd></dl> <p>Geometrically, the derivative is the slope of the <a href="/wiki/Tangent_line" class="mw-redirect" title="Tangent line">tangent line</a> to the graph of <span class="texhtml"><i>f</i></span> at <span class="texhtml"><i> a</i></span>. The tangent line is a limit of secant lines just as the derivative is a limit of difference quotients. For this reason, the derivative is sometimes called the slope of the function <span class="texhtml"><i>f</i></span>.<sup id="cite_ref-:4_46-1" class="reference"><a href="#cite_note-:4-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 61–63">: 61–63 </span></sup> </p><p>Here is a particular example, the derivative of the squaring function at the input 3. Let <span class="texhtml"><i>f</i>(<i>x</i>) = <i>x</i><sup>2</sup></span> be the squaring function. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sec2tan.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Sec2tan.gif/300px-Sec2tan.gif" decoding="async" width="300" height="289" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/34/Sec2tan.gif/450px-Sec2tan.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/3/34/Sec2tan.gif 2x" data-file-width="586" data-file-height="565" /></a><figcaption>The derivative <span class="texhtml"><i>f′</i>(<i>x</i>)</span> of a curve at a point is the slope of the line tangent to that curve at that point. This slope is determined by considering the limiting value of the slopes of the second lines. Here the function involved (drawn in red) is <span class="texhtml"><i>f</i>(<i>x</i>) = <i>x</i><sup>3</sup> − <i>x</i></span>. The tangent line (in green) which passes through the point <span class="nowrap">(−3/2, −15/8)</span> has a slope of 23/4. The vertical and horizontal scales in this image are different.</figcaption></figure> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}f'(3)&=\lim _{h\to 0}{(3+h)^{2}-3^{2} \over {h}}\\&=\lim _{h\to 0}{9+6h+h^{2}-9 \over {h}}\\&=\lim _{h\to 0}{6h+h^{2} \over {h}}\\&=\lim _{h\to 0}(6+h)\\&=6\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>+</mo> <mi>h</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>9</mn> <mo>+</mo> <mn>6</mn> <mi>h</mi> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>9</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>6</mn> <mi>h</mi> <mo>+</mo> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mo stretchy="false">(</mo> <mn>6</mn> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>6</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}f'(3)&=\lim _{h\to 0}{(3+h)^{2}-3^{2} \over {h}}\\&=\lim _{h\to 0}{9+6h+h^{2}-9 \over {h}}\\&=\lim _{h\to 0}{6h+h^{2} \over {h}}\\&=\lim _{h\to 0}(6+h)\\&=6\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ac4f244e335714a06d06c32b6f91097d713615bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -12.171ex; width:29.203ex; height:25.509ex;" alt="{\displaystyle {\begin{aligned}f'(3)&=\lim _{h\to 0}{(3+h)^{2}-3^{2} \over {h}}\\&=\lim _{h\to 0}{9+6h+h^{2}-9 \over {h}}\\&=\lim _{h\to 0}{6h+h^{2} \over {h}}\\&=\lim _{h\to 0}(6+h)\\&=6\end{aligned}}}"></span></dd></dl> <p>The slope of the tangent line to the squaring function at the point (3, 9) is 6, that is to say, it is going up six times as fast as it is going to the right. The limit process just described can be performed for any point in the domain of the squaring function. This defines the <i>derivative function</i> of the squaring function or just the <i>derivative</i> of the squaring function for short. A computation similar to the one above shows that the derivative of the squaring function is the doubling function.<sup id="cite_ref-:4_46-2" class="reference"><a href="#cite_note-:4-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 63">: 63 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Leibniz_notation">Leibniz notation</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Leibniz%27s_notation" title="Leibniz's notation">Leibniz's notation</a></div> <p>A common notation, introduced by Leibniz, for the derivative in the example above is </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}y&=x^{2}\\{\frac {dy}{dx}}&=2x.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>y</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>y</mi> </mrow> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>2</mn> <mi>x</mi> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}y&=x^{2}\\{\frac {dy}{dx}}&=2x.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/071de0d7365a25822c9ff04f42b1e71a22969eaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:10.371ex; height:8.843ex;" alt="{\displaystyle {\begin{aligned}y&=x^{2}\\{\frac {dy}{dx}}&=2x.\end{aligned}}}"></span></dd></dl> <p>In an approach based on limits, the symbol <span class="texhtml"><style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num"><i>dy</i></span><span class="sr-only">/</span><span class="den"><i> dx</i></span></span>⁠</span></span> is to be interpreted not as the quotient of two numbers but as a shorthand for the limit computed above.<sup id="cite_ref-:4_46-3" class="reference"><a href="#cite_note-:4-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 74">: 74 </span></sup> Leibniz, however, did intend it to represent the quotient of two infinitesimally small numbers, <span class="texhtml"><i>dy</i></span> being the infinitesimally small change in <span class="texhtml"><i>y</i></span> caused by an infinitesimally small change <span class="texhtml"><i> dx</i></span> applied to <span class="texhtml"><i>x</i></span>. We can also think of <span class="texhtml"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>d</i></span><span class="sr-only">/</span><span class="den"><i> dx</i></span></span>⁠</span></span> as a differentiation operator, which takes a function as an input and gives another function, the derivative, as the output. For example: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d}{dx}}(x^{2})=2x.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>x</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d}{dx}}(x^{2})=2x.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c4fd3f805c38024f3887477b61fd2297f4e8050" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.812ex; height:5.509ex;" alt="{\displaystyle {\frac {d}{dx}}(x^{2})=2x.}"></span></dd></dl> <p>In this usage, the <span class="texhtml"><i>dx</i></span> in the denominator is read as "with respect to <span class="texhtml"><i>x</i></span>".<sup id="cite_ref-:4_46-4" class="reference"><a href="#cite_note-:4-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 79">: 79 </span></sup> Another example of correct notation could be: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}g(t)&=t^{2}+2t+4\\{d \over dt}g(t)&=2t+2\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi>g</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>2</mn> <mi>t</mi> <mo>+</mo> <mn>2</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}g(t)&=t^{2}+2t+4\\{d \over dt}g(t)&=2t+2\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3027f5cc71e051e302d6deccab3c362f53a30b1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:21.246ex; height:8.843ex;" alt="{\displaystyle {\begin{aligned}g(t)&=t^{2}+2t+4\\{d \over dt}g(t)&=2t+2\end{aligned}}}"></span></dd></dl> <p>Even when calculus is developed using limits rather than infinitesimals, it is common to manipulate symbols like <span class="texhtml"><i> dx</i></span> and <span class="texhtml"><i>dy</i></span> as if they were real numbers; although it is possible to avoid such manipulations, they are sometimes notationally convenient in expressing operations such as the <a href="/wiki/Total_derivative" title="Total derivative">total derivative</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Integral_calculus">Integral calculus</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Integral" title="Integral">Integral</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237032888/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:292px;max-width:292px"><div class="trow"><div class="tsingle" style="width:290px;max-width:290px"><div class="thumbimage" style="height:268px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Integral_as_region_under_curve.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/288px-Integral_as_region_under_curve.svg.png" decoding="async" width="288" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/432px-Integral_as_region_under_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/576px-Integral_as_region_under_curve.svg.png 2x" data-file-width="750" data-file-height="700" /></a></span></div><div class="thumbcaption">Integration can be thought of as measuring the area under a curve, defined by <span class="texhtml"><i>f</i>(<i>x</i>)</span>, between two points (here <span class="texhtml"><i> a</i></span> and <span class="texhtml"><i>b</i></span>).</div></div></div><div class="trow"><div class="tsingle" style="width:290px;max-width:290px"><div class="thumbimage" style="height:154px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Riemann_integral_regular.gif" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Riemann_integral_regular.gif/288px-Riemann_integral_regular.gif" decoding="async" width="288" height="155" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Riemann_integral_regular.gif/432px-Riemann_integral_regular.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/2/28/Riemann_integral_regular.gif 2x" data-file-width="558" data-file-height="300" /></a></span></div><div class="thumbcaption">A sequence of midpoint Riemann sums over a regular partition of an interval: the total area of the rectangles converges to the integral of the function.</div></div></div></div></div> <p><i>Integral calculus</i> is the study of the definitions, properties, and applications of two related concepts, the <i>indefinite integral</i> and the <i>definite integral</i>. The process of finding the value of an integral is called <i>integration</i>.<sup id="cite_ref-:5_44-2" class="reference"><a href="#cite_note-:5-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 508">: 508 </span></sup> The indefinite integral, also known as the <i><a href="/wiki/Antiderivative" title="Antiderivative">antiderivative</a></i>, is the inverse operation to the derivative.<sup id="cite_ref-:4_46-5" class="reference"><a href="#cite_note-:4-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 163–165">: 163–165 </span></sup> <span class="texhtml"><i>F</i></span> is an indefinite integral of <span class="texhtml"><i>f</i></span> when <span class="texhtml"><i>f</i></span> is a derivative of <span class="texhtml"><i>F</i></span>. (This use of lower- and upper-case letters for a function and its indefinite integral is common in calculus.) The definite integral inputs a function and outputs a number, which gives the algebraic sum of areas between the graph of the input and the <a href="/wiki/X-axis" class="mw-redirect" title="X-axis">x-axis</a>. The technical definition of the definite integral involves the <a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">limit</a> of a sum of areas of rectangles, called a <a href="/wiki/Riemann_sum" title="Riemann sum">Riemann sum</a>.<sup id="cite_ref-:2_47-0" class="reference"><a href="#cite_note-:2-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 282">: 282 </span></sup> </p><p>A motivating example is the distance traveled in a given time.<sup id="cite_ref-:4_46-6" class="reference"><a href="#cite_note-:4-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 153">: 153 </span></sup> If the speed is constant, only multiplication is needed: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Distance} =\mathrm {Speed} \cdot \mathrm {Time} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">t</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">e</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">d</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">T</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Distance} =\mathrm {Speed} \cdot \mathrm {Time} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a2a54be44a458fc96b0fe0083ed6dc1a4f7da48" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:24.776ex; height:2.509ex;" alt="{\displaystyle \mathrm {Distance} =\mathrm {Speed} \cdot \mathrm {Time} }"></span></dd></dl> <p>But if the speed changes, a more powerful method of finding the distance is necessary. One such method is to approximate the distance traveled by breaking up the time into many short intervals of time, then multiplying the time elapsed in each interval by one of the speeds in that interval, and then taking the sum (a <a href="/wiki/Riemann_sum" title="Riemann sum">Riemann sum</a>) of the approximate distance traveled in each interval. The basic idea is that if only a short time elapses, then the speed will stay more or less the same. However, a Riemann sum only gives an approximation of the distance traveled. We must take the limit of all such Riemann sums to find the exact distance traveled. </p><p>When velocity is constant, the total distance traveled over the given time interval can be computed by multiplying velocity and time. For example, traveling a steady 50 mph for 3 hours results in a total distance of 150 miles. Plotting the velocity as a function of time yields a rectangle with a height equal to the velocity and a width equal to the time elapsed. Therefore, the product of velocity and time also calculates the rectangular area under the (constant) velocity curve.<sup id="cite_ref-:5_44-3" class="reference"><a href="#cite_note-:5-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 535">: 535 </span></sup> This connection between the area under a curve and the distance traveled can be extended to <i>any</i> irregularly shaped region exhibiting a fluctuating velocity over a given period. If <span class="texhtml"><i>f</i>(<i>x</i>)</span> represents speed as it varies over time, the distance traveled between the times represented by <span class="texhtml"><i> a</i></span> and <span class="texhtml"><i>b</i></span> is the area of the region between <span class="texhtml"><i>f</i>(<i>x</i>)</span> and the <span class="texhtml"><i>x</i></span>-axis, between <span class="texhtml"><i>x</i> = <i>a</i></span> and <span class="texhtml"><i>x</i> = <i>b</i></span>. </p><p>To approximate that area, an intuitive method would be to divide up the distance between <span class="texhtml"><i> a</i></span> and <span class="texhtml"><i>b</i></span> into several equal segments, the length of each segment represented by the symbol <span class="texhtml">Δ<i>x</i></span>. For each small segment, we can choose one value of the function <span class="texhtml"><i>f</i>(<i>x</i>)</span>. Call that value <span class="texhtml"><i>h</i></span>. Then the area of the rectangle with base <span class="texhtml">Δ<i>x</i></span> and height <span class="texhtml"><i>h</i></span> gives the distance (time <span class="texhtml">Δ<i>x</i></span> multiplied by speed <span class="texhtml"><i>h</i></span>) traveled in that segment. Associated with each segment is the average value of the function above it, <span class="texhtml"><i>f</i>(<i>x</i>) = <i>h</i></span>. The sum of all such rectangles gives an approximation of the area between the axis and the curve, which is an approximation of the total distance traveled. A smaller value for <span class="texhtml">Δ<i>x</i></span> will give more rectangles and in most cases a better approximation, but for an exact answer, we need to take a limit as <span class="texhtml">Δ<i>x</i></span> approaches zero.<sup id="cite_ref-:5_44-4" class="reference"><a href="#cite_note-:5-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 512–522">: 512–522 </span></sup> </p><p>The symbol of integration is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca732e5519cd2210bd59f1ab281b4e8f5a6a4413" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:2.194ex; height:5.676ex;" alt="{\displaystyle \int }"></span>, an <a href="/wiki/Long_s" title="Long s">elongated <i>S</i></a> chosen to suggest summation.<sup id="cite_ref-:5_44-5" class="reference"><a href="#cite_note-:5-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 529">: 529 </span></sup> The definite integral is written as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{a}^{b}f(x)\,dx.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{a}^{b}f(x)\,dx.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/249ee3fdbced31dfc328ff357f67bb134ca66b8d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.786ex; height:6.343ex;" alt="{\displaystyle \int _{a}^{b}f(x)\,dx.}"></span></dd></dl> <p>and is read "the integral from <i>a</i> to <i>b</i> of <i>f</i>-of-<i>x</i> with respect to <i>x</i>." The Leibniz notation <span class="texhtml"><i> dx</i></span> is intended to suggest dividing the area under the curve into an infinite number of rectangles so that their width <span class="texhtml">Δ<i>x</i></span> becomes the infinitesimally small <span class="texhtml"><i> dx</i></span>.<sup id="cite_ref-TMU_28-3" class="reference"><a href="#cite_note-TMU-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 44">: 44 </span></sup> </p><p>The indefinite integral, or antiderivative, is written: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int f(x)\,dx.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int f(x)\,dx.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbbae4f208c1a8c2f6ed7a0cee104f8710e39dee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.578ex; height:5.676ex;" alt="{\displaystyle \int f(x)\,dx.}"></span></dd></dl> <p>Functions differing by only a constant have the same derivative, and it can be shown that the antiderivative of a given function is a family of functions differing only by a constant.<sup id="cite_ref-:2_47-1" class="reference"><a href="#cite_note-:2-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 326">: 326 </span></sup> Since the derivative of the function <span class="texhtml"><i>y</i> = <i>x</i><sup>2</sup> + <i>C</i></span>, where <span class="texhtml"><i>C</i></span> is any constant, is <span class="texhtml"><i>y′</i> = 2<i>x</i></span>, the antiderivative of the latter is given by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int 2x\,dx=x^{2}+C.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∫</mo> <mn>2</mn> <mi>x</mi> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>C</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int 2x\,dx=x^{2}+C.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20b5d8e0b09ed96af70a130b188f2058c9f0324a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.742ex; height:5.676ex;" alt="{\displaystyle \int 2x\,dx=x^{2}+C.}"></span></dd></dl> <p>The unspecified constant <span class="texhtml"><i> C</i></span> present in the indefinite integral or antiderivative is known as the <a href="/wiki/Constant_of_integration" title="Constant of integration">constant of integration</a>.<sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 135">: 135 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Fundamental_theorem">Fundamental theorem</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">Fundamental theorem of calculus</a></div> <p>The <a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">fundamental theorem of calculus</a> states that differentiation and integration are inverse operations.<sup id="cite_ref-:2_47-2" class="reference"><a href="#cite_note-:2-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 290">: 290 </span></sup> More precisely, it relates the values of antiderivatives to definite integrals. Because it is usually easier to compute an antiderivative than to apply the definition of a definite integral, the fundamental theorem of calculus provides a practical way of computing definite integrals. It can also be interpreted as a precise statement of the fact that differentiation is the inverse of integration. </p><p>The fundamental theorem of calculus states: If a function <span class="texhtml"><i>f</i></span> is <a href="/wiki/Continuous_function" title="Continuous function">continuous</a> on the interval <span class="texhtml">[<i>a</i>, <i>b</i>]</span> and if <span class="texhtml"><i>F</i></span> is a function whose derivative is <span class="texhtml"><i>f</i></span> on the interval <span class="texhtml">(<i>a</i>, <i>b</i>)</span>, then </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{a}^{b}f(x)\,dx=F(b)-F(a).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>F</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{a}^{b}f(x)\,dx=F(b)-F(a).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f470e7743fda04c3d353a4dee2f441ae454f528" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:27.052ex; height:6.343ex;" alt="{\displaystyle \int _{a}^{b}f(x)\,dx=F(b)-F(a).}"></span></dd></dl> <p>Furthermore, for every <span class="texhtml"><i>x</i></span> in the interval <span class="texhtml">(<i>a</i>, <i>b</i>)</span>, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {d}{dx}}\int _{a}^{x}f(t)\,dt=f(x).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>d</mi> <mrow> <mi>d</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msubsup> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>t</mi> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {d}{dx}}\int _{a}^{x}f(t)\,dt=f(x).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf4f64cc882e88a4d7b634c37b7c1684630c3687" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.325ex; height:5.843ex;" alt="{\displaystyle {\frac {d}{dx}}\int _{a}^{x}f(t)\,dt=f(x).}"></span></dd></dl> <p>This realization, made by both <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> and <a href="/wiki/Gottfried_Leibniz" class="mw-redirect" title="Gottfried Leibniz">Leibniz</a>, was key to the proliferation of analytic results after their work became known. (The extent to which Newton and Leibniz were influenced by immediate predecessors, and particularly what Leibniz may have learned from the work of <a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a>, is difficult to determine because of the priority dispute between them.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup>) The fundamental theorem provides an algebraic method of computing many definite integrals—without performing limit processes—by finding formulae for <a href="/wiki/Antiderivative" title="Antiderivative">antiderivatives</a>. It is also a prototype solution of a <a href="/wiki/Differential_equation" title="Differential equation">differential equation</a>. Differential equations relate an unknown function to its derivatives and are ubiquitous in the sciences.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 351–352">: 351–352 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:NautilusCutawayLogarithmicSpiral.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/220px-NautilusCutawayLogarithmicSpiral.jpg" decoding="async" width="220" height="166" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/330px-NautilusCutawayLogarithmicSpiral.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/08/NautilusCutawayLogarithmicSpiral.jpg/440px-NautilusCutawayLogarithmicSpiral.jpg 2x" data-file-width="2240" data-file-height="1693" /></a><figcaption>The <a href="/wiki/Logarithmic_spiral" title="Logarithmic spiral">logarithmic spiral</a> of the <a href="/wiki/Nautilus" title="Nautilus">nautilus shell</a> is a classical image used to depict the growth and change related to calculus.</figcaption></figure> <p>Calculus is used in every branch of the physical sciences,<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 1">: 1 </span></sup> <a href="/wiki/Actuarial_science" title="Actuarial science">actuarial science</a>, <a href="/wiki/Computer_science" title="Computer science">computer science</a>, <a href="/wiki/Statistics" title="Statistics">statistics</a>, <a href="/wiki/Engineering" title="Engineering">engineering</a>, <a href="/wiki/Economics" title="Economics">economics</a>, <a href="/wiki/Business" title="Business">business</a>, <a href="/wiki/Medicine" title="Medicine">medicine</a>, <a href="/wiki/Demography" title="Demography">demography</a>, and in other fields wherever a problem can be <a href="/wiki/Mathematical_model" title="Mathematical model">mathematically modeled</a> and an <a href="/wiki/Optimization_(mathematics)" class="mw-redirect" title="Optimization (mathematics)">optimal</a> solution is desired.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> It allows one to go from (non-constant) rates of change to the total change or vice versa, and many times in studying a problem we know one and are trying to find the other.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> Calculus can be used in conjunction with other mathematical disciplines. For example, it can be used with <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a> to find the "best fit" linear approximation for a set of points in a domain. Or, it can be used in <a href="/wiki/Probability_theory" title="Probability theory">probability theory</a> to determine the <a href="/wiki/Expectation_value" class="mw-redirect" title="Expectation value">expectation value</a> of a continuous random variable given a <a href="/wiki/Probability_density_function" title="Probability density function">probability density function</a>.<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 37">: 37 </span></sup> In <a href="/wiki/Analytic_geometry" title="Analytic geometry">analytic geometry</a>, the study of graphs of functions, calculus is used to find high points and low points (maxima and minima), slope, <a href="/wiki/Concave_function" title="Concave function">concavity</a> and <a href="/wiki/Inflection_points" class="mw-redirect" title="Inflection points">inflection points</a>. Calculus is also used to find approximate solutions to equations; in practice, it is the standard way to solve differential equations and do root finding in most applications. Examples are methods such as <a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a>, <a href="/wiki/Fixed_point_iteration" class="mw-redirect" title="Fixed point iteration">fixed point iteration</a>, and <a href="/wiki/Linear_approximation" title="Linear approximation">linear approximation</a>. For instance, spacecraft use a variation of the <a href="/wiki/Euler_method" title="Euler method">Euler method</a> to approximate curved courses within zero-gravity environments. </p><p><a href="/wiki/Physics" title="Physics">Physics</a> makes particular use of calculus; all concepts in <a href="/wiki/Classical_mechanics" title="Classical mechanics">classical mechanics</a> and <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> are related through calculus. The <a href="/wiki/Mass" title="Mass">mass</a> of an object of known <a href="/wiki/Density" title="Density">density</a>, the <a href="/wiki/Moment_of_inertia" title="Moment of inertia">moment of inertia</a> of objects, and the <a href="/wiki/Potential_energy" title="Potential energy">potential energies</a> due to gravitational and electromagnetic forces can all be found by the use of calculus. An example of the use of calculus in mechanics is <a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's second law of motion</a>, which states that the derivative of an object's <a href="/wiki/Momentum" title="Momentum">momentum</a> concerning time equals the net <a href="/wiki/Force" title="Force">force</a> upon it. Alternatively, Newton's second law can be expressed by saying that the net force equals the object's mass times its <a href="/wiki/Acceleration" title="Acceleration">acceleration</a>, which is the time derivative of velocity and thus the second time derivative of spatial position. Starting from knowing how an object is accelerating, we use calculus to derive its path.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p><p>Maxwell's theory of <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetism</a> and <a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a>'s theory of <a href="/wiki/General_relativity" title="General relativity">general relativity</a> are also expressed in the language of differential calculus.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 52–55">: 52–55 </span></sup> Chemistry also uses calculus in determining reaction rates<sup id="cite_ref-:3_58-0" class="reference"><a href="#cite_note-:3-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 599">: 599 </span></sup> and in studying radioactive decay.<sup id="cite_ref-:3_58-1" class="reference"><a href="#cite_note-:3-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 814">: 814 </span></sup> In biology, population dynamics starts with reproduction and death rates to model population changes.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 631">: 631 </span></sup> </p><p><a href="/wiki/Green%27s_theorem" title="Green's theorem">Green's theorem</a>, which gives the relationship between a line integral around a simple closed curve C and a double integral over the plane region D bounded by C, is applied in an instrument known as a <a href="/wiki/Planimeter" title="Planimeter">planimeter</a>, which is used to calculate the area of a flat surface on a drawing.<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup> For example, it can be used to calculate the amount of area taken up by an irregularly shaped flower bed or swimming pool when designing the layout of a piece of property. </p><p>In the realm of medicine, calculus can be used to find the optimal branching angle of a <a href="/wiki/Blood_vessel" title="Blood vessel">blood vessel</a> to maximize flow.<sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> Calculus can be applied to understand how quickly a drug is eliminated from a body or how quickly a <a href="/wiki/Cancer" title="Cancer">cancerous</a> tumor grows.<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup> </p><p>In economics, calculus allows for the determination of maximal profit by providing a way to easily calculate both <a href="/wiki/Marginal_cost" title="Marginal cost">marginal cost</a> and <a href="/wiki/Marginal_revenue" title="Marginal revenue">marginal revenue</a>.<sup id="cite_ref-64" class="reference"><a href="#cite_note-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 387">: 387 </span></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Outline_of_calculus" title="Outline of calculus">Outline of calculus</a></div> <ul><li><a href="/wiki/Glossary_of_calculus" title="Glossary of calculus">Glossary of calculus</a></li> <li><a href="/wiki/List_of_calculus_topics" title="List of calculus topics">List of calculus topics</a></li> <li><a href="/wiki/List_of_derivatives_and_integrals_in_alternative_calculi" title="List of derivatives and integrals in alternative calculi">List of derivatives and integrals in alternative calculi</a></li> <li><a href="/wiki/List_of_differentiation_identities" class="mw-redirect" title="List of differentiation identities">List of differentiation identities</a></li> <li><a href="/wiki/List_of_publications_in_mathematics#Calculus" class="mw-redirect" title="List of publications in mathematics">Publications in calculus</a></li> <li><a href="/wiki/Table_of_integrals" class="mw-redirect" title="Table of integrals">Table of integrals</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFDeBaggisMiller1966" class="citation book cs1">DeBaggis, Henry F.; Miller, Kenneth S. (1966). <i>Foundations of the Calculus</i>. Philadelphia: Saunders. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/527896">527896</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Foundations+of+the+Calculus&rft.place=Philadelphia&rft.pub=Saunders&rft.date=1966&rft_id=info%3Aoclcnum%2F527896&rft.aulast=DeBaggis&rft.aufirst=Henry+F.&rft.au=Miller%2C+Kenneth+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoyer1959" class="citation book cs1"><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, Carl B.</a> (1959). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/historyofcalculu0000boye"><i>The History of the Calculus and its Conceptual Development</i></a></span>. New York: Dover. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/643872">643872</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+History+of+the+Calculus+and+its+Conceptual+Development&rft.place=New+York&rft.pub=Dover&rft.date=1959&rft_id=info%3Aoclcnum%2F643872&rft.aulast=Boyer&rft.aufirst=Carl+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofcalculu0000boye&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBardi2006" class="citation book cs1">Bardi, Jason Socrates (2006). <i>The Calculus Wars : Newton, Leibniz, and the Greatest Mathematical Clash of All Time</i>. New York: Thunder's Mouth Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1-56025-706-7" title="Special:BookSources/1-56025-706-7"><bdi>1-56025-706-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Calculus+Wars+%3A+Newton%2C+Leibniz%2C+and+the+Greatest+Mathematical+Clash+of+All+Time&rft.place=New+York&rft.pub=Thunder%27s+Mouth+Press&rft.date=2006&rft.isbn=1-56025-706-7&rft.aulast=Bardi&rft.aufirst=Jason+Socrates&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoffmannBradley2004" class="citation book cs1">Hoffmann, Laurence D.; Bradley, Gerald L. (2004). <i>Calculus for Business, Economics, and the Social and Life Sciences</i> (8th ed.). Boston: McGraw Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-07-242432-X" title="Special:BookSources/0-07-242432-X"><bdi>0-07-242432-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus+for+Business%2C+Economics%2C+and+the+Social+and+Life+Sciences&rft.place=Boston&rft.edition=8th&rft.pub=McGraw+Hill&rft.date=2004&rft.isbn=0-07-242432-X&rft.aulast=Hoffmann&rft.aufirst=Laurence+D.&rft.au=Bradley%2C+Gerald+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">See, for example: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://skeptics.stackexchange.com/questions/8841/were-metered-taxis-busy-roaming-imperial-rome">"History – Were metered taxis busy roaming Imperial Rome?"</a>. <i>Skeptics Stack Exchange</i>. 17 June 2020. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120525035132/https://skeptics.stackexchange.com/questions/8841/were-metered-taxis-busy-roaming-imperial-rome">Archived</a> from the original on 25 May 2012<span class="reference-accessdate">. Retrieved <span class="nowrap">13 February</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Skeptics+Stack+Exchange&rft.atitle=History+%E2%80%93+Were+metered+taxis+busy+roaming+Imperial+Rome%3F&rft.date=2020-06-17&rft_id=https%3A%2F%2Fskeptics.stackexchange.com%2Fquestions%2F8841%2Fwere-metered-taxis-busy-roaming-imperial-rome&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCousineau2010" class="citation book cs1">Cousineau, Phil (2010). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=m8lJVgizhbQC&q=Ancient+Roman+taximeter+calculus&pg=PT80"><i>Wordcatcher: An Odyssey into the World of Weird and Wonderful Words</i></a>. Simon and Schuster. p. 58. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-57344-550-4" title="Special:BookSources/978-1-57344-550-4"><bdi>978-1-57344-550-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/811492876">811492876</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150357/https://books.google.com/books?id=m8lJVgizhbQC&q=Ancient+Roman+taximeter+calculus&pg=PT80">Archived</a> from the original on 1 March 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">15 February</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Wordcatcher%3A+An+Odyssey+into+the+World+of+Weird+and+Wonderful+Words&rft.pages=58&rft.pub=Simon+and+Schuster&rft.date=2010&rft_id=info%3Aoclcnum%2F811492876&rft.isbn=978-1-57344-550-4&rft.aulast=Cousineau&rft.aufirst=Phil&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Dm8lJVgizhbQC%26q%3DAncient%2BRoman%2Btaximeter%2Bcalculus%26pg%3DPT80&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReference-OED-calculus" class="citation encyclopaedia cs1"><span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oed.com/search/dictionary/?q=calculus">"calculus"</a></span>. <i><a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> (Online ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=calculus&rft.btitle=Oxford+English+Dictionary&rft.edition=Online&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Fwww.oed.com%2Fsearch%2Fdictionary%2F%3Fq%3Dcalculus&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span> <span style="font-size:0.95em; font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKline1990" class="citation book cs1"><a href="/wiki/Morris_Kline" title="Morris Kline">Kline, Morris</a> (1990). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=wKsYrT691yIC"><i>Mathematical Thought from Ancient to Modern Times: Volume 1</i></a>. Oxford University Press. pp. 15–21. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-506135-2" title="Special:BookSources/978-0-19-506135-2"><bdi>978-0-19-506135-2</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150420/https://books.google.com/books?id=wKsYrT691yIC">Archived</a> from the original on 1 March 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">20 February</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Thought+from+Ancient+to+Modern+Times%3A+Volume+1&rft.pages=15-21&rft.pub=Oxford+University+Press&rft.date=1990&rft.isbn=978-0-19-506135-2&rft.aulast=Kline&rft.aufirst=Morris&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DwKsYrT691yIC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFImhausen2016" class="citation book cs1"><a href="/wiki/Annette_Imhausen" title="Annette Imhausen">Imhausen, Annette</a> (2016). <a href="/wiki/Mathematics_in_Ancient_Egypt:_A_Contextual_History" title="Mathematics in Ancient Egypt: A Contextual History"><i>Mathematics in Ancient Egypt: A Contextual History</i></a>. Princeton University Press. p. 112. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4008-7430-9" title="Special:BookSources/978-1-4008-7430-9"><bdi>978-1-4008-7430-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/934433864">934433864</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+in+Ancient+Egypt%3A+A+Contextual+History&rft.pages=112&rft.pub=Princeton+University+Press&rft.date=2016&rft_id=info%3Aoclcnum%2F934433864&rft.isbn=978-1-4008-7430-9&rft.aulast=Imhausen&rft.aufirst=Annette&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">See, for example: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPowers2020" class="citation web cs1">Powers, J. (2020). <a rel="nofollow" class="external text" href="https://www.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/2020-Jeffery%20Powers.pdf">"<span class="cs1-kern-left"></span>"Did Archimedes do calculus?"<span class="cs1-kern-right"></span>"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a></i>. <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/https://www.maa.org/sites/default/files/images/upload_library/46/HOMSIGMAA/2020-Jeffery%20Powers.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 9 October 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Mathematical+Association+of+America&rft.atitle=%22Did+Archimedes+do+calculus%3F%22&rft.date=2020&rft.aulast=Powers&rft.aufirst=J.&rft_id=https%3A%2F%2Fwww.maa.org%2Fsites%2Fdefault%2Ffiles%2Fimages%2Fupload_library%2F46%2FHOMSIGMAA%2F2020-Jeffery%2520Powers.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJullien2015" class="citation book cs1">Jullien, Vincent (2015). "Archimedes and Indivisibles". <i>Seventeenth-Century Indivisibles Revisited</i>. Science Networks. Historical Studies. Vol. 49. Cham: Springer International Publishing. pp. 451–457. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-319-00131-9_18">10.1007/978-3-319-00131-9_18</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-00130-2" title="Special:BookSources/978-3-319-00130-2"><bdi>978-3-319-00130-2</bdi></a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1421-6329">1421-6329</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Archimedes+and+Indivisibles&rft.btitle=Seventeenth-Century+Indivisibles+Revisited&rft.place=Cham&rft.series=Science+Networks.+Historical+Studies&rft.pages=451-457&rft.pub=Springer+International+Publishing&rft.date=2015&rft.issn=1421-6329&rft_id=info%3Adoi%2F10.1007%2F978-3-319-00131-9_18&rft.isbn=978-3-319-00130-2&rft.aulast=Jullien&rft.aufirst=Vincent&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPlummer2006" class="citation web cs1">Plummer, Brad (9 August 2006). <a rel="nofollow" class="external text" href="http://news.stanford.edu/news/2006/august9/arch-080906.html">"Modern X-ray technology reveals Archimedes' math theory under forged painting"</a>. <i>Stanford University</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220120065134/https://news.stanford.edu/news/2006/august9/arch-080906.html">Archived</a> from the original on 20 January 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">28 February</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Stanford+University&rft.atitle=Modern+X-ray+technology+reveals+Archimedes%27+math+theory+under+forged+painting&rft.date=2006-08-09&rft.aulast=Plummer&rft.aufirst=Brad&rft_id=http%3A%2F%2Fnews.stanford.edu%2Fnews%2F2006%2Faugust9%2Farch-080906.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArchimedes2004" class="citation book cs1">Archimedes (2004). <i>The Works of Archimedes, Volume 1: The Two Books On the Sphere and the Cylinder</i>. Translated by Netz, Reviel. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-66160-7" title="Special:BookSources/978-0-521-66160-7"><bdi>978-0-521-66160-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Works+of+Archimedes%2C+Volume+1%3A+The+Two+Books+On+the+Sphere+and+the+Cylinder&rft.pub=Cambridge+University+Press&rft.date=2004&rft.isbn=978-0-521-66160-7&rft.au=Archimedes&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrayWaldman2018" class="citation journal cs1">Gray, Shirley; Waldman, Cye H. (20 October 2018). "Archimedes Redux: Center of Mass Applications from The Method". <i>The College Mathematics Journal</i>. <b>49</b> (5): 346–352. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F07468342.2018.1524647">10.1080/07468342.2018.1524647</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0746-8342">0746-8342</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:125411353">125411353</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+College+Mathematics+Journal&rft.atitle=Archimedes+Redux%3A+Center+of+Mass+Applications+from+The+Method&rft.volume=49&rft.issue=5&rft.pages=346-352&rft.date=2018-10-20&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A125411353%23id-name%3DS2CID&rft.issn=0746-8342&rft_id=info%3Adoi%2F10.1080%2F07468342.2018.1524647&rft.aulast=Gray&rft.aufirst=Shirley&rft.au=Waldman%2C+Cye+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDunFanCohen1966" class="citation book cs1">Dun, Liu; Fan, Dainian; Cohen, Robert Sonné (1966). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=jaQH6_8Ju-MC"><i>A comparison of Archimdes' and Liu Hui's studies of circles</i></a>. Chinese studies in the history and philosophy of science and technology. Vol. 130. Springer. p. 279. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-3463-7" title="Special:BookSources/978-0-7923-3463-7"><bdi>978-0-7923-3463-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150353/https://books.google.com/books?id=jaQH6_8Ju-MC">Archived</a> from the original on 1 March 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">15 November</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+comparison+of+Archimdes%27+and+Liu+Hui%27s+studies+of+circles&rft.series=Chinese+studies+in+the+history+and+philosophy+of+science+and+technology&rft.pages=279&rft.pub=Springer&rft.date=1966&rft.isbn=978-0-7923-3463-7&rft.aulast=Dun&rft.aufirst=Liu&rft.au=Fan%2C+Dainian&rft.au=Cohen%2C+Robert+Sonn%C3%A9&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DjaQH6_8Ju-MC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span>,<a rel="nofollow" class="external text" href="https://books.google.com/books?id=jaQH6_8Ju-MC&pg=PA279">pp. 279ff</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150353/https://books.google.com/books?id=jaQH6_8Ju-MC&pg=PA279">Archived</a> 1 March 2023 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-:0-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDainian_FanR._S._Cohen1996" class="citation book cs1">Dainian Fan; R. S. Cohen (1996). <i>Chinese studies in the history and philosophy of science and technology</i>. Dordrecht: Kluwer Academic Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7923-3463-9" title="Special:BookSources/0-7923-3463-9"><bdi>0-7923-3463-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/32272485">32272485</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chinese+studies+in+the+history+and+philosophy+of+science+and+technology&rft.place=Dordrecht&rft.pub=Kluwer+Academic+Publishers&rft.date=1996&rft_id=info%3Aoclcnum%2F32272485&rft.isbn=0-7923-3463-9&rft.au=Dainian+Fan&rft.au=R.+S.+Cohen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKatz2008" class="citation book cs1"><a href="/wiki/Victor_J._Katz" title="Victor J. Katz">Katz, Victor J.</a> (2008). <i>A history of mathematics</i> (3rd ed.). Boston, MA: Addison-Wesley. p. 203. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-321-38700-4" title="Special:BookSources/978-0-321-38700-4"><bdi>978-0-321-38700-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+history+of+mathematics&rft.place=Boston%2C+MA&rft.pages=203&rft.edition=3rd&rft.pub=Addison-Wesley&rft.date=2008&rft.isbn=978-0-321-38700-4&rft.aulast=Katz&rft.aufirst=Victor+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFZillWrightWright2009" class="citation book cs1">Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=R3Hk4Uhb1Z0C"><i>Calculus: Early Transcendentals</i></a> (3rd ed.). Jones & Bartlett Learning. p. xxvii. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7637-5995-7" title="Special:BookSources/978-0-7637-5995-7"><bdi>978-0-7637-5995-7</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150357/https://books.google.com/books?id=R3Hk4Uhb1Z0C">Archived</a> from the original on 1 March 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">15 November</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+Early+Transcendentals&rft.pages=xxvii&rft.edition=3rd&rft.pub=Jones+%26+Bartlett+Learning&rft.date=2009&rft.isbn=978-0-7637-5995-7&rft.aulast=Zill&rft.aufirst=Dennis+G.&rft.au=Wright%2C+Scott&rft.au=Wright%2C+Warren+S.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DR3Hk4Uhb1Z0C&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span> <a rel="nofollow" class="external text" href="https://books.google.com/books?id=R3Hk4Uhb1Z0C&pg=PR27">Extract of page 27</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150353/https://books.google.com/books?id=R3Hk4Uhb1Z0C&pg=PR27">Archived</a> 1 March 2023 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-katz-14"><span class="mw-cite-backlink">^ <a href="#cite_ref-katz_14-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-katz_14-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKatz1995" class="citation journal cs1"><a href="/wiki/Victor_J._Katz" title="Victor J. Katz">Katz, Victor J.</a> (June 1995). "Ideas of Calculus in Islam and India". <i><a href="/wiki/Mathematics_Magazine" title="Mathematics Magazine">Mathematics Magazine</a></i>. <b>68</b> (3): 163–174. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1080%2F0025570X.1995.11996307">10.1080/0025570X.1995.11996307</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0025-570X">0025-570X</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2691411">2691411</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+Magazine&rft.atitle=Ideas+of+Calculus+in+Islam+and+India&rft.volume=68&rft.issue=3&rft.pages=163-174&rft.date=1995-06&rft.issn=0025-570X&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2691411%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1080%2F0025570X.1995.11996307&rft.aulast=Katz&rft.aufirst=Victor+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShukla1984" class="citation journal cs1">Shukla, Kripa Shankar (1984). "Use of Calculus in Hindu Mathematics". <i>Indian Journal of History of Science</i>. <b>19</b>: 95–104.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Indian+Journal+of+History+of+Science&rft.atitle=Use+of+Calculus+in+Hindu+Mathematics&rft.volume=19&rft.pages=95-104&rft.date=1984&rft.aulast=Shukla&rft.aufirst=Kripa+Shankar&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCooke1997" class="citation book cs1">Cooke, Roger (1997). <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema0000cook/page/213">"The Mathematics of the Hindus"</a>. <i>The History of Mathematics: A Brief Course</i>. Wiley-Interscience. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema0000cook/page/213">213–215</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-471-18082-3" title="Special:BookSources/0-471-18082-3"><bdi>0-471-18082-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Mathematics+of+the+Hindus&rft.btitle=The+History+of+Mathematics%3A+A+Brief+Course&rft.pages=213-215&rft.pub=Wiley-Interscience&rft.date=1997&rft.isbn=0-471-18082-3&rft.aulast=Cooke&rft.aufirst=Roger&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofmathema0000cook%2Fpage%2F213&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.nasa.gov/kepler/education/johannes">"Johannes Kepler: His Life, His Laws and Times"</a>. NASA. 24 September 2016. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210624003856/https://www.nasa.gov/kepler/education/johannes/">Archived</a> from the original on 24 June 2021<span class="reference-accessdate">. Retrieved <span class="nowrap">10 June</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Johannes+Kepler%3A+His+Life%2C+His+Laws+and+Times&rft.pub=NASA&rft.date=2016-09-24&rft_id=https%3A%2F%2Fwww.nasa.gov%2Fkepler%2Feducation%2Fjohannes&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-EB1911-18"><span class="mw-cite-backlink">^ <a href="#cite_ref-EB1911_18-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-EB1911_18-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChisholm1911" class="citation encyclopaedia cs1"><a href="/wiki/Hugh_Chisholm" title="Hugh Chisholm">Chisholm, Hugh</a>, ed. (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Infinitesimal Calculus/History"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Infinitesimal_Calculus/History">"Infinitesimal Calculus § History" </a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i>. Vol. 14 (11th ed.). Cambridge University Press. p. 537.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Infinitesimal+Calculus+%C2%A7+History&rft.btitle=Encyclop%C3%A6dia+Britannica&rft.pages=537&rft.edition=11th&rft.pub=Cambridge+University+Press&rft.date=1911&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeil1984" class="citation book cs1"><a href="/wiki/Andr%C3%A9_Weil" title="André Weil">Weil, André</a> (1984). <i>Number theory: An approach through History from Hammurapi to Legendre</i>. Boston: Birkhauser Boston. p. 28. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8176-4565-9" title="Special:BookSources/0-8176-4565-9"><bdi>0-8176-4565-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Number+theory%3A+An+approach+through+History+from+Hammurapi+to+Legendre&rft.place=Boston&rft.pages=28&rft.pub=Birkhauser+Boston&rft.date=1984&rft.isbn=0-8176-4565-9&rft.aulast=Weil&rft.aufirst=Andr%C3%A9&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHollingdale1991" class="citation journal cs1">Hollingdale, Stuart (1991). "Review of Before Newton: The Life and Times of Isaac Barrow". <i><a href="/wiki/Notes_and_Records_of_the_Royal_Society_of_London" class="mw-redirect" title="Notes and Records of the Royal Society of London">Notes and Records of the Royal Society of London</a></i>. <b>45</b> (2): 277–279. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsnr.1991.0027">10.1098/rsnr.1991.0027</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0035-9149">0035-9149</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/531707">531707</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:165043307">165043307</a>. <q>The most interesting to us are Lectures X–XII, in which Barrow comes close to providing a geometrical demonstration of the fundamental theorem of the calculus... He did not realize, however, the full significance of his results, and his rejection of algebra means that his work must remain a piece of mid-17th century geometrical analysis of mainly historic interest.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Notes+and+Records+of+the+Royal+Society+of+London&rft.atitle=Review+of+Before+Newton%3A+The+Life+and+Times+of+Isaac+Barrow&rft.volume=45&rft.issue=2&rft.pages=277-279&rft.date=1991&rft.issn=0035-9149&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A165043307%23id-name%3DS2CID&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F531707%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.1098%2Frsnr.1991.0027&rft.aulast=Hollingdale&rft.aufirst=Stuart&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBressoud2011" class="citation journal cs1"><a href="/wiki/David_Bressoud" title="David Bressoud">Bressoud, David M.</a> (2011). "Historical Reflections on Teaching the Fundamental Theorem of Integral Calculus". <i><a href="/wiki/The_American_Mathematical_Monthly" title="The American Mathematical Monthly">The American Mathematical Monthly</a></i>. <b>118</b> (2): 99. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4169%2Famer.math.monthly.118.02.099">10.4169/amer.math.monthly.118.02.099</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:21473035">21473035</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=Historical+Reflections+on+Teaching+the+Fundamental+Theorem+of+Integral+Calculus&rft.volume=118&rft.issue=2&rft.pages=99&rft.date=2011&rft_id=info%3Adoi%2F10.4169%2Famer.math.monthly.118.02.099&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A21473035%23id-name%3DS2CID&rft.aulast=Bressoud&rft.aufirst=David+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBlankKrantz2006" class="citation book cs1">Blank, Brian E.; Krantz, Steven George (2006). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=hMY8lbX87Y8C&pg=PA248"><i>Calculus: Single Variable, Volume 1</i></a> (Illustrated ed.). Springer Science & Business Media. p. 248. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-931914-59-8" title="Special:BookSources/978-1-931914-59-8"><bdi>978-1-931914-59-8</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150354/https://books.google.com/books?id=hMY8lbX87Y8C&pg=PA248">Archived</a> from the original on 1 March 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">31 August</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+Single+Variable%2C+Volume+1&rft.pages=248&rft.edition=Illustrated&rft.pub=Springer+Science+%26+Business+Media&rft.date=2006&rft.isbn=978-1-931914-59-8&rft.aulast=Blank&rft.aufirst=Brian+E.&rft.au=Krantz%2C+Steven+George&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DhMY8lbX87Y8C%26pg%3DPA248&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFerraro2007" class="citation book cs1">Ferraro, Giovanni (2007). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=vLBJSmA9zgAC&pg=PA87"><i>The Rise and Development of the Theory of Series up to the Early 1820s</i></a> (Illustrated ed.). Springer Science & Business Media. p. 87. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-73468-2" title="Special:BookSources/978-0-387-73468-2"><bdi>978-0-387-73468-2</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150355/https://books.google.com/books?id=vLBJSmA9zgAC&pg=PA87">Archived</a> from the original on 1 March 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">31 August</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Rise+and+Development+of+the+Theory+of+Series+up+to+the+Early+1820s&rft.pages=87&rft.edition=Illustrated&rft.pub=Springer+Science+%26+Business+Media&rft.date=2007&rft.isbn=978-0-387-73468-2&rft.aulast=Ferraro&rft.aufirst=Giovanni&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DvLBJSmA9zgAC%26pg%3DPA87&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuicciardini2005" class="citation book cs1">Guicciardini, Niccolò (2005). "Isaac Newton, Philosophiae naturalis principia mathematica, first edition (1687)". <i>Landmark Writings in Western Mathematics 1640–1940</i>. Elsevier. pp. 59–87. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fb978-044450871-3%2F50086-3">10.1016/b978-044450871-3/50086-3</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-444-50871-3" title="Special:BookSources/978-0-444-50871-3"><bdi>978-0-444-50871-3</bdi></a>. <q>[Newton] immediately realised that quadrature problems (the inverse problems) could be tackled via infinite series: as we would say nowadays, by expanding the integrand in power series and integrating term-wise.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Isaac+Newton%2C+Philosophiae+naturalis+principia+mathematica%2C+first+edition+%281687%29&rft.btitle=Landmark+Writings+in+Western+Mathematics+1640%E2%80%931940&rft.pages=59-87&rft.pub=Elsevier&rft.date=2005&rft_id=info%3Adoi%2F10.1016%2Fb978-044450871-3%2F50086-3&rft.isbn=978-0-444-50871-3&rft.aulast=Guicciardini&rft.aufirst=Niccol%C3%B2&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-:1-25"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_25-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_25-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrattan-Guinness2005" class="citation book cs1"><a href="/wiki/Ivor_Grattan-Guinness" title="Ivor Grattan-Guinness">Grattan-Guinness, I.</a>, ed. (2005). <i>Landmark writings in Western mathematics 1640–1940</i>. Amsterdam: Elsevier. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-444-50871-6" title="Special:BookSources/0-444-50871-6"><bdi>0-444-50871-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/60416766">60416766</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Landmark+writings+in+Western+mathematics+1640%E2%80%931940&rft.place=Amsterdam&rft.pub=Elsevier&rft.date=2005&rft_id=info%3Aoclcnum%2F60416766&rft.isbn=0-444-50871-6&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-leib-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-leib_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeibniz2008" class="citation book cs1">Leibniz, Gottfried Wilhelm (2008). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=7d8_4WPc9SMC&pg=PA3"><i>The Early Mathematical Manuscripts of Leibniz</i></a>. Cosimo, Inc. p. 228. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-605-20533-5" title="Special:BookSources/978-1-605-20533-5"><bdi>978-1-605-20533-5</bdi></a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230301150355/https://books.google.com/books?id=7d8_4WPc9SMC&pg=PA3">Archived</a> from the original on 1 March 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">5 June</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Early+Mathematical+Manuscripts+of+Leibniz&rft.pages=228&rft.pub=Cosimo%2C+Inc.&rft.date=2008&rft.isbn=978-1-605-20533-5&rft.aulast=Leibniz&rft.aufirst=Gottfried+Wilhelm&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D7d8_4WPc9SMC%26pg%3DPA3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMazur2014" class="citation book cs1"><a href="/wiki/Joseph_Mazur" title="Joseph Mazur">Mazur, Joseph</a> (2014). <i>Enlightening Symbols / A Short History of Mathematical Notation and Its Hidden Powers</i>. Princeton University Press. p. 166. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-17337-5" title="Special:BookSources/978-0-691-17337-5"><bdi>978-0-691-17337-5</bdi></a>. <q>Leibniz understood symbols, their conceptual powers as well as their limitations. He would spend years experimenting with some—adjusting, rejecting, and corresponding with everyone he knew, consulting with as many of the leading mathematicians of the time who were sympathetic to his fastidiousness.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Enlightening+Symbols+%2F+A+Short+History+of+Mathematical+Notation+and+Its+Hidden+Powers&rft.pages=166&rft.pub=Princeton+University+Press&rft.date=2014&rft.isbn=978-0-691-17337-5&rft.aulast=Mazur&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-TMU-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-TMU_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-TMU_28-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-TMU_28-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-TMU_28-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrautschiOlenickApostolGoodstein2007" class="citation book cs1"><a href="/wiki/Steven_Frautschi" title="Steven Frautschi">Frautschi, Steven C.</a>; Olenick, Richard P.; <a href="/wiki/Tom_M._Apostol" title="Tom M. Apostol">Apostol, Tom M.</a>; <a href="/wiki/David_L._Goodstein" class="mw-redirect" title="David L. Goodstein">Goodstein, David L.</a> (2007). <a href="/wiki/The_Mechanical_Universe" title="The Mechanical Universe"><i>The Mechanical Universe: Mechanics and Heat</i></a> (Advanced ed.). Cambridge [Cambridgeshire]: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-71590-4" title="Special:BookSources/978-0-521-71590-4"><bdi>978-0-521-71590-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/227002144">227002144</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Mechanical+Universe%3A+Mechanics+and+Heat&rft.place=Cambridge+%5BCambridgeshire%5D&rft.edition=Advanced&rft.pub=Cambridge+University+Press&rft.date=2007&rft_id=info%3Aoclcnum%2F227002144&rft.isbn=978-0-521-71590-4&rft.aulast=Frautschi&rft.aufirst=Steven+C.&rft.au=Olenick%2C+Richard+P.&rft.au=Apostol%2C+Tom+M.&rft.au=Goodstein%2C+David+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSchrader1962" class="citation journal cs1">Schrader, Dorothy V. (1962). "The Newton-Leibniz controversy concerning the discovery of the calculus". <i>The Mathematics Teacher</i>. <b>55</b> (5): 385–396. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5951%2FMT.55.5.0385">10.5951/MT.55.5.0385</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0025-5769">0025-5769</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/27956626">27956626</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Mathematics+Teacher&rft.atitle=The+Newton-Leibniz+controversy+concerning+the+discovery+of+the+calculus&rft.volume=55&rft.issue=5&rft.pages=385-396&rft.date=1962&rft.issn=0025-5769&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F27956626%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.5951%2FMT.55.5.0385&rft.aulast=Schrader&rft.aufirst=Dorothy+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStedall2012" class="citation book cs1"><a href="/wiki/Jackie_Stedall" title="Jackie Stedall">Stedall, Jacqueline</a> (2012). <a href="/wiki/The_History_of_Mathematics:_A_Very_Short_Introduction" title="The History of Mathematics: A Very Short Introduction"><i>The History of Mathematics: A Very Short Introduction</i></a>. Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-191-63396-6" title="Special:BookSources/978-0-191-63396-6"><bdi>978-0-191-63396-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+History+of+Mathematics%3A+A+Very+Short+Introduction&rft.pub=Oxford+University+Press&rft.date=2012&rft.isbn=978-0-191-63396-6&rft.aulast=Stedall&rft.aufirst=Jacqueline&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStenhouse2020" class="citation journal cs1">Stenhouse, Brigitte (May 2020). <a rel="nofollow" class="external text" href="http://oro.open.ac.uk/68466/1/accepted_manuscript.pdf">"Mary Somerville's early contributions to the circulation of differential calculus"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Historia_Mathematica" title="Historia Mathematica">Historia Mathematica</a></i>. <b>51</b>: 1–25. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.hm.2019.12.001">10.1016/j.hm.2019.12.001</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:214472568">214472568</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historia+Mathematica&rft.atitle=Mary+Somerville%27s+early+contributions+to+the+circulation+of+differential+calculus&rft.volume=51&rft.pages=1-25&rft.date=2020-05&rft_id=info%3Adoi%2F10.1016%2Fj.hm.2019.12.001&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A214472568%23id-name%3DS2CID&rft.aulast=Stenhouse&rft.aufirst=Brigitte&rft_id=http%3A%2F%2Foro.open.ac.uk%2F68466%2F1%2Faccepted_manuscript.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAllaire2007" class="citation book cs1">Allaire, Patricia R. (2007). Foreword. <a href="/wiki/A_Biography_of_Maria_Gaetana_Agnesi" title="A Biography of Maria Gaetana Agnesi"><i>A Biography of Maria Gaetana Agnesi, an Eighteenth-century Woman Mathematician</i></a>. By <a href="/wiki/Antonella_Cupillari" title="Antonella Cupillari">Cupillari, Antonella</a>. <a href="/wiki/Lewiston,_New_York" title="Lewiston, New York">Lewiston, New York</a>: <a href="/wiki/Edwin_Mellen_Press" title="Edwin Mellen Press">Edwin Mellen Press</a>. p. iii. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7734-5226-8" title="Special:BookSources/978-0-7734-5226-8"><bdi>978-0-7734-5226-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Foreword&rft.btitle=A+Biography+of+Maria+Gaetana+Agnesi%2C+an+Eighteenth-century+Woman+Mathematician&rft.place=Lewiston%2C+New+York&rft.pages=iii&rft.pub=Edwin+Mellen+Press&rft.date=2007&rft.isbn=978-0-7734-5226-8&rft.aulast=Allaire&rft.aufirst=Patricia+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUnlu1995" class="citation web cs1">Unlu, Elif (April 1995). <a rel="nofollow" class="external text" href="http://www.agnesscott.edu/lriddle/women/agnesi.htm">"Maria Gaetana Agnesi"</a>. <a href="/wiki/Agnes_Scott_College" title="Agnes Scott College">Agnes Scott College</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/19981203075738/http://www.agnesscott.edu/lriddle/women/agnesi.htm">Archived</a> from the original on 3 December 1998<span class="reference-accessdate">. Retrieved <span class="nowrap">7 December</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Maria+Gaetana+Agnesi&rft.pub=Agnes+Scott+College&rft.date=1995-04&rft.aulast=Unlu&rft.aufirst=Elif&rft_id=http%3A%2F%2Fwww.agnesscott.edu%2Flriddle%2Fwomen%2Fagnesi.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-Bell-SEP-34"><span class="mw-cite-backlink">^ <a href="#cite_ref-Bell-SEP_34-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Bell-SEP_34-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Bell-SEP_34-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Bell-SEP_34-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Bell-SEP_34-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-Bell-SEP_34-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBell2013" class="citation web cs1"><a href="/wiki/John_Lane_Bell" title="John Lane Bell">Bell, John L.</a> (6 September 2013). <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/continuity/">"Continuity and Infinitesimals"</a>. <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220316170134/https://plato.stanford.edu/entries/continuity/">Archived</a> from the original on 16 March 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">20 February</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Stanford+Encyclopedia+of+Philosophy&rft.atitle=Continuity+and+Infinitesimals&rft.date=2013-09-06&rft.aulast=Bell&rft.aufirst=John+L.&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fcontinuity%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRussell1946" class="citation book cs1"><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russell, Bertrand</a> (1946). <a href="/wiki/A_History_of_Western_Philosophy" title="A History of Western Philosophy"><i>History of Western Philosophy</i></a>. London: <a href="/wiki/George_Allen_%26_Unwin_Ltd" class="mw-redirect" title="George Allen & Unwin Ltd">George Allen & Unwin Ltd</a>. p. <a rel="nofollow" class="external text" href="https://archive.org/stream/westernphilosoph035502mbp#page/n857/mode/2up">857</a>. <q>The great mathematicians of the seventeenth century were optimistic and anxious for quick results; consequently they left the foundations of analytical geometry and the infinitesimal calculus insecure. Leibniz believed in actual infinitesimals, but although this belief suited his metaphysics it had no sound basis in mathematics. Weierstrass, soon after the middle of the nineteenth century, showed how to establish calculus without infinitesimals, and thus, at last, made it logically secure. Next came Georg Cantor, who developed the theory of continuity and infinite number. "Continuity" had been, until he defined it, a vague word, convenient for philosophers like Hegel, who wished to introduce metaphysical muddles into mathematics. Cantor gave a precise significance to the word and showed that continuity, as he defined it, was the concept needed by mathematicians and physicists. By this means a great deal of mysticism, such as that of Bergson, was rendered antiquated.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=History+of+Western+Philosophy&rft.place=London&rft.pages=857&rft.pub=George+Allen+%26+Unwin+Ltd&rft.date=1946&rft.aulast=Russell&rft.aufirst=Bertrand&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrabiner1981" class="citation book cs1"><a href="/wiki/Judith_Grabiner" title="Judith Grabiner">Grabiner, Judith V.</a> (1981). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/originsofcauchys00judi"><i>The Origins of Cauchy's Rigorous Calculus</i></a></span>. Cambridge: MIT Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-387-90527-3" title="Special:BookSources/978-0-387-90527-3"><bdi>978-0-387-90527-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Origins+of+Cauchy%27s+Rigorous+Calculus&rft.place=Cambridge&rft.pub=MIT+Press&rft.date=1981&rft.isbn=978-0-387-90527-3&rft.aulast=Grabiner&rft.aufirst=Judith+V.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Foriginsofcauchys00judi&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFArchibald2008" class="citation book cs1">Archibald, Tom (2008). "The Development of Rigor in Mathematical Analysis". In <a href="/wiki/Timothy_Gowers" title="Timothy Gowers">Gowers, Timothy</a>; <a href="/wiki/June_Barrow-Green" title="June Barrow-Green">Barrow-Green, June</a>; <a href="/wiki/Imre_Leader" title="Imre Leader">Leader, Imre</a> (eds.). <a href="/wiki/The_Princeton_Companion_to_Mathematics" title="The Princeton Companion to Mathematics"><i>The Princeton Companion to Mathematics</i></a>. Princeton University Press. pp. 117–129. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11880-2" title="Special:BookSources/978-0-691-11880-2"><bdi>978-0-691-11880-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/682200048">682200048</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Development+of+Rigor+in+Mathematical+Analysis&rft.btitle=The+Princeton+Companion+to+Mathematics&rft.pages=117-129&rft.pub=Princeton+University+Press&rft.date=2008&rft_id=info%3Aoclcnum%2F682200048&rft.isbn=978-0-691-11880-2&rft.aulast=Archibald&rft.aufirst=Tom&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRice2008" class="citation book cs1">Rice, Adrian (2008). "A Chronology of Mathematical Events". In <a href="/wiki/Timothy_Gowers" title="Timothy Gowers">Gowers, Timothy</a>; <a href="/wiki/June_Barrow-Green" title="June Barrow-Green">Barrow-Green, June</a>; <a href="/wiki/Imre_Leader" title="Imre Leader">Leader, Imre</a> (eds.). <a href="/wiki/The_Princeton_Companion_to_Mathematics" title="The Princeton Companion to Mathematics"><i>The Princeton Companion to Mathematics</i></a>. Princeton University Press. pp. 1010–1014. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11880-2" title="Special:BookSources/978-0-691-11880-2"><bdi>978-0-691-11880-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/682200048">682200048</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=A+Chronology+of+Mathematical+Events&rft.btitle=The+Princeton+Companion+to+Mathematics&rft.pages=1010-1014&rft.pub=Princeton+University+Press&rft.date=2008&rft_id=info%3Aoclcnum%2F682200048&rft.isbn=978-0-691-11880-2&rft.aulast=Rice&rft.aufirst=Adrian&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSiegmund-Schultze2008" class="citation book cs1">Siegmund-Schultze, Reinhard (2008). "Henri Lebesgue". In <a href="/wiki/Timothy_Gowers" title="Timothy Gowers">Gowers, Timothy</a>; <a href="/wiki/June_Barrow-Green" title="June Barrow-Green">Barrow-Green, June</a>; <a href="/wiki/Imre_Leader" title="Imre Leader">Leader, Imre</a> (eds.). <a href="/wiki/The_Princeton_Companion_to_Mathematics" title="The Princeton Companion to Mathematics"><i>The Princeton Companion to Mathematics</i></a>. Princeton University Press. pp. 796–797. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11880-2" title="Special:BookSources/978-0-691-11880-2"><bdi>978-0-691-11880-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/682200048">682200048</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Henri+Lebesgue&rft.btitle=The+Princeton+Companion+to+Mathematics&rft.pages=796-797&rft.pub=Princeton+University+Press&rft.date=2008&rft_id=info%3Aoclcnum%2F682200048&rft.isbn=978-0-691-11880-2&rft.aulast=Siegmund-Schultze&rft.aufirst=Reinhard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaranyPaumierLützen2017" class="citation journal cs1">Barany, Michael J.; Paumier, Anne-Sandrine; Lützen, Jesper (November 2017). <a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.hm.2017.04.002">"From Nancy to Copenhagen to the World: The internationalization of Laurent Schwartz and his theory of distributions"</a>. <i><a href="/wiki/Historia_Mathematica" title="Historia Mathematica">Historia Mathematica</a></i>. <b>44</b> (4): 367–394. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1016%2Fj.hm.2017.04.002">10.1016/j.hm.2017.04.002</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Historia+Mathematica&rft.atitle=From+Nancy+to+Copenhagen+to+the+World%3A+The+internationalization+of+Laurent+Schwartz+and+his+theory+of+distributions&rft.volume=44&rft.issue=4&rft.pages=367-394&rft.date=2017-11&rft_id=info%3Adoi%2F10.1016%2Fj.hm.2017.04.002&rft.aulast=Barany&rft.aufirst=Michael+J.&rft.au=Paumier%2C+Anne-Sandrine&rft.au=L%C3%BCtzen%2C+Jesper&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%252Fj.hm.2017.04.002&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaubin2008" class="citation book cs1">Daubin, Joseph W. (2008). "Abraham Robinson". In <a href="/wiki/Timothy_Gowers" title="Timothy Gowers">Gowers, Timothy</a>; <a href="/wiki/June_Barrow-Green" title="June Barrow-Green">Barrow-Green, June</a>; <a href="/wiki/Imre_Leader" title="Imre Leader">Leader, Imre</a> (eds.). <a href="/wiki/The_Princeton_Companion_to_Mathematics" title="The Princeton Companion to Mathematics"><i>The Princeton Companion to Mathematics</i></a>. Princeton University Press. pp. 822–823. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-691-11880-2" title="Special:BookSources/978-0-691-11880-2"><bdi>978-0-691-11880-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/682200048">682200048</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Abraham+Robinson&rft.btitle=The+Princeton+Companion+to+Mathematics&rft.pages=822-823&rft.pub=Princeton+University+Press&rft.date=2008&rft_id=info%3Aoclcnum%2F682200048&rft.isbn=978-0-691-11880-2&rft.aulast=Daubin&rft.aufirst=Joseph+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKline1990" class="citation book cs1"><a href="/wiki/Morris_Kline" title="Morris Kline">Kline, Morris</a> (1990). <i>Mathematical thought from ancient to modern times</i>. Vol. 3. New York: Oxford University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-19-977048-9" title="Special:BookSources/978-0-19-977048-9"><bdi>978-0-19-977048-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/726764443">726764443</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+thought+from+ancient+to+modern+times&rft.place=New+York&rft.pub=Oxford+University+Press&rft.date=1990&rft_id=info%3Aoclcnum%2F726764443&rft.isbn=978-0-19-977048-9&rft.aulast=Kline&rft.aufirst=Morris&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFvon_Neumann1947" class="citation book cs1"><a href="/wiki/John_von_Neumann" title="John von Neumann">von Neumann, J.</a> (1947). "The Mathematician". In Heywood, R. B. (ed.). <i>The Works of the Mind</i>. University of Chicago Press. pp. 180–196.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Mathematician&rft.btitle=The+Works+of+the+Mind&rft.pages=180-196&rft.pub=University+of+Chicago+Press&rft.date=1947&rft.aulast=von+Neumann&rft.aufirst=J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span> Reprinted in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBródyVámos1995" class="citation book cs1">Bródy, F.; Vámos, T., eds. (1995). <i>The Neumann Compendium</i>. World Scientific Publishing Co. Pte. Ltd. pp. 618–626. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/981-02-2201-7" title="Special:BookSources/981-02-2201-7"><bdi>981-02-2201-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Neumann+Compendium&rft.pages=618-626&rft.pub=World+Scientific+Publishing+Co.+Pte.+Ltd.&rft.date=1995&rft.isbn=981-02-2201-7&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-:5-44"><span class="mw-cite-backlink">^ <a href="#cite_ref-:5_44-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:5_44-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:5_44-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:5_44-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:5_44-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:5_44-5"><sup><i><b>f</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHermanStrang2017" class="citation book cs1">Herman, Edwin; <a href="/wiki/Gilbert_Strang" title="Gilbert Strang">Strang, Gilbert</a>; et al. (2017). <a rel="nofollow" class="external text" href="https://openstax.org/details/books/calculus-volume-1"><i>Calculus</i></a>. Vol. 1. Houston, Texas: OpenStax. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-938168-02-4" title="Special:BookSources/978-1-938168-02-4"><bdi>978-1-938168-02-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1022848630">1022848630</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220923230919/https://openstax.org/details/books/calculus-volume-1">Archived</a> from the original on 23 September 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">26 July</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus&rft.place=Houston%2C+Texas&rft.pub=OpenStax&rft.date=2017&rft_id=info%3Aoclcnum%2F1022848630&rft.isbn=978-1-938168-02-4&rft.aulast=Herman&rft.aufirst=Edwin&rft.au=Strang%2C+Gilbert&rft_id=https%3A%2F%2Fopenstax.org%2Fdetails%2Fbooks%2Fcalculus-volume-1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCheng2017" class="citation book cs1"><a href="/wiki/Eugenia_Cheng" title="Eugenia Cheng">Cheng, Eugenia</a> (2017). <a href="/wiki/Beyond_Infinity_(mathematics_book)" title="Beyond Infinity (mathematics book)"><i>Beyond Infinity: An Expedition to the Outer Limits of Mathematics</i></a>. Basic Books. pp. 206–210. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-541-64413-7" title="Special:BookSources/978-1-541-64413-7"><bdi>978-1-541-64413-7</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1003309980">1003309980</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Beyond+Infinity%3A+An+Expedition+to+the+Outer+Limits+of+Mathematics&rft.pages=206-210&rft.pub=Basic+Books&rft.date=2017&rft_id=info%3Aoclcnum%2F1003309980&rft.isbn=978-1-541-64413-7&rft.aulast=Cheng&rft.aufirst=Eugenia&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-:4-46"><span class="mw-cite-backlink">^ <a href="#cite_ref-:4_46-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:4_46-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:4_46-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:4_46-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:4_46-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:4_46-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-:4_46-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSalasHille1971" class="citation book cs1">Salas, Saturnino L.; Hille, Einar (1971). <i>Calculus; one and several variables</i>. Waltham, MA: Xerox College Pub. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/135567">135567</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3B+one+and+several+variables&rft.place=Waltham%2C+MA&rft.pub=Xerox+College+Pub.&rft.date=1971&rft_id=info%3Aoclcnum%2F135567&rft.aulast=Salas&rft.aufirst=Saturnino+L.&rft.au=Hille%2C+Einar&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-:2-47"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_47-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_47-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:2_47-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHughes-HallettMcCallumGleasonConnally2013" class="citation book cs1"><a href="/wiki/Deborah_Hughes_Hallett" title="Deborah Hughes Hallett">Hughes-Hallett, Deborah</a>; <a href="/wiki/William_G._McCallum" title="William G. McCallum">McCallum, William G.</a>; <a href="/wiki/Andrew_M._Gleason" title="Andrew M. Gleason">Gleason, Andrew M.</a>; et al. (2013). <i>Calculus: Single and Multivariable</i> (6th ed.). Hoboken, NJ: Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-88861-2" title="Special:BookSources/978-0-470-88861-2"><bdi>978-0-470-88861-2</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/794034942">794034942</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+Single+and+Multivariable&rft.place=Hoboken%2C+NJ&rft.edition=6th&rft.pub=Wiley&rft.date=2013&rft_id=info%3Aoclcnum%2F794034942&rft.isbn=978-0-470-88861-2&rft.aulast=Hughes-Hallett&rft.aufirst=Deborah&rft.au=McCallum%2C+William+G.&rft.au=Gleason%2C+Andrew+M.&rft.au=Connally%2C+Eric&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMoebsLingSanny2022" class="citation book cs1">Moebs, William; Ling, Samuel J.; Sanny, Jeff; et al. (2022). <i>University Physics, Volume 1</i>. OpenStax. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-947172-20-3" title="Special:BookSources/978-1-947172-20-3"><bdi>978-1-947172-20-3</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/961352944">961352944</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=University+Physics%2C+Volume+1&rft.pub=OpenStax&rft.date=2022&rft_id=info%3Aoclcnum%2F961352944&rft.isbn=978-1-947172-20-3&rft.aulast=Moebs&rft.aufirst=William&rft.au=Ling%2C+Samuel+J.&rft.au=Sanny%2C+Jeff&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-49">^</a></b></span> <span class="reference-text">See, for example: <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMahoney1990" class="citation book cs1">Mahoney, Michael S. (1990). "Barrow's mathematics: Between ancients and moderns". In Feingold, M. (ed.). <i>Before Newton</i>. Cambridge University Press. pp. 179–249. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-06385-2" title="Special:BookSources/978-0-521-06385-2"><bdi>978-0-521-06385-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Barrow%27s+mathematics%3A+Between+ancients+and+moderns&rft.btitle=Before+Newton&rft.pages=179-249&rft.pub=Cambridge+University+Press&rft.date=1990&rft.isbn=978-0-521-06385-2&rft.aulast=Mahoney&rft.aufirst=Michael+S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFeingold1993" class="citation journal cs1">Feingold, M. (June 1993). "Newton, Leibniz, and Barrow Too: An Attempt at a Reinterpretation". <i><a href="/wiki/Isis_(journal)" title="Isis (journal)">Isis</a></i>. <b>84</b> (2): 310–338. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1993Isis...84..310F">1993Isis...84..310F</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F356464">10.1086/356464</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0021-1753">0021-1753</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:144019197">144019197</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Isis&rft.atitle=Newton%2C+Leibniz%2C+and+Barrow+Too%3A+An+Attempt+at+a+Reinterpretation&rft.volume=84&rft.issue=2&rft.pages=310-338&rft.date=1993-06&rft_id=info%3Adoi%2F10.1086%2F356464&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A144019197%23id-name%3DS2CID&rft.issn=0021-1753&rft_id=info%3Abibcode%2F1993Isis...84..310F&rft.aulast=Feingold&rft.aufirst=M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFProbst2015" class="citation book cs1">Probst, Siegmund (2015). "Leibniz as Reader and Second Inventor: The Cases of Barrow and Mengoli". In Goethe, Norma B.; Beeley, Philip; Rabouin, David (eds.). <i>G.W. Leibniz, Interrelations Between Mathematics and Philosophy</i>. Archimedes: New Studies in the History and Philosophy of Science and Technology. Vol. 41. Springer. pp. 111–134. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-9-401-79663-7" title="Special:BookSources/978-9-401-79663-7"><bdi>978-9-401-79663-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Leibniz+as+Reader+and+Second+Inventor%3A+The+Cases+of+Barrow+and+Mengoli&rft.btitle=G.W.+Leibniz%2C+Interrelations+Between+Mathematics+and+Philosophy&rft.series=Archimedes%3A+New+Studies+in+the+History+and+Philosophy+of+Science+and+Technology&rft.pages=111-134&rft.pub=Springer&rft.date=2015&rft.isbn=978-9-401-79663-7&rft.aulast=Probst&rft.aufirst=Siegmund&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li></ul> </span></li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHermanStrang2017" class="citation book cs1">Herman, Edwin; Strang, Gilbert; et al. (2017). <a rel="nofollow" class="external text" href="https://openstax.org/details/books/calculus-volume-2"><i>Calculus. Volume 2</i></a>. Houston: OpenStax. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-5066-9807-6" title="Special:BookSources/978-1-5066-9807-6"><bdi>978-1-5066-9807-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1127050110">1127050110</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220726140351/https://openstax.org/details/books/calculus-volume-2">Archived</a> from the original on 26 July 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">26 July</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus.+Volume+2&rft.place=Houston&rft.pub=OpenStax&rft.date=2017&rft_id=info%3Aoclcnum%2F1127050110&rft.isbn=978-1-5066-9807-6&rft.aulast=Herman&rft.aufirst=Edwin&rft.au=Strang%2C+Gilbert&rft_id=https%3A%2F%2Fopenstax.org%2Fdetails%2Fbooks%2Fcalculus-volume-2&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-51"><span class="mw-cite-backlink"><b><a href="#cite_ref-51">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBaron1969" class="citation book cs1"><a href="/wiki/Margaret_Baron" title="Margaret Baron">Baron, Margaret E.</a> (1969). <i>The origins of the infinitesimal calculus</i>. Oxford: Pergamon Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-483-28092-9" title="Special:BookSources/978-1-483-28092-9"><bdi>978-1-483-28092-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/892067655">892067655</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+origins+of+the+infinitesimal+calculus&rft.place=Oxford&rft.pub=Pergamon+Press&rft.date=1969&rft_id=info%3Aoclcnum%2F892067655&rft.isbn=978-1-483-28092-9&rft.aulast=Baron&rft.aufirst=Margaret+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-52"><span class="mw-cite-backlink"><b><a href="#cite_ref-52">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKayaspor2022" class="citation news cs1">Kayaspor, Ali (28 August 2022). <a rel="nofollow" class="external text" href="https://ali.medium.com/the-beautiful-applications-of-calculus-in-real-life-81331dc1bc5a">"The Beautiful Applications of Calculus in Real Life"</a>. <i>Medium</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220926011601/https://ali.medium.com/the-beautiful-applications-of-calculus-in-real-life-81331dc1bc5a">Archived</a> from the original on 26 September 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">26 September</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Medium&rft.atitle=The+Beautiful+Applications+of+Calculus+in+Real+Life&rft.date=2022-08-28&rft.aulast=Kayaspor&rft.aufirst=Ali&rft_id=https%3A%2F%2Fali.medium.com%2Fthe-beautiful-applications-of-calculus-in-real-life-81331dc1bc5a&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHu2021" class="citation book cs1">Hu, Zhiying (14 April 2021). "The Application and Value of Calculus in Daily Life". <i>2021 2nd Asia-Pacific Conference on Image Processing, Electronics, and Computers</i>. Ipec2021. Dalian China: ACM. pp. 562–564. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1145%2F3452446.3452583">10.1145/3452446.3452583</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4503-8981-5" title="Special:BookSources/978-1-4503-8981-5"><bdi>978-1-4503-8981-5</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:233384462">233384462</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Application+and+Value+of+Calculus+in+Daily+Life&rft.btitle=2021+2nd+Asia-Pacific+Conference+on+Image+Processing%2C+Electronics%2C+and+Computers&rft.place=Dalian+China&rft.series=Ipec2021&rft.pages=562-564&rft.pub=ACM&rft.date=2021-04-14&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A233384462%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1145%2F3452446.3452583&rft.isbn=978-1-4503-8981-5&rft.aulast=Hu&rft.aufirst=Zhiying&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKardar2007" class="citation book cs1"><a href="/wiki/Mehran_Kardar" title="Mehran Kardar">Kardar, Mehran</a> (2007). <a href="/wiki/Statistical_Physics_of_Particles" title="Statistical Physics of Particles"><i>Statistical Physics of Particles</i></a>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-87342-0" title="Special:BookSources/978-0-521-87342-0"><bdi>978-0-521-87342-0</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/860391091">860391091</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+Physics+of+Particles&rft.pub=Cambridge+University+Press&rft.date=2007&rft_id=info%3Aoclcnum%2F860391091&rft.isbn=978-0-521-87342-0&rft.aulast=Kardar&rft.aufirst=Mehran&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGarber2001" class="citation book cs1">Garber, Elizabeth (2001). <i>The language of physics: the calculus and the development of theoretical physics in Europe, 1750–1914</i>. Springer Science+Business Media. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4612-7272-4" title="Special:BookSources/978-1-4612-7272-4"><bdi>978-1-4612-7272-4</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/921230825">921230825</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+language+of+physics%3A+the+calculus+and+the+development+of+theoretical+physics+in+Europe%2C+1750%E2%80%931914&rft.pub=Springer+Science%2BBusiness+Media&rft.date=2001&rft_id=info%3Aoclcnum%2F921230825&rft.isbn=978-1-4612-7272-4&rft.aulast=Garber&rft.aufirst=Elizabeth&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-56"><span class="mw-cite-backlink"><b><a href="#cite_ref-56">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHall2008" class="citation journal cs1">Hall, Graham (2008). "Maxwell's Electromagnetic Theory and Special Relativity". <i>Philosophical Transactions: Mathematical, Physical and Engineering Sciences</i>. <b>366</b> (1871): 1849–1860. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008RSPTA.366.1849H">2008RSPTA.366.1849H</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.2007.2192">10.1098/rsta.2007.2192</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1364-503X">1364-503X</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/25190792">25190792</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18218598">18218598</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:502776">502776</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions%3A+Mathematical%2C+Physical+and+Engineering+Sciences&rft.atitle=Maxwell%27s+Electromagnetic+Theory+and+Special+Relativity&rft.volume=366&rft.issue=1871&rft.pages=1849-1860&rft.date=2008&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A502776%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2008RSPTA.366.1849H&rft_id=info%3Adoi%2F10.1098%2Frsta.2007.2192&rft.issn=1364-503X&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F25190792%23id-name%3DJSTOR&rft_id=info%3Apmid%2F18218598&rft.aulast=Hall&rft.aufirst=Graham&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGbur2011" class="citation book cs1"><a href="/wiki/Greg_Gbur" title="Greg Gbur">Gbur, Greg</a> (2011). <i>Mathematical Methods for Optical Physics and Engineering</i>. Cambridge: Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-511-91510-9" title="Special:BookSources/978-0-511-91510-9"><bdi>978-0-511-91510-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/704518582">704518582</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Methods+for+Optical+Physics+and+Engineering&rft.place=Cambridge&rft.pub=Cambridge+University+Press&rft.date=2011&rft_id=info%3Aoclcnum%2F704518582&rft.isbn=978-0-511-91510-9&rft.aulast=Gbur&rft.aufirst=Greg&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-:3-58"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_58-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_58-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAtkinsJones2010" class="citation book cs1">Atkins, Peter W.; Jones, Loretta (2010). <i>Chemical principles: the quest for insight</i> (5th ed.). New York: W.H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4292-1955-6" title="Special:BookSources/978-1-4292-1955-6"><bdi>978-1-4292-1955-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/501943698">501943698</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Chemical+principles%3A+the+quest+for+insight&rft.place=New+York&rft.edition=5th&rft.pub=W.H.+Freeman&rft.date=2010&rft_id=info%3Aoclcnum%2F501943698&rft.isbn=978-1-4292-1955-6&rft.aulast=Atkins&rft.aufirst=Peter+W.&rft.au=Jones%2C+Loretta&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMurray2002" class="citation book cs1">Murray, J. D. (2002). <i>Mathematical biology. I, Introduction</i> (3rd ed.). New York: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-22437-8" title="Special:BookSources/0-387-22437-8"><bdi>0-387-22437-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/53165394">53165394</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+biology.+I%2C+Introduction&rft.place=New+York&rft.edition=3rd&rft.pub=Springer&rft.date=2002&rft_id=info%3Aoclcnum%2F53165394&rft.isbn=0-387-22437-8&rft.aulast=Murray&rft.aufirst=J.+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNeuhauser2011" class="citation book cs1"><a href="/wiki/Claudia_Neuhauser" title="Claudia Neuhauser">Neuhauser, Claudia</a> (2011). <i>Calculus for biology and medicine</i> (3rd ed.). Boston: Prentice Hall. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-321-64468-8" title="Special:BookSources/978-0-321-64468-8"><bdi>978-0-321-64468-8</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/426065941">426065941</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus+for+biology+and+medicine&rft.place=Boston&rft.edition=3rd&rft.pub=Prentice+Hall&rft.date=2011&rft_id=info%3Aoclcnum%2F426065941&rft.isbn=978-0-321-64468-8&rft.aulast=Neuhauser&rft.aufirst=Claudia&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGatterdam1981" class="citation journal cs1">Gatterdam, R. W. (1981). "The planimeter as an example of Green's theorem". <i><a href="/wiki/The_American_Mathematical_Monthly" title="The American Mathematical Monthly">The American Mathematical Monthly</a></i>. <b>88</b> (9): 701–704. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2320679">10.2307/2320679</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2320679">2320679</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+American+Mathematical+Monthly&rft.atitle=The+planimeter+as+an+example+of+Green%27s+theorem&rft.volume=88&rft.issue=9&rft.pages=701-704&rft.date=1981&rft_id=info%3Adoi%2F10.2307%2F2320679&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2320679%23id-name%3DJSTOR&rft.aulast=Gatterdam&rft.aufirst=R.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdam2011" class="citation journal cs1">Adam, John A. (June 2011). "Blood Vessel Branching: Beyond the Standard Calculus Problem". <i><a href="/wiki/Mathematics_Magazine" title="Mathematics Magazine">Mathematics Magazine</a></i>. <b>84</b> (3): 196–207. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4169%2Fmath.mag.84.3.196">10.4169/math.mag.84.3.196</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0025-570X">0025-570X</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:8259705">8259705</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematics+Magazine&rft.atitle=Blood+Vessel+Branching%3A+Beyond+the+Standard+Calculus+Problem&rft.volume=84&rft.issue=3&rft.pages=196-207&rft.date=2011-06&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A8259705%23id-name%3DS2CID&rft.issn=0025-570X&rft_id=info%3Adoi%2F10.4169%2Fmath.mag.84.3.196&rft.aulast=Adam&rft.aufirst=John+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-63"><span class="mw-cite-backlink"><b><a href="#cite_ref-63">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMackenzie2004" class="citation journal cs1">Mackenzie, Dana (2004). <a rel="nofollow" class="external text" href="https://archive.siam.org/pdf/news/203.pdf">"Mathematical Modeling and Cancer"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/SIAM_News" class="mw-redirect" title="SIAM News">SIAM News</a></i>. <b>37</b> (1). <a rel="nofollow" class="external text" href="https://ghostarchive.org/archive/20221009/https://archive.siam.org/pdf/news/203.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 9 October 2022.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+News&rft.atitle=Mathematical+Modeling+and+Cancer&rft.volume=37&rft.issue=1&rft.date=2004&rft.aulast=Mackenzie&rft.aufirst=Dana&rft_id=https%3A%2F%2Farchive.siam.org%2Fpdf%2Fnews%2F203.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> <li id="cite_note-64"><span class="mw-cite-backlink"><b><a href="#cite_ref-64">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPerloff2018" class="citation book cs1">Perloff, Jeffrey M. (2018). <i>Microeconomics: Theory and Applications with Calculus</i> (4th global ed.). Harlow: Pearson. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-292-15446-6" title="Special:BookSources/978-1-292-15446-6"><bdi>978-1-292-15446-6</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/1064041906">1064041906</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Microeconomics%3A+Theory+and+Applications+with+Calculus&rft.place=Harlow&rft.edition=4th+global&rft.pub=Pearson&rft.date=2018&rft_id=info%3Aoclcnum%2F1064041906&rft.isbn=978-1-292-15446-6&rft.aulast=Perloff&rft.aufirst=Jeffrey+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin refbegin-columns references-column-width" style="column-width: 30em"> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdams1999" class="citation book cs1">Adams, Robert A. (1999). <i>Calculus: A complete course</i>. Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-39607-2" title="Special:BookSources/978-0-201-39607-2"><bdi>978-0-201-39607-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+A+complete+course&rft.pub=Addison-Wesley&rft.date=1999&rft.isbn=978-0-201-39607-2&rft.aulast=Adams&rft.aufirst=Robert+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAlbersAndersonLoftsgaarden1986" class="citation book cs1">Albers, Donald J.; Anderson, Richard D.; Loftsgaarden, Don O., eds. (1986). <i>Undergraduate Programs in the Mathematics and Computer Sciences: The 1985–1986 Survey</i>. Mathematical Association of America.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Undergraduate+Programs+in+the+Mathematics+and+Computer+Sciences%3A+The+1985%E2%80%931986+Survey&rft.pub=Mathematical+Association+of+America&rft.date=1986&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAntonBivensDavis2002" class="citation book cs1">Anton, Howard; Bivens, Irl; Davis, Stephen (2002). <i>Calculus</i>. John Wiley and Sons Pte. Ltd. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-81-265-1259-1" title="Special:BookSources/978-81-265-1259-1"><bdi>978-81-265-1259-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus&rft.pub=John+Wiley+and+Sons+Pte.+Ltd.&rft.date=2002&rft.isbn=978-81-265-1259-1&rft.aulast=Anton&rft.aufirst=Howard&rft.au=Bivens%2C+Irl&rft.au=Davis%2C+Stephen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFApostol1967" class="citation book cs1"><a href="/wiki/Tom_M._Apostol" title="Tom M. Apostol">Apostol, Tom M.</a> (1967). <i>Calculus, Volume 1, One-Variable Calculus with an Introduction to Linear Algebra</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-00005-1" title="Special:BookSources/978-0-471-00005-1"><bdi>978-0-471-00005-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%2C+Volume+1%2C+One-Variable+Calculus+with+an+Introduction+to+Linear+Algebra&rft.pub=Wiley&rft.date=1967&rft.isbn=978-0-471-00005-1&rft.aulast=Apostol&rft.aufirst=Tom+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFApostol1969" class="citation book cs1"><a href="/wiki/Tom_M._Apostol" title="Tom M. Apostol">Apostol, Tom M.</a> (1969). <i>Calculus, Volume 2, Multi-Variable Calculus and Linear Algebra with Applications</i>. Wiley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-00007-5" title="Special:BookSources/978-0-471-00007-5"><bdi>978-0-471-00007-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%2C+Volume+2%2C+Multi-Variable+Calculus+and+Linear+Algebra+with+Applications&rft.pub=Wiley&rft.date=1969&rft.isbn=978-0-471-00007-5&rft.aulast=Apostol&rft.aufirst=Tom+M.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBell1998" class="citation book cs1"><a href="/wiki/John_Lane_Bell" title="John Lane Bell">Bell, John Lane</a> (1998). <i>A Primer of Infinitesimal Analysis</i>. Cambridge University Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-62401-5" title="Special:BookSources/978-0-521-62401-5"><bdi>978-0-521-62401-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Primer+of+Infinitesimal+Analysis&rft.pub=Cambridge+University+Press&rft.date=1998&rft.isbn=978-0-521-62401-5&rft.aulast=Bell&rft.aufirst=John+Lane&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span> Uses <a href="/wiki/Synthetic_differential_geometry" title="Synthetic differential geometry">synthetic differential geometry</a> and nilpotent infinitesimals.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoelkins,_M.2012" class="citation book cs1">Boelkins, M. (2012). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130530024317/http://faculty.gvsu.edu/boelkinm/Home/Download_files/Active%20Calculus%20ch1-8%20%28v.1.1%20W13%29.pdf"><i>Active Calculus: a free, open text</i></a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://gvsu.edu/s/km">the original</a> on 30 May 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">1 February</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Active+Calculus%3A+a+free%2C+open+text&rft.date=2012&rft.au=Boelkins%2C+M.&rft_id=http%3A%2F%2Fgvsu.edu%2Fs%2Fkm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBoyer1959" class="citation book cs1"><a href="/wiki/Carl_Benjamin_Boyer" title="Carl Benjamin Boyer">Boyer, Carl Benjamin</a> (1959) [1949]. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=KLQSHUW8FnUC"><i>The History of the Calculus and its Conceptual Development</i></a> (Dover ed.). Hafner. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-60509-4" title="Special:BookSources/0-486-60509-4"><bdi>0-486-60509-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+History+of+the+Calculus+and+its+Conceptual+Development&rft.edition=Dover&rft.pub=Hafner&rft.date=1959&rft.isbn=0-486-60509-4&rft.aulast=Boyer&rft.aufirst=Carl+Benjamin&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DKLQSHUW8FnUC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCajori1923" class="citation journal cs1"><a href="/wiki/Florian_Cajori" title="Florian Cajori">Cajori, Florian</a> (September 1923). "The History of Notations of the Calculus". <i>Annals of Mathematics</i>. 2nd Series. <b>25</b> (1): 1–46. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F1967725">10.2307/1967725</a>. <a href="/wiki/Hdl_(identifier)" class="mw-redirect" title="Hdl (identifier)">hdl</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://hdl.handle.net/2027%2Fmdp.39015017345896">2027/mdp.39015017345896</a></span>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/1967725">1967725</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+Mathematics&rft.atitle=The+History+of+Notations+of+the+Calculus&rft.volume=25&rft.issue=1&rft.pages=1-46&rft.date=1923-09&rft_id=info%3Ahdl%2F2027%2Fmdp.39015017345896&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F1967725%23id-name%3DJSTOR&rft_id=info%3Adoi%2F10.2307%2F1967725&rft.aulast=Cajori&rft.aufirst=Florian&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCourant1998" class="citation book cs1"><a href="/wiki/Richard_Courant" title="Richard Courant">Courant, Richard</a> (3 December 1998). <i>Introduction to calculus and analysis 1</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-65058-4" title="Special:BookSources/978-3-540-65058-4"><bdi>978-3-540-65058-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+calculus+and+analysis+1.&rft.date=1998-12-03&rft.isbn=978-3-540-65058-4&rft.aulast=Courant&rft.aufirst=Richard&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGonick2012" class="citation book cs1"><a href="/wiki/Larry_Gonick" title="Larry Gonick">Gonick, Larry</a> (2012). <i>The Cartoon Guide to Calculus</i>. William Morrow. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-061-68909-3" title="Special:BookSources/978-0-061-68909-3"><bdi>978-0-061-68909-3</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/932781617">932781617</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Cartoon+Guide+to+Calculus&rft.pub=William+Morrow&rft.date=2012&rft_id=info%3Aoclcnum%2F932781617&rft.isbn=978-0-061-68909-3&rft.aulast=Gonick&rft.aufirst=Larry&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li>Keisler, H.J. (2000). <i>Elementary Calculus: An Approach Using Infinitesimals</i>. Retrieved 29 August 2010 from <a rel="nofollow" class="external text" href="http://www.math.wisc.edu/~keisler/calc.html">http://www.math.wisc.edu/~keisler/calc.html</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110501113944/http://www.math.wisc.edu/~keisler/calc.html">Archived</a> 1 May 2011 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLandau2001" class="citation book cs1"><a href="/wiki/Edmund_Landau" title="Edmund Landau">Landau, Edmund</a> (2001). <i>Differential and Integral Calculus</i>. <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-8218-2830-4" title="Special:BookSources/0-8218-2830-4"><bdi>0-8218-2830-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Differential+and+Integral+Calculus&rft.pub=American+Mathematical+Society&rft.date=2001&rft.isbn=0-8218-2830-4&rft.aulast=Landau&rft.aufirst=Edmund&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLebedevCloud2004" class="citation book cs1">Lebedev, Leonid P.; Cloud, Michael J. (2004). "The Tools of Calculus". <i>Approximating Perfection: a Mathematician's Journey into the World of Mechanics</i>. Princeton University Press. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2004apmj.book.....L">2004apmj.book.....L</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=The+Tools+of+Calculus&rft.btitle=Approximating+Perfection%3A+a+Mathematician%27s+Journey+into+the+World+of+Mechanics&rft.pub=Princeton+University+Press&rft.date=2004&rft_id=info%3Abibcode%2F2004apmj.book.....L&rft.aulast=Lebedev&rft.aufirst=Leonid+P.&rft.au=Cloud%2C+Michael+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLarsonEdwards2010" class="citation book cs1"><a href="/wiki/Ron_Larson_(mathematician)" class="mw-redirect" title="Ron Larson (mathematician)">Larson, Ron</a>; Edwards, Bruce H. (2010). <i>Calculus</i> (9th ed.). Brooks Cole Cengage Learning. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-547-16702-2" title="Special:BookSources/978-0-547-16702-2"><bdi>978-0-547-16702-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus&rft.edition=9th&rft.pub=Brooks+Cole+Cengage+Learning&rft.date=2010&rft.isbn=978-0-547-16702-2&rft.aulast=Larson&rft.aufirst=Ron&rft.au=Edwards%2C+Bruce+H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcQuarrie2003" class="citation book cs1">McQuarrie, Donald A. (2003). <i>Mathematical Methods for Scientists and Engineers</i>. University Science Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-891389-24-5" title="Special:BookSources/978-1-891389-24-5"><bdi>978-1-891389-24-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Methods+for+Scientists+and+Engineers&rft.pub=University+Science+Books&rft.date=2003&rft.isbn=978-1-891389-24-5&rft.aulast=McQuarrie&rft.aufirst=Donald+A.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPickover2003" class="citation book cs1"><a href="/wiki/Cliff_Pickover" class="mw-redirect" title="Cliff Pickover">Pickover, Cliff</a> (2003). <i>Calculus and Pizza: A Math Cookbook for the Hungry Mind</i>. John Wiley & Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-26987-8" title="Special:BookSources/978-0-471-26987-8"><bdi>978-0-471-26987-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus+and+Pizza%3A+A+Math+Cookbook+for+the+Hungry+Mind&rft.pub=John+Wiley+%26+Sons&rft.date=2003&rft.isbn=978-0-471-26987-8&rft.aulast=Pickover&rft.aufirst=Cliff&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSalasHilleEtgen2007" class="citation book cs1">Salas, Saturnino L.; <a href="/wiki/Einar_Hille" title="Einar Hille">Hille, Einar</a>; Etgen, Garret J. (2007). <i>Calculus: One and Several Variables</i> (10th ed.). <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">Wiley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-69804-3" title="Special:BookSources/978-0-471-69804-3"><bdi>978-0-471-69804-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+One+and+Several+Variables&rft.edition=10th&rft.pub=Wiley&rft.date=2007&rft.isbn=978-0-471-69804-3&rft.aulast=Salas&rft.aufirst=Saturnino+L.&rft.au=Hille%2C+Einar&rft.au=Etgen%2C+Garret+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSpivak1994" class="citation book cs1"><a href="/wiki/Michael_Spivak" title="Michael Spivak">Spivak, Michael</a> (September 1994). <i>Calculus</i>. Publish or Perish publishing. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-914098-89-8" title="Special:BookSources/978-0-914098-89-8"><bdi>978-0-914098-89-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus&rft.pub=Publish+or+Perish+publishing&rft.date=1994-09&rft.isbn=978-0-914098-89-8&rft.aulast=Spivak&rft.aufirst=Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSteen1988" class="citation book cs1"><a href="/wiki/Lynn_Steen" title="Lynn Steen">Steen, Lynn Arthur</a>, ed. (1988). <i>Calculus for a New Century; A Pump, Not a Filter</i>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-88385-058-3" title="Special:BookSources/0-88385-058-3"><bdi>0-88385-058-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus+for+a+New+Century%3B+A+Pump%2C+Not+a+Filter&rft.pub=Mathematical+Association+of+America&rft.date=1988&rft.isbn=0-88385-058-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFStewart2012" class="citation book cs1"><a href="/wiki/James_Stewart_(mathematician)" title="James Stewart (mathematician)">Stewart, James</a> (2012). <i>Calculus: Early Transcendentals</i> (7th ed.). Brooks Cole Cengage Learning. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-538-49790-9" title="Special:BookSources/978-0-538-49790-9"><bdi>978-0-538-49790-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus%3A+Early+Transcendentals&rft.edition=7th&rft.pub=Brooks+Cole+Cengage+Learning&rft.date=2012&rft.isbn=978-0-538-49790-9&rft.aulast=Stewart&rft.aufirst=James&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThomasFinneyWeir1996" class="citation book cs1"><a href="/wiki/George_B._Thomas" title="George B. Thomas">Thomas, George Brinton</a>; Finney, Ross L.; Weir, Maurice D. (1996). <i>Calculus and Analytic Geometry, Part 1</i>. Addison Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-201-53174-9" title="Special:BookSources/978-0-201-53174-9"><bdi>978-0-201-53174-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus+and+Analytic+Geometry%2C+Part+1&rft.pub=Addison+Wesley&rft.date=1996&rft.isbn=978-0-201-53174-9&rft.aulast=Thomas&rft.aufirst=George+Brinton&rft.au=Finney%2C+Ross+L.&rft.au=Weir%2C+Maurice+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThomasWeirHassGiordano2008" class="citation book cs1"><a href="/wiki/George_B._Thomas" title="George B. Thomas">Thomas, George B.</a>; Weir, Maurice D.; <a href="/wiki/Joel_Hass" title="Joel Hass">Hass, Joel</a>; Giordano, Frank R. (2008). <i>Calculus</i> (11th ed.). Addison-Wesley. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-321-48987-6" title="Special:BookSources/978-0-321-48987-6"><bdi>978-0-321-48987-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus&rft.edition=11th&rft.pub=Addison-Wesley&rft.date=2008&rft.isbn=978-0-321-48987-6&rft.aulast=Thomas&rft.aufirst=George+B.&rft.au=Weir%2C+Maurice+D.&rft.au=Hass%2C+Joel&rft.au=Giordano%2C+Frank+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFThompsonGardner1998" class="citation book cs1"><a href="/wiki/Silvanus_P._Thompson" title="Silvanus P. Thompson">Thompson, Silvanus P.</a>; <a href="/wiki/Martin_Gardner" title="Martin Gardner">Gardner, Martin</a> (1998). <a href="/wiki/Calculus_Made_Easy" title="Calculus Made Easy"><i>Calculus Made Easy</i></a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-312-18548-0" title="Special:BookSources/978-0-312-18548-0"><bdi>978-0-312-18548-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Calculus+Made+Easy&rft.date=1998&rft.isbn=978-0-312-18548-0&rft.aulast=Thompson&rft.aufirst=Silvanus+P.&rft.au=Gardner%2C+Martin&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><style 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typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/27px-Wikiversity_logo_2017.svg.png" decoding="async" width="27" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/41px-Wikiversity_logo_2017.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0b/Wikiversity_logo_2017.svg/54px-Wikiversity_logo_2017.svg.png 2x" data-file-width="626" data-file-height="512" /></span></span></span><span class="sister-link"><a href="https://en.wikiversity.org/wiki/Calculus" class="extiw" title="v:Calculus">Resources</a> from Wikiversity</span></li></ul></div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://www.encyclopediaofmath.org/index.php?title=Calculus">"Calculus"</a>, <i><a href="/wiki/Encyclopedia_of_Mathematics" title="Encyclopedia of Mathematics">Encyclopedia of Mathematics</a></i>, <a href="/wiki/European_Mathematical_Society" title="European Mathematical Society">EMS Press</a>, 2001 [1994]</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Calculus&rft.btitle=Encyclopedia+of+Mathematics&rft.pub=EMS+Press&rft.date=2001&rft_id=https%3A%2F%2Fwww.encyclopediaofmath.org%2Findex.php%3Ftitle%3DCalculus&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><span class="citation mathworld" id="Reference-Mathworld-Calculus"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeisstein" class="citation web cs1"><a href="/wiki/Eric_W._Weisstein" title="Eric W. Weisstein">Weisstein, Eric W.</a> <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Calculus.html">"Calculus"</a>. <i><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MathWorld&rft.atitle=Calculus&rft.au=Weisstein%2C+Eric+W.&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FCalculus.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></span></li> <li><a rel="nofollow" class="external text" href="https://planetmath.org/TopicsOnCalculus">Topics on Calculus</a> at <a href="/wiki/PlanetMath" title="PlanetMath">PlanetMath</a>.</li> <li><a rel="nofollow" class="external text" href="http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf">Calculus Made Easy (1914) by Silvanus P. Thompson</a> Full text in PDF</li> <li><a rel="nofollow" class="external text" href="https://www.bbc.co.uk/programmes/b00mrfwq">Calculus</a> on <a href="/wiki/In_Our_Time_(radio_series)" title="In Our Time (radio series)"><i>In Our Time</i></a> at the <a href="/wiki/BBC" title="BBC">BBC</a></li> <li><a rel="nofollow" class="external text" href="http://www.calculus.org">Calculus.org: The Calculus page</a> at University of California, Davis – contains resources and links to other sites</li> <li><a rel="nofollow" class="external text" href="http://www.economics.soton.ac.uk/staff/aldrich/Calculus%20and%20Analysis%20Earliest%20Uses.htm">Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis</a></li> <li><a rel="nofollow" class="external text" href="http://www.ericdigests.org/pre-9217/calculus.htm">The Role of Calculus in College Mathematics</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210726234750/http://www.ericdigests.org/pre-9217/calculus.htm">Archived</a> 26 July 2021 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> from ERICDigests.org</li> <li><a rel="nofollow" class="external text" href="https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/">OpenCourseWare Calculus</a> from the <a href="/wiki/Massachusetts_Institute_of_Technology" title="Massachusetts Institute of Technology">Massachusetts Institute of Technology</a></li> <li><a rel="nofollow" class="external text" href="http://www.encyclopediaofmath.org/index.php?title=Infinitesimal_calculus&oldid=18648">Infinitesimal Calculus</a> – an article on its historical development, in <i>Encyclopedia of Mathematics</i>, ed. <a href="/wiki/Michiel_Hazewinkel" title="Michiel Hazewinkel">Michiel Hazewinkel</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaniel_Kleitman,_MIT" class="citation web cs1">Daniel Kleitman, MIT. <a rel="nofollow" class="external text" href="http://math.mit.edu/~djk/calculus_beginners/">"Calculus for Beginners and Artists"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Calculus+for+Beginners+and+Artists&rft.au=Daniel+Kleitman%2C+MIT&rft_id=http%3A%2F%2Fmath.mit.edu%2F~djk%2Fcalculus_beginners%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ACalculus" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.imomath.com/index.php?options=277">Calculus training materials at imomath.com</a></li> <li><span class="languageicon">(in English and Arabic)</span> <a rel="nofollow" class="external text" href="http://www.wdl.org/en/item/4327/">The Excursion of Calculus</a>, 1772</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style 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.navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Integrals" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Integrals" title="Template:Integrals"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Integrals" title="Template talk:Integrals"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Integrals" title="Special:EditPage/Template:Integrals"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Integrals" style="font-size:114%;margin:0 4em"><a href="/wiki/Integral" title="Integral">Integrals</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of <br /> integrals</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Riemann_integral" title="Riemann integral">Riemann integral</a></li> <li><a href="/wiki/Lebesgue_integration" class="mw-redirect" title="Lebesgue integration">Lebesgue integral</a></li> <li><a href="/wiki/Burkill_integral" title="Burkill integral">Burkill integral</a></li> <li><a href="/wiki/Bochner_integral" title="Bochner integral">Bochner integral</a></li> <li><a href="/wiki/Daniell_integral" title="Daniell integral">Daniell integral</a></li> <li><a href="/wiki/Darboux_integral" title="Darboux integral">Darboux integral</a></li> <li><a href="/wiki/Henstock%E2%80%93Kurzweil_integral" title="Henstock–Kurzweil integral">Henstock–Kurzweil integral</a></li> <li><a href="/wiki/Haar_measure" title="Haar measure">Haar integral</a></li> <li><a href="/wiki/Hellinger_integral" title="Hellinger integral">Hellinger integral</a></li> <li><a href="/wiki/Khinchin_integral" title="Khinchin integral">Khinchin integral</a></li> <li><a href="/wiki/Kolmogorov_integral" title="Kolmogorov integral">Kolmogorov integral</a></li> <li><a href="/wiki/Lebesgue%E2%80%93Stieltjes_integration" title="Lebesgue–Stieltjes integration">Lebesgue–Stieltjes integral</a></li> <li><a href="/wiki/Pettis_integral" title="Pettis integral">Pettis integral</a></li> <li><a href="/wiki/Pfeffer_integral" title="Pfeffer integral">Pfeffer integral</a></li> <li><a href="/wiki/Riemann%E2%80%93Stieltjes_integral" title="Riemann–Stieltjes integral">Riemann–Stieltjes integral</a></li> <li><a href="/wiki/Regulated_integral" title="Regulated integral">Regulated integral</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Integration <br /> techniques</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Integration_by_substitution" title="Integration by substitution">Substitution</a> <ul><li><a href="/wiki/Trigonometric_substitution" title="Trigonometric substitution">Trigonometric</a></li> <li><a href="/wiki/Euler_substitution" title="Euler substitution">Euler</a></li> <li><a href="/wiki/Weierstrass_substitution" class="mw-redirect" title="Weierstrass substitution">Weierstrass</a></li></ul></li> <li><a href="/wiki/Integration_by_parts" title="Integration by parts">By parts</a></li> <li><a href="/wiki/Integration_by_partial_fractions" class="mw-redirect" title="Integration by partial fractions">Partial fractions</a></li> <li><a href="/wiki/Integration_using_Euler%27s_formula" title="Integration using Euler's formula">Euler's formula</a></li> <li><a href="/wiki/Integral_of_inverse_functions" title="Integral of inverse functions">Inverse functions</a></li> <li><a href="/wiki/Order_of_integration_(calculus)" title="Order of integration (calculus)">Changing order</a></li> <li><a href="/wiki/Integration_by_reduction_formulae" title="Integration by reduction formulae">Reduction formulas</a></li> <li><a href="/wiki/Integration_using_parametric_derivatives" title="Integration using parametric derivatives">Parametric derivatives</a></li> <li><a href="/wiki/Leibniz_integral_rule#Evaluating_definite_integrals" title="Leibniz integral rule">Differentiation under the integral sign</a></li> <li><a href="/wiki/Laplace_transform#Evaluating_improper_integrals" title="Laplace transform">Laplace transform</a></li> <li><a href="/wiki/Contour_integration" title="Contour integration">Contour integration</a></li> <li><a href="/wiki/Laplace%27s_method" title="Laplace's method">Laplace's method</a></li> <li><a href="/wiki/Numerical_integration" title="Numerical integration">Numerical integration</a> <ul><li><a href="/wiki/Simpson%27s_rule" title="Simpson's rule">Simpson's rule</a></li> <li><a href="/wiki/Trapezoidal_rule" title="Trapezoidal rule">Trapezoidal rule</a></li></ul></li> <li><a href="/wiki/Risch_algorithm" title="Risch algorithm">Risch algorithm</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Improper_integral" title="Improper integral">Improper integrals</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gaussian_integral" title="Gaussian integral">Gaussian integral</a></li> <li><a href="/wiki/Dirichlet_integral" title="Dirichlet integral">Dirichlet integral</a></li> <li>Fermi–Dirac integral <ul><li><a href="/wiki/Complete_Fermi%E2%80%93Dirac_integral" title="Complete Fermi–Dirac integral">complete</a></li> <li><a href="/wiki/Incomplete_Fermi%E2%80%93Dirac_integral" title="Incomplete Fermi–Dirac integral">incomplete</a></li></ul></li> <li><a href="/wiki/Bose%E2%80%93Einstein_integral" class="mw-redirect" title="Bose–Einstein integral">Bose–Einstein integral</a></li> <li><a href="/wiki/Frullani_integral" title="Frullani integral">Frullani integral</a></li> <li><a href="/wiki/Common_integrals_in_quantum_field_theory" title="Common integrals in quantum field theory">Common integrals in quantum field theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Stochastic_integral" class="mw-redirect" title="Stochastic integral">Stochastic integrals</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/It%C3%B4_calculus" title="Itô calculus">Itô integral</a></li> <li><a href="/wiki/Russo%E2%80%93Vallois_integral" title="Russo–Vallois integral">Russo–Vallois integral</a></li> <li><a href="/wiki/Stratonovich_integral" title="Stratonovich integral">Stratonovich integral</a></li> <li><a href="/wiki/Skorokhod_integral" title="Skorokhod integral">Skorokhod integral</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Basel_problem" title="Basel problem">Basel problem</a></li> <li><a href="/wiki/Euler%E2%80%93Maclaurin_formula" title="Euler–Maclaurin formula">Euler–Maclaurin formula</a></li> <li><a href="/wiki/Gabriel%27s_horn" title="Gabriel's horn">Gabriel's horn</a></li> <li><a href="/wiki/Integration_Bee" title="Integration Bee">Integration Bee</a></li> <li><a href="/wiki/Proof_that_22/7_exceeds_%CF%80" title="Proof that 22/7 exceeds π">Proof that 22/7 exceeds π</a></li> <li>Volumes <ul><li><a href="/wiki/Disc_integration" title="Disc integration">Washers</a></li> <li><a href="/wiki/Shell_integration" title="Shell integration">Shells</a></li></ul></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Infinitesimals" style="padding:3px"><table class="nowraplinks mw-collapsible expanded navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Infinitesimals" title="Template:Infinitesimals"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Infinitesimals" title="Template talk:Infinitesimals"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Infinitesimals" title="Special:EditPage/Template:Infinitesimals"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Infinitesimals" style="font-size:114%;margin:0 4em"><a href="/wiki/Infinitesimal" title="Infinitesimal">Infinitesimals</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">History</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adequality" title="Adequality">Adequality</a></li> <li><a href="/wiki/Leibniz%27s_notation" title="Leibniz's notation">Leibniz's notation</a></li> <li><a href="/wiki/Integral_symbol" title="Integral symbol">Integral symbol</a></li> <li><a href="/wiki/Criticism_of_nonstandard_analysis" title="Criticism of nonstandard analysis">Criticism of nonstandard analysis</a></li> <li><i><a href="/wiki/The_Analyst" title="The Analyst">The Analyst</a></i></li> <li><i><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></i></li> <li><a href="/wiki/Cavalieri%27s_principle" title="Cavalieri's principle">Cavalieri's principle</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:German_integral.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/German_integral.gif/50px-German_integral.gif" decoding="async" width="50" height="92" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b5/German_integral.gif/75px-German_integral.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/b/b5/German_integral.gif 2x" data-file-width="84" data-file-height="155" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related branches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nonstandard_analysis" title="Nonstandard analysis">Nonstandard analysis</a></li> <li><a href="/wiki/Nonstandard_calculus" title="Nonstandard calculus">Nonstandard calculus</a></li> <li><a href="/wiki/Internal_set_theory" title="Internal set theory">Internal set theory</a></li> <li><a href="/wiki/Synthetic_differential_geometry" title="Synthetic differential geometry">Synthetic differential geometry</a></li> <li><a href="/wiki/Smooth_infinitesimal_analysis" title="Smooth infinitesimal analysis">Smooth infinitesimal analysis</a></li> <li><a href="/wiki/Constructive_nonstandard_analysis" title="Constructive nonstandard analysis">Constructive nonstandard analysis</a></li> <li><a href="/wiki/Infinitesimal_strain_theory" title="Infinitesimal strain theory">Infinitesimal strain theory (physics)</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formalizations</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Differential_(mathematics)" title="Differential (mathematics)">Differentials</a></li> <li><a href="/wiki/Hyperreal_number" title="Hyperreal number">Hyperreal numbers</a></li> <li><a href="/wiki/Dual_number" title="Dual number">Dual numbers</a></li> <li><a href="/wiki/Surreal_number" title="Surreal number">Surreal numbers</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Individual concepts</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Standard_part_function" title="Standard part function">Standard part function</a></li> <li><a href="/wiki/Transfer_principle" title="Transfer principle">Transfer principle</a></li> <li><a href="/wiki/Hyperinteger" title="Hyperinteger">Hyperinteger</a></li> <li><a href="/wiki/Increment_theorem" title="Increment theorem">Increment theorem</a></li> <li><a href="/wiki/Monad_(nonstandard_analysis)" title="Monad (nonstandard analysis)">Monad</a></li> <li><a href="/wiki/Internal_set" title="Internal set">Internal set</a></li> <li><a href="/wiki/Levi-Civita_field" title="Levi-Civita field">Levi-Civita field</a></li> <li><a href="/wiki/Hyperfinite_set" title="Hyperfinite set">Hyperfinite set</a></li> <li><a href="/wiki/Law_of_continuity" title="Law of continuity">Law of continuity</a></li> <li><a href="/wiki/Overspill" title="Overspill">Overspill</a></li> <li><a href="/wiki/Microcontinuity" title="Microcontinuity">Microcontinuity</a></li> <li><a href="/wiki/Transcendental_law_of_homogeneity" title="Transcendental law of homogeneity">Transcendental law of homogeneity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Mathematicians</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a></li> <li><a href="/wiki/Abraham_Robinson" title="Abraham Robinson">Abraham Robinson</a></li> <li><a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a></li> <li><a href="/wiki/Augustin-Louis_Cauchy" title="Augustin-Louis Cauchy">Augustin-Louis Cauchy</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Textbooks</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;font-style:italic;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Analyse_des_Infiniment_Petits_pour_l%27Intelligence_des_Lignes_Courbes" title="Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes">Analyse des Infiniment Petits</a></li> <li><a href="/wiki/Elementary_Calculus:_An_Infinitesimal_Approach" title="Elementary Calculus: An Infinitesimal Approach">Elementary Calculus</a></li> <li><a href="/wiki/Cours_d%27Analyse" title="Cours d'Analyse">Cours d'Analyse</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Calculus" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Calculus_topics" title="Template:Calculus topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Calculus_topics" title="Template talk:Calculus topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Calculus_topics" title="Special:EditPage/Template:Calculus topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Calculus" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Calculus</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Precalculus" title="Precalculus">Precalculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Binomial_theorem" title="Binomial theorem">Binomial theorem</a></li> <li><a href="/wiki/Concave_function" title="Concave function">Concave function</a></li> <li><a href="/wiki/Continuous_function" title="Continuous function">Continuous function</a></li> <li><a href="/wiki/Factorial" title="Factorial">Factorial</a></li> <li><a href="/wiki/Finite_difference" title="Finite difference">Finite difference</a></li> <li><a href="/wiki/Free_variables_and_bound_variables" title="Free variables and bound variables">Free variables and bound variables</a></li> <li><a href="/wiki/Graph_of_a_function" title="Graph of a function">Graph of a function</a></li> <li><a href="/wiki/Linear_function" title="Linear function">Linear function</a></li> <li><a href="/wiki/Radian" title="Radian">Radian</a></li> <li><a href="/wiki/Rolle%27s_theorem" title="Rolle's theorem">Rolle's theorem</a></li> <li><a href="/wiki/Secant_line" title="Secant line">Secant</a></li> <li><a href="/wiki/Slope" title="Slope">Slope</a></li> <li><a href="/wiki/Tangent" title="Tangent">Tangent</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">Limits</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Indeterminate_form" title="Indeterminate form">Indeterminate form</a></li> <li><a href="/wiki/Limit_of_a_function" title="Limit of a function">Limit of a function</a> <ul><li><a href="/wiki/One-sided_limit" title="One-sided limit">One-sided limit</a></li></ul></li> <li><a href="/wiki/Limit_of_a_sequence" title="Limit of a sequence">Limit of a sequence</a></li> <li><a href="/wiki/Order_of_approximation" title="Order of approximation">Order of approximation</a></li> <li><a href="/wiki/(%CE%B5,_%CE%B4)-definition_of_limit" class="mw-redirect" title="(ε, δ)-definition of limit">(ε, δ)-definition of limit</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Differential_calculus" title="Differential calculus">Differential calculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Derivative" title="Derivative">Derivative</a></li> <li><a href="/wiki/Second_derivative" title="Second derivative">Second derivative</a></li> <li><a href="/wiki/Partial_derivative" title="Partial derivative">Partial derivative</a></li> <li><a href="/wiki/Differential_(mathematics)" title="Differential (mathematics)">Differential</a></li> <li><a href="/wiki/Differential_operator" title="Differential operator">Differential operator</a></li> <li><a href="/wiki/Mean_value_theorem" title="Mean value theorem">Mean value theorem</a></li> <li><a href="/wiki/Notation_for_differentiation" title="Notation for differentiation">Notation</a> <ul><li><a href="/wiki/Leibniz%27s_notation" title="Leibniz's notation">Leibniz's notation</a></li> <li><a href="/wiki/Newton%27s_notation_for_differentiation" class="mw-redirect" title="Newton's notation for differentiation">Newton's notation</a></li></ul></li> <li><a href="/wiki/Differentiation_rules" title="Differentiation rules">Rules of differentiation</a> <ul><li><a href="/wiki/Linearity_of_differentiation" title="Linearity of differentiation">linearity</a></li> <li><a href="/wiki/Power_rule" title="Power rule">Power</a></li> <li><a href="/wiki/Sum_rule_in_differentiation" class="mw-redirect" title="Sum rule in differentiation">Sum</a></li> <li><a href="/wiki/Chain_rule" title="Chain rule">Chain</a></li> <li><a href="/wiki/L%27H%C3%B4pital%27s_rule" title="L'Hôpital's rule">L'Hôpital's</a></li> <li><a href="/wiki/Product_rule" title="Product rule">Product</a> <ul><li><a href="/wiki/General_Leibniz_rule" title="General Leibniz rule">General Leibniz's rule</a></li></ul></li> <li><a href="/wiki/Quotient_rule" title="Quotient rule">Quotient</a></li></ul></li> <li>Other techniques <ul><li><a href="/wiki/Implicit_differentiation" class="mw-redirect" title="Implicit differentiation">Implicit differentiation</a></li> <li><a href="/wiki/Inverse_functions_and_differentiation" class="mw-redirect" title="Inverse functions and differentiation">Inverse functions and differentiation</a></li> <li><a href="/wiki/Logarithmic_derivative" title="Logarithmic derivative">Logarithmic derivative</a></li> <li><a href="/wiki/Related_rates" title="Related rates">Related rates</a></li></ul></li> <li><a href="/wiki/Stationary_point" title="Stationary point">Stationary points</a> <ul><li><a href="/wiki/First_derivative_test" class="mw-redirect" title="First derivative test">First derivative test</a></li> <li><a href="/wiki/Second_derivative_test" class="mw-redirect" title="Second derivative test">Second derivative test</a></li> <li><a href="/wiki/Extreme_value_theorem" title="Extreme value theorem">Extreme value theorem</a></li> <li><a href="/wiki/Maximum_and_minimum" title="Maximum and minimum">Maximum and minimum</a></li></ul></li> <li>Further applications <ul><li><a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a></li> <li><a href="/wiki/Taylor%27s_theorem" title="Taylor's theorem">Taylor's theorem</a></li></ul></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equation</a> <ul><li><a href="/wiki/Ordinary_differential_equation" title="Ordinary differential equation">Ordinary differential equation</a></li> <li><a href="/wiki/Partial_differential_equation" title="Partial differential equation">Partial differential equation</a></li> <li><a href="/wiki/Stochastic_differential_equation" title="Stochastic differential equation">Stochastic differential equation</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Integral_calculus" class="mw-redirect" title="Integral calculus">Integral calculus</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Antiderivative" title="Antiderivative">Antiderivative</a></li> <li><a href="/wiki/Arc_length" title="Arc length">Arc length</a></li> <li><a href="/wiki/Riemann_integral" title="Riemann integral">Riemann integral</a></li> <li><a href="/wiki/Integral#Properties" title="Integral">Basic properties</a></li> <li><a href="/wiki/Constant_of_integration" title="Constant of integration">Constant of integration</a></li> <li><a href="/wiki/Fundamental_theorem_of_calculus" title="Fundamental theorem of calculus">Fundamental theorem of calculus</a> <ul><li><a href="/wiki/Leibniz_integral_rule" title="Leibniz integral rule">Differentiating under the integral sign</a></li></ul></li> <li><a href="/wiki/Integration_by_parts" title="Integration by parts">Integration by parts</a></li> <li><a href="/wiki/Integration_by_substitution" title="Integration by substitution">Integration by substitution</a> <ul><li><a href="/wiki/Trigonometric_substitution" title="Trigonometric substitution">trigonometric</a></li> <li><a href="/wiki/Euler_substitution" title="Euler substitution">Euler</a></li> <li><a href="/wiki/Tangent_half-angle_substitution" title="Tangent half-angle substitution">Tangent half-angle substitution</a></li></ul></li> <li><a href="/wiki/Partial_fractions_in_integration" class="mw-redirect" title="Partial fractions in integration">Partial fractions in integration</a> <ul><li><a href="/wiki/Quadratic_integral" title="Quadratic integral">Quadratic integral</a></li></ul></li> <li><a href="/wiki/Trapezoidal_rule" title="Trapezoidal rule">Trapezoidal rule</a></li> <li>Volumes <ul><li><a href="/wiki/Disc_integration" title="Disc integration">Washer method</a></li> <li><a href="/wiki/Shell_integration" title="Shell integration">Shell method</a></li></ul></li> <li><a href="/wiki/Integral_equation" title="Integral equation">Integral equation</a></li> <li><a href="/wiki/Integro-differential_equation" title="Integro-differential equation">Integro-differential equation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Vector_calculus" title="Vector calculus">Vector calculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Derivatives <ul><li><a href="/wiki/Curl_(mathematics)" title="Curl (mathematics)">Curl</a></li> <li><a href="/wiki/Directional_derivative" title="Directional derivative">Directional derivative</a></li> <li><a href="/wiki/Divergence" title="Divergence">Divergence</a></li> <li><a href="/wiki/Gradient" title="Gradient">Gradient</a></li> <li><a href="/wiki/Laplace_operator" title="Laplace operator">Laplacian</a></li></ul></li> <li>Basic theorems <ul><li><a href="/wiki/Fundamental_Theorem_of_Line_Integrals" class="mw-redirect" title="Fundamental Theorem of Line Integrals">Line integrals</a></li> <li><a href="/wiki/Green%27s_theorem" title="Green's theorem">Green's</a></li> <li><a href="/wiki/Stokes%27_theorem" title="Stokes' theorem">Stokes'</a></li> <li><a href="/wiki/Divergence_theorem" title="Divergence theorem">Gauss'</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Multivariable_calculus" title="Multivariable calculus">Multivariable calculus</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Divergence_theorem" title="Divergence theorem">Divergence theorem</a></li> <li><a href="/wiki/Geometric_calculus" title="Geometric calculus">Geometric</a></li> <li><a href="/wiki/Hessian_matrix" title="Hessian matrix">Hessian matrix</a></li> <li><a href="/wiki/Jacobian_matrix_and_determinant" title="Jacobian matrix and determinant">Jacobian matrix and determinant</a></li> <li><a href="/wiki/Lagrange_multiplier" title="Lagrange multiplier">Lagrange multiplier</a></li> <li><a href="/wiki/Line_integral" title="Line integral">Line integral</a></li> <li><a href="/wiki/Matrix_calculus" title="Matrix calculus">Matrix</a></li> <li><a href="/wiki/Multiple_integral" title="Multiple integral">Multiple integral</a></li> <li><a href="/wiki/Partial_derivative" title="Partial derivative">Partial derivative</a></li> <li><a href="/wiki/Surface_integral" title="Surface integral">Surface integral</a></li> <li><a href="/wiki/Volume_integral" title="Volume integral">Volume integral</a></li> <li>Advanced topics <ul><li><a href="/wiki/Differential_form" title="Differential form">Differential forms</a></li> <li><a href="/wiki/Exterior_derivative" title="Exterior derivative">Exterior derivative</a></li> <li><a href="/wiki/Generalized_Stokes%27_theorem" class="mw-redirect" title="Generalized Stokes' theorem">Generalized Stokes' theorem</a></li> <li><a href="/wiki/Tensor_calculus" class="mw-redirect" title="Tensor calculus">Tensor calculus</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Sequences and series</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arithmetico-geometric_sequence" title="Arithmetico-geometric sequence">Arithmetico-geometric sequence</a></li> <li>Types of series <ul><li><a href="/wiki/Alternating_series" title="Alternating series">Alternating</a></li> <li><a href="/wiki/Binomial_series" title="Binomial series">Binomial</a></li> <li><a href="/wiki/Fourier_series" title="Fourier series">Fourier</a></li> <li><a href="/wiki/Geometric_series" title="Geometric series">Geometric</a></li> <li><a href="/wiki/Harmonic_series_(mathematics)" title="Harmonic series (mathematics)">Harmonic</a></li> <li><a href="/wiki/Infinite_series" class="mw-redirect" title="Infinite series">Infinite</a></li> <li><a href="/wiki/Power_series" title="Power series">Power</a> <ul><li><a href="/wiki/Maclaurin_series" class="mw-redirect" title="Maclaurin series">Maclaurin</a></li> <li><a href="/wiki/Taylor_series" title="Taylor series">Taylor</a></li></ul></li> <li><a href="/wiki/Telescoping_series" title="Telescoping series">Telescoping</a></li></ul></li> <li>Tests of convergence <ul><li><a href="/wiki/Abel%27s_test" title="Abel's test">Abel's</a></li> <li><a href="/wiki/Alternating_series_test" title="Alternating series test">Alternating series</a></li> <li><a href="/wiki/Cauchy_condensation_test" title="Cauchy condensation test">Cauchy condensation</a></li> <li><a href="/wiki/Direct_comparison_test" title="Direct comparison test">Direct comparison</a></li> <li><a href="/wiki/Dirichlet%27s_test" title="Dirichlet's test">Dirichlet's</a></li> <li><a href="/wiki/Integral_test_for_convergence" title="Integral test for convergence">Integral</a></li> <li><a href="/wiki/Limit_comparison_test" title="Limit comparison test">Limit comparison</a></li> <li><a href="/wiki/Ratio_test" title="Ratio test">Ratio</a></li> <li><a href="/wiki/Root_test" title="Root test">Root</a></li> <li><a href="/wiki/Term_test" class="mw-redirect" title="Term test">Term</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Special functions<br />and numbers</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bernoulli_number" title="Bernoulli number">Bernoulli numbers</a></li> <li><a href="/wiki/E_(mathematical_constant)" title="E (mathematical constant)">e (mathematical constant)</a></li> <li><a href="/wiki/Exponential_function" title="Exponential function">Exponential function</a></li> <li><a href="/wiki/Natural_logarithm" title="Natural logarithm">Natural logarithm</a></li> <li><a href="/wiki/Stirling%27s_approximation" title="Stirling's approximation">Stirling's approximation</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/History_of_calculus" title="History of calculus">History of calculus</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Adequality" title="Adequality">Adequality</a></li> <li><a href="/wiki/Brook_Taylor" title="Brook Taylor">Brook Taylor</a></li> <li><a href="/wiki/Colin_Maclaurin" title="Colin Maclaurin">Colin Maclaurin</a></li> <li><a href="/wiki/Generality_of_algebra" title="Generality of algebra">Generality of algebra</a></li> <li><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a></li> <li><a href="/wiki/Infinitesimal" title="Infinitesimal">Infinitesimal</a></li> <li><a href="/wiki/Infinitesimal_calculus" class="mw-redirect" title="Infinitesimal calculus">Infinitesimal calculus</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a></li> <li><a href="/wiki/Fluxion" title="Fluxion">Fluxion</a></li> <li><a href="/wiki/Law_of_Continuity" class="mw-redirect" title="Law of Continuity">Law of Continuity</a></li> <li><a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a></li> <li><i><a href="/wiki/Method_of_Fluxions" title="Method of Fluxions">Method of Fluxions</a></i></li> <li><i><a href="/wiki/The_Method_of_Mechanical_Theorems" title="The Method of Mechanical Theorems">The Method of Mechanical Theorems</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Integrals" scope="row" class="navbox-group" style="width:1%;text-align:left"><a href="/wiki/Lists_of_integrals" title="Lists of integrals">Integrals</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_integrals_of_rational_functions" title="List of integrals of rational functions">rational functions</a></li> <li><a href="/wiki/List_of_integrals_of_irrational_functions" title="List of integrals of irrational functions">irrational functions</a></li> <li><a href="/wiki/List_of_integrals_of_exponential_functions" title="List of integrals of exponential functions">exponential functions</a></li> <li><a href="/wiki/List_of_integrals_of_logarithmic_functions" title="List of integrals of logarithmic functions">logarithmic functions</a></li> <li><a href="/wiki/List_of_integrals_of_hyperbolic_functions" title="List of integrals of hyperbolic functions">hyperbolic functions</a> <ul><li><a href="/wiki/List_of_integrals_of_inverse_hyperbolic_functions" title="List of integrals of inverse hyperbolic functions">inverse</a></li></ul></li> <li><a href="/wiki/List_of_integrals_of_trigonometric_functions" title="List of integrals of trigonometric functions">trigonometric functions</a> <ul><li><a href="/wiki/List_of_integrals_of_inverse_trigonometric_functions" title="List of integrals of inverse trigonometric functions">inverse</a></li> <li><a href="/wiki/Integral_of_the_secant_function" title="Integral of the secant function">Secant</a></li> <li><a href="/wiki/Integral_of_secant_cubed" title="Integral of secant cubed">Secant cubed</a></li></ul></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_limits" title="List of limits">List of limits</a></li> <li><a href="/wiki/Differentiation_rules" title="Differentiation rules">List of derivatives</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Miscellaneous topics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Complex calculus <ul><li><a href="/wiki/Contour_integral" class="mw-redirect" title="Contour integral">Contour integral</a></li></ul></li> <li>Differential geometry <ul><li><a href="/wiki/Manifold" title="Manifold">Manifold</a></li> <li><a href="/wiki/Curvature" title="Curvature">Curvature</a></li> <li><a href="/wiki/Differential_geometry_of_curves" class="mw-redirect" title="Differential geometry of curves">of curves</a></li> <li><a href="/wiki/Differential_geometry_of_surfaces" title="Differential geometry of surfaces">of surfaces</a></li> <li><a href="/wiki/Tensor" title="Tensor">Tensor</a></li></ul></li> <li><a href="/wiki/Euler%E2%80%93Maclaurin_formula" title="Euler–Maclaurin formula">Euler–Maclaurin formula</a></li> <li><a href="/wiki/Gabriel%27s_horn" title="Gabriel's horn">Gabriel's horn</a></li> <li><a href="/wiki/Integration_Bee" title="Integration Bee">Integration Bee</a></li> <li><a href="/wiki/Proof_that_22/7_exceeds_%CF%80" title="Proof that 22/7 exceeds π">Proof that 22/7 exceeds π</a></li> <li><a href="/wiki/Regiomontanus%27_angle_maximization_problem" title="Regiomontanus' angle maximization problem">Regiomontanus' angle maximization problem</a></li> <li><a href="/wiki/Steinmetz_solid" title="Steinmetz solid">Steinmetz solid</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" 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theory</a></li></ul> <ul><li><a href="/wiki/Function_(mathematics)" title="Function (mathematics)">Functions</a></li> <li><a href="/wiki/Continuous_function" title="Continuous function">Continuous function</a></li> <li><a href="/wiki/Special_functions" title="Special functions">Special functions</a></li> <li><a href="/wiki/Limit_(mathematics)" title="Limit (mathematics)">Limit</a></li> <li><a href="/wiki/Series_(mathematics)" title="Series (mathematics)">Series</a></li> <li><a href="/wiki/Infinity" title="Infinity">Infinity</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></b></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Major_mathematics_areas" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Areas_of_mathematics" title="Template:Areas of mathematics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Areas_of_mathematics" title="Template talk:Areas of mathematics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Areas_of_mathematics" title="Special:EditPage/Template:Areas of mathematics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Major_mathematics_areas" style="font-size:114%;margin:0 4em">Major <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> areas</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History</a> <ul><li><a href="/wiki/Timeline_of_mathematics" title="Timeline of mathematics">Timeline</a></li> <li><a href="/wiki/Future_of_mathematics" title="Future of mathematics">Future</a></li></ul></li> <li><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Lists</a></li> <li><a href="/wiki/Glossary_of_mathematical_symbols" title="Glossary of mathematical symbols">Glossary</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">Foundations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Category_theory" title="Category theory">Category theory</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical logic</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Set_theory" title="Set theory">Set theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Algebra" title="Algebra">Algebra</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abstract_algebra" title="Abstract algebra">Abstract</a></li> <li><a href="/wiki/Commutative_algebra" title="Commutative algebra">Commutative</a></li> <li><a href="/wiki/Elementary_algebra" title="Elementary algebra">Elementary</a></li> <li><a href="/wiki/Group_theory" title="Group theory">Group theory</a></li> <li><a href="/wiki/Linear_algebra" title="Linear algebra">Linear</a></li> <li><a href="/wiki/Multilinear_algebra" title="Multilinear algebra">Multilinear</a></li> <li><a href="/wiki/Universal_algebra" title="Universal algebra">Universal</a></li> <li><a href="/wiki/Homological_algebra" title="Homological algebra">Homological</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Analysis</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Calculus</a></li> <li><a href="/wiki/Real_analysis" title="Real analysis">Real analysis</a></li> <li><a href="/wiki/Complex_analysis" title="Complex analysis">Complex analysis</a></li> <li><a href="/wiki/Hypercomplex_analysis" title="Hypercomplex analysis">Hypercomplex analysis</a></li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a></li> <li><a href="/wiki/Functional_analysis" title="Functional analysis">Functional analysis</a></li> <li><a href="/wiki/Harmonic_analysis" title="Harmonic analysis">Harmonic analysis</a></li> <li><a href="/wiki/Measure_(mathematics)" title="Measure (mathematics)">Measure theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Discrete_mathematics" title="Discrete mathematics">Discrete</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Combinatorics" title="Combinatorics">Combinatorics</a></li> <li><a href="/wiki/Graph_theory" title="Graph theory">Graph theory</a></li> <li><a href="/wiki/Order_theory" title="Order theory">Order theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geometry" title="Geometry">Geometry</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Algebraic_geometry" title="Algebraic geometry">Algebraic</a></li> <li><a href="/wiki/Analytic_geometry" title="Analytic geometry">Analytic</a></li> <li><a href="/wiki/Arithmetic_geometry" title="Arithmetic geometry">Arithmetic</a></li> <li><a href="/wiki/Differential_geometry" title="Differential geometry">Differential</a></li> <li><a href="/wiki/Discrete_geometry" title="Discrete geometry">Discrete</a></li> <li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean</a></li> <li><a href="/wiki/Finite_geometry" title="Finite geometry">Finite</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Number_theory" title="Number theory">Number theory</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arithmetic" title="Arithmetic">Arithmetic</a></li> <li><a href="/wiki/Algebraic_number_theory" title="Algebraic number theory">Algebraic number theory</a></li> <li><a href="/wiki/Analytic_number_theory" title="Analytic number theory">Analytic number theory</a></li> <li><a href="/wiki/Diophantine_geometry" title="Diophantine geometry">Diophantine geometry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Topology" title="Topology">Topology</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/General_topology" title="General topology">General</a></li> <li><a href="/wiki/Algebraic_topology" title="Algebraic topology">Algebraic</a></li> <li><a href="/wiki/Differential_topology" title="Differential topology">Differential</a></li> <li><a href="/wiki/Geometric_topology" title="Geometric topology">Geometric</a></li> <li><a href="/wiki/Homotopy_theory" title="Homotopy theory">Homotopy theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Applied_mathematics" title="Applied mathematics">Applied</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Engineering_mathematics" title="Engineering mathematics">Engineering mathematics</a></li> <li><a href="/wiki/Mathematical_and_theoretical_biology" title="Mathematical and theoretical biology">Mathematical biology</a></li> <li><a href="/wiki/Mathematical_chemistry" title="Mathematical chemistry">Mathematical chemistry</a></li> <li><a href="/wiki/Mathematical_economics" title="Mathematical economics">Mathematical economics</a></li> <li><a href="/wiki/Mathematical_finance" title="Mathematical finance">Mathematical finance</a></li> <li><a href="/wiki/Mathematical_physics" title="Mathematical physics">Mathematical physics</a></li> <li><a href="/wiki/Mathematical_psychology" title="Mathematical psychology">Mathematical psychology</a></li> <li><a href="/wiki/Mathematical_sociology" title="Mathematical sociology">Mathematical sociology</a></li> <li><a href="/wiki/Mathematical_statistics" title="Mathematical statistics">Mathematical statistics</a></li> <li><a href="/wiki/Probability_theory" title="Probability theory">Probability</a></li> <li><a href="/wiki/Statistics" title="Statistics">Statistics</a></li> <li><a href="/wiki/Systems_science" title="Systems science">Systems science</a> <ul><li><a href="/wiki/Control_theory" title="Control theory">Control theory</a></li> <li><a href="/wiki/Game_theory" title="Game theory">Game theory</a></li> <li><a href="/wiki/Operations_research" title="Operations research">Operations research</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computational_mathematics" title="Computational mathematics">Computational</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Computer_science" title="Computer science">Computer science</a></li> <li><a href="/wiki/Theory_of_computation" title="Theory of computation">Theory of computation</a></li> <li><a href="/wiki/Computational_complexity_theory" title="Computational complexity theory">Computational complexity theory</a></li> <li><a href="/wiki/Numerical_analysis" title="Numerical analysis">Numerical analysis</a></li> <li><a href="/wiki/Mathematical_optimization" title="Mathematical optimization">Optimization</a></li> <li><a href="/wiki/Computer_algebra" title="Computer algebra">Computer algebra</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Related topics</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Mathematicians" class="mw-redirect" title="Mathematicians">Mathematicians</a> <ul><li><a href="/wiki/List_of_mathematicians" class="mw-redirect" title="List of mathematicians">lists</a></li></ul></li> <li><a href="/wiki/Informal_mathematics" title="Informal mathematics">Informal mathematics</a></li> <li><a href="/wiki/List_of_films_about_mathematicians" title="List of films about mathematicians">Films about mathematicians</a></li> <li><a href="/wiki/Recreational_mathematics" title="Recreational mathematics">Recreational mathematics</a></li> <li><a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a></li> <li><a href="/wiki/Mathematics_education" title="Mathematics education">Mathematics education</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/24px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/32px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> </span><a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics portal</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:Fields_of_mathematics" title="Category:Fields of mathematics">Category</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <b><a href="https://commons.wikimedia.org/wiki/Category:Mathematics" class="extiw" title="commons:Category:Mathematics">Commons</a></b></li> <li><span class="noviewer" typeof="mw:File"><span title="WikiProject"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span> <b><a href="/wiki/Wikipedia:WikiProject_Mathematics" title="Wikipedia:WikiProject Mathematics">WikiProject</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style></div><div role="navigation" class="navbox" aria-labelledby="Sir_Isaac_Newton" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Isaac_Newton" title="Template:Isaac Newton"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Isaac_Newton" title="Template talk:Isaac Newton"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Isaac_Newton" title="Special:EditPage/Template:Isaac Newton"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Sir_Isaac_Newton" style="font-size:114%;margin:0 4em"><a href="/wiki/Isaac_Newton" title="Isaac Newton">Sir Isaac Newton</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Publications</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Method_of_Fluxions" title="Method of Fluxions">Fluxions</a></i> (1671)</li> <li><i><a href="/wiki/De_motu_corporum_in_gyrum" title="De motu corporum in gyrum">De Motu</a></i> (1684)</li> <li><i><a href="/wiki/Philosophi%C3%A6_Naturalis_Principia_Mathematica" title="Philosophiæ Naturalis Principia Mathematica">Principia</a></i> (1687)</li> <li><i><a href="/wiki/Opticks" title="Opticks">Opticks</a></i> (1704)</li> <li><i><a href="/wiki/The_Queries" class="mw-redirect" title="The Queries">Queries</a></i> (1704)</li> <li><i><a href="/wiki/Arithmetica_Universalis" title="Arithmetica Universalis">Arithmetica</a></i> (1707)</li> <li><i><a href="/wiki/De_analysi_per_aequationes_numero_terminorum_infinitas" title="De analysi per aequationes numero terminorum infinitas">De Analysi</a></i> (1711)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Other writings</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Quaestiones_quaedam_philosophicae" title="Quaestiones quaedam philosophicae">Quaestiones</a></i> (1661–1665)</li> <li>"<a href="/wiki/Standing_on_the_shoulders_of_giants" title="Standing on the shoulders of giants">standing on the shoulders of giants</a>" (1675)</li> <li><i><a href="/wiki/Notes_on_the_Jewish_Temple" title="Notes on the Jewish Temple">Notes on the Jewish Temple</a></i> (c. 1680)</li> <li>"<a href="/wiki/General_Scholium" title="General Scholium">General Scholium</a>" (1713; <i>"<a href="/wiki/Hypotheses_non_fingo" title="Hypotheses non fingo">hypotheses non fingo</a>"</i> )</li> <li><i><a href="/wiki/The_Chronology_of_Ancient_Kingdoms_Amended" title="The Chronology of Ancient Kingdoms Amended">Ancient Kingdoms Amended</a></i> (1728)</li> <li><i><a href="/wiki/An_Historical_Account_of_Two_Notable_Corruptions_of_Scripture" title="An Historical Account of Two Notable Corruptions of Scripture">Corruptions of Scripture</a></i> (1754)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Contributions</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Calculus</a> <ul><li><a href="/wiki/Fluxion" title="Fluxion">fluxion</a></li></ul></li> <li><a href="/wiki/Impact_depth" title="Impact depth">Impact depth</a></li> <li><a href="/wiki/Inertia" title="Inertia">Inertia</a></li> <li><a href="/wiki/Newton_disc" title="Newton disc">Newton disc</a></li> <li><a href="/wiki/Newton_polygon" title="Newton polygon">Newton polygon</a> <ul><li><a href="/wiki/Newton%E2%80%93Okounkov_body" title="Newton–Okounkov body">Newton–Okounkov body</a></li></ul></li> <li><a href="/wiki/Newton%27s_reflector" title="Newton's reflector">Newton's reflector</a></li> <li><a href="/wiki/Newtonian_telescope" title="Newtonian telescope">Newtonian telescope</a></li> <li><a href="/wiki/Newton_scale" title="Newton scale">Newton scale</a></li> <li><a href="/wiki/Newton%27s_metal" title="Newton's metal">Newton's metal</a></li> <li><a href="/wiki/Spectrum" title="Spectrum">Spectrum</a></li> <li><a href="/wiki/Structural_coloration" title="Structural coloration">Structural coloration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/Newtonianism" title="Newtonianism">Newtonianism</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bucket_argument" title="Bucket argument">Bucket argument</a></li> <li><a href="/wiki/Newton%27s_inequalities" title="Newton's inequalities">Newton's inequalities</a></li> <li><a href="/wiki/Newton%27s_law_of_cooling" title="Newton's law of cooling">Newton's law of cooling</a></li> <li><a href="/wiki/Newton%27s_law_of_universal_gravitation" title="Newton's law of universal gravitation">Newton's law of universal gravitation</a> <ul><li><a href="/wiki/Post-Newtonian_expansion" title="Post-Newtonian expansion">post-Newtonian expansion</a></li> <li><a href="/wiki/Parameterized_post-Newtonian_formalism" title="Parameterized post-Newtonian formalism">parameterized</a></li> <li><a href="/wiki/Gravitational_constant" title="Gravitational constant">gravitational constant</a></li></ul></li> <li><a href="/wiki/Newton%E2%80%93Cartan_theory" title="Newton–Cartan theory">Newton–Cartan theory</a></li> <li><a href="/wiki/Schr%C3%B6dinger%E2%80%93Newton_equation" title="Schrödinger–Newton equation">Schrödinger–Newton equation</a></li> <li><a href="/wiki/Newton%27s_laws_of_motion" title="Newton's laws of motion">Newton's laws of motion</a> <ul><li><a href="/wiki/Kepler%27s_laws_of_planetary_motion" title="Kepler's laws of planetary motion">Kepler's laws</a></li></ul></li> <li><a href="/wiki/Newtonian_dynamics" title="Newtonian dynamics">Newtonian dynamics</a></li> <li><a href="/wiki/Newton%27s_method_in_optimization" title="Newton's method in optimization">Newton's method in optimization</a> <ul><li><a href="/wiki/Problem_of_Apollonius" title="Problem of Apollonius">Apollonius's problem</a></li> <li><a href="/wiki/Truncated_Newton_method" title="Truncated Newton method">truncated Newton method</a></li></ul></li> <li><a href="/wiki/Gauss%E2%80%93Newton_algorithm" title="Gauss–Newton algorithm">Gauss–Newton algorithm</a></li> <li><a href="/wiki/Newton%27s_rings" title="Newton's rings">Newton's rings</a></li> <li><a href="/wiki/Newton%27s_theorem_about_ovals" title="Newton's theorem about ovals">Newton's theorem about ovals</a></li> <li><a href="/wiki/Newton%E2%80%93Pepys_problem" title="Newton–Pepys problem">Newton–Pepys problem</a></li> <li><a href="/wiki/Newtonian_potential" title="Newtonian potential">Newtonian potential</a></li> <li><a href="/wiki/Newtonian_fluid" title="Newtonian fluid">Newtonian fluid</a></li> <li><a href="/wiki/Classical_mechanics" title="Classical mechanics">Classical mechanics</a></li> <li><a href="/wiki/Corpuscular_theory_of_light" title="Corpuscular theory of light">Corpuscular theory of light</a></li> <li><a href="/wiki/Leibniz%E2%80%93Newton_calculus_controversy" title="Leibniz–Newton calculus controversy">Leibniz–Newton calculus controversy</a></li> <li><a href="/wiki/Newton%27s_notation" class="mw-redirect" title="Newton's notation">Newton's notation</a></li> <li><a href="/wiki/Rotating_spheres" title="Rotating spheres">Rotating spheres</a></li> <li><a href="/wiki/Newton%27s_cannonball" title="Newton's cannonball">Newton's cannonball</a></li> <li><a href="/wiki/Newton%E2%80%93Cotes_formulas" title="Newton–Cotes formulas">Newton–Cotes formulas</a></li> <li><a href="/wiki/Newton%27s_method" title="Newton's method">Newton's method</a> <ul><li><a href="/wiki/Generalized_Gauss%E2%80%93Newton_method" title="Generalized Gauss–Newton method">generalized Gauss–Newton method</a></li></ul></li> <li><a href="/wiki/Newton_fractal" title="Newton fractal">Newton fractal</a></li> <li><a href="/wiki/Newton%27s_identities" title="Newton's identities">Newton's identities</a></li> <li><a href="/wiki/Newton_polynomial" title="Newton polynomial">Newton polynomial</a></li> <li><a href="/wiki/Newton%27s_theorem_of_revolving_orbits" title="Newton's theorem of revolving orbits">Newton's theorem of revolving orbits</a></li> <li><a href="/wiki/Newton%E2%80%93Euler_equations" title="Newton–Euler equations">Newton–Euler equations</a></li> <li><a href="/wiki/Power_number" title="Power number">Newton number</a> <ul><li><a href="/wiki/Kissing_number" title="Kissing number">kissing number problem</a></li></ul></li> <li><a href="/wiki/Difference_quotient" title="Difference quotient">Newton's quotient</a></li> <li><a href="/wiki/Parallelogram_of_force" title="Parallelogram of force">Parallelogram of force</a></li> <li><a href="/wiki/Puiseux_series" title="Puiseux series">Newton–Puiseux theorem</a></li> <li><a href="/wiki/Absolute_space_and_time#Newton" title="Absolute space and time">Absolute space and time</a></li> <li><a href="/wiki/Luminiferous_aether" title="Luminiferous aether">Luminiferous aether</a></li> <li><a href="/wiki/Finite_difference" title="Finite difference">Newtonian series</a> <ul><li><a href="/wiki/Table_of_Newtonian_series" title="Table of Newtonian series">table</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Personal life</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Woolsthorpe_Manor" title="Woolsthorpe Manor">Woolsthorpe Manor</a> (birthplace)</li> <li><a href="/wiki/Cranbury_Park" title="Cranbury Park">Cranbury Park</a> (home)</li> <li><a href="/wiki/Early_life_of_Isaac_Newton" title="Early life of Isaac Newton">Early life</a></li> <li><a href="/wiki/Later_life_of_Isaac_Newton" title="Later life of Isaac Newton">Later life</a></li> <li><a href="/wiki/Isaac_Newton%27s_apple_tree" title="Isaac Newton's apple tree">Apple tree</a></li> <li><a href="/wiki/Religious_views_of_Isaac_Newton" title="Religious views of Isaac Newton">Religious views</a></li> <li><a href="/wiki/Isaac_Newton%27s_occult_studies" title="Isaac Newton's occult studies">Occult studies</a></li> <li><a href="/wiki/Scientific_Revolution" title="Scientific Revolution">Scientific Revolution</a></li> <li><a href="/wiki/Copernican_Revolution" title="Copernican Revolution">Copernican Revolution</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Relations</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Catherine_Barton" title="Catherine Barton">Catherine Barton</a> (niece)</li> <li><a href="/wiki/John_Conduitt" title="John Conduitt">John Conduitt</a> (nephew-in-law)</li> <li><a href="/wiki/Isaac_Barrow" title="Isaac Barrow">Isaac Barrow</a> (professor)</li> <li><a href="/wiki/William_Clarke_(apothecary)" title="William Clarke (apothecary)">William Clarke</a> (mentor)</li> <li><a href="/wiki/Benjamin_Pulleyn" title="Benjamin Pulleyn">Benjamin Pulleyn</a> (tutor)</li> <li><a href="/wiki/Roger_Cotes" title="Roger Cotes">Roger Cotes</a> (student)</li> <li><a href="/wiki/William_Whiston" title="William Whiston">William Whiston</a> (student)</li> <li><a href="/wiki/John_Keill" title="John Keill">John Keill</a> (disciple)</li> <li><a href="/wiki/William_Stukeley" title="William Stukeley">William Stukeley</a> (friend)</li> <li><a href="/wiki/William_Jones_(mathematician)" title="William Jones (mathematician)">William Jones</a> (friend)</li> <li><a href="/wiki/Abraham_de_Moivre" title="Abraham de Moivre">Abraham de Moivre</a> (friend)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/Isaac_Newton_in_popular_culture" title="Isaac Newton in popular culture">Depictions</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Newton_(Blake)" title="Newton (Blake)"><i>Newton</i> by Blake</a> (monotype)</li> <li><a href="/wiki/Newton_(Paolozzi)" title="Newton (Paolozzi)"><i>Newton</i> by Paolozzi</a> (sculpture)</li> <li><i><a href="/wiki/Isaac_Newton_Gargoyle" title="Isaac Newton Gargoyle">Isaac Newton Gargoyle</a></i></li> <li><i><a href="/wiki/Astronomers_Monument" title="Astronomers Monument">Astronomers Monument</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;"><a href="/wiki/List_of_things_named_after_Isaac_Newton" title="List of things named after Isaac Newton">Namesake</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Newton_(unit)" title="Newton (unit)">Newton (unit)</a></li> <li><a href="/wiki/Newton%27s_cradle" title="Newton's cradle">Newton's cradle</a></li> <li><a href="/wiki/Isaac_Newton_Institute" title="Isaac Newton Institute">Isaac Newton Institute</a></li> <li><a href="/wiki/Institute_of_Physics_Isaac_Newton_Medal" class="mw-redirect" title="Institute of Physics Isaac Newton Medal">Isaac Newton Medal</a></li> <li><a href="/wiki/Isaac_Newton_Telescope" title="Isaac Newton Telescope">Isaac Newton Telescope</a></li> <li><a href="/wiki/Isaac_Newton_Group_of_Telescopes" title="Isaac Newton Group of Telescopes">Isaac Newton Group of Telescopes</a></li> <li><a href="/wiki/XMM-Newton" title="XMM-Newton">XMM-Newton</a></li> <li><a href="/wiki/Sir_Isaac_Newton_Sixth_Form" title="Sir Isaac Newton Sixth Form">Sir Isaac Newton Sixth Form</a></li> <li><a href="/wiki/Statal_Institute_of_Higher_Education_Isaac_Newton" title="Statal Institute of Higher Education Isaac Newton">Statal Institute of Higher Education Isaac Newton</a></li> <li><a href="/wiki/Newton_International_Fellowship" title="Newton International Fellowship">Newton International Fellowship</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;vertical-align:top;">Categories</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"><div class="div-col"> <div class="CategoryTreeTag" data-ct-options="{"mode":20,"hideprefix":20,"showcount":false,"namespaces":false,"notranslations":false}"><div class="CategoryTreeSection"><div class="CategoryTreeItem"><span class="CategoryTreeBullet"><a class="CategoryTreeToggle" data-ct-title="Isaac_Newton" aria-expanded="false"></a> </span> <bdi dir="ltr"><a href="/wiki/Category:Isaac_Newton" title="Category:Isaac Newton">Isaac Newton</a></bdi></div><div class="CategoryTreeChildren" style="display:none"></div></div></div> </div></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Glossaries_of_science_and_engineering" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks 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title="Glossary of electrical and electronics engineering">Electrical and electronics engineering</a></li> <li>Engineering <ul><li><a href="/wiki/Glossary_of_engineering:_A%E2%80%93L" title="Glossary of engineering: A–L">A–L</a></li> <li><a href="/wiki/Glossary_of_engineering:_M%E2%80%93Z" title="Glossary of engineering: M–Z">M–Z</a></li></ul></li> <li><a href="/wiki/Glossary_of_entomology_terms" title="Glossary of entomology terms">Entomology</a></li> <li><a href="/wiki/Glossary_of_environmental_science" title="Glossary of environmental science">Environmental science</a></li> <li><a href="/wiki/Glossary_of_genetics_and_evolutionary_biology" title="Glossary of genetics and evolutionary biology">Genetics and evolutionary biology</a></li> <li>Cellular and molecular biology <ul><li><a href="/wiki/Glossary_of_cellular_and_molecular_biology_(0%E2%80%93L)" title="Glossary of cellular and molecular biology (0–L)">0–L</a></li> <li><a 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title="Glossary of machine vision">Machine vision</a></li> <li><a href="/wiki/Glossary_of_areas_of_mathematics" title="Glossary of areas of mathematics">Mathematics</a></li> <li><a href="/wiki/Glossary_of_mechanical_engineering" title="Glossary of mechanical engineering">Mechanical engineering</a></li> <li><a href="/wiki/Glossary_of_medicine" title="Glossary of medicine">Medicine</a></li> <li><a href="/wiki/Glossary_of_meteorology" title="Glossary of meteorology">Meteorology</a></li> <li><a href="/wiki/Glossary_of_mycology" title="Glossary of mycology">Mycology</a></li> <li><a href="/wiki/Glossary_of_nanotechnology" title="Glossary of nanotechnology">Nanotechnology</a></li> <li><a href="/wiki/Glossary_of_bird_terms" title="Glossary of bird terms">Ornithology</a></li> <li><a href="/wiki/Glossary_of_physics" title="Glossary of physics">Physics</a></li> <li><a href="/wiki/Glossary_of_probability_and_statistics" title="Glossary of probability and statistics">Probability and 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