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<span>Analysen sitt fundamentalteorem</span> </div> </a> <ul id="toc-Analysen_sitt_fundamentalteorem-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Kjelder" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kjelder"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Kjelder</span> </div> </a> <ul id="toc-Kjelder-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bakgrunnsstoff" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bakgrunnsstoff"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bakgrunnsstoff</span> </div> </a> <ul id="toc-Bakgrunnsstoff-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 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mw-first-heading"><span class="mw-page-title-main">Matematisk analyse</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="Gå til ein artikkel på eit anna språk. Tilgjengeleg på 114 språk" > <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-114" 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">114 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Matematisk_analyse" title="Matematisk analyse – norsk bokmål" lang="nb" hreflang="nb" data-title="Matematisk analyse" data-language-autonym="Norsk bokmål" data-language-local-name="norsk bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Matematisk_analys" title="Matematisk analys – svensk" lang="sv" hreflang="sv" data-title="Matematisk analys" data-language-autonym="Svenska" data-language-local-name="svensk" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Matematisk_analyse" title="Matematisk analyse – dansk" lang="da" hreflang="da" data-title="Matematisk analyse" data-language-autonym="Dansk" data-language-local-name="dansk" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Wiskundige_analise" title="Wiskundige analise – afrikaans" lang="af" hreflang="af" data-title="Wiskundige analise" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Analysis" title="Analysis – sveitsertysk" lang="gsw" hreflang="gsw" data-title="Analysis" data-language-autonym="Alemannisch" data-language-local-name="sveitsertysk" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%95%E0%A4%B2%E0%A4%A8_%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="कलन शास्त्र – angika" lang="anp" hreflang="anp" data-title="कलन शास्त्र" data-language-autonym="अंगिका" data-language-local-name="angika" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%AD%D9%84%D9%8A%D9%84_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A" title="تحليل رياضي – arabisk" lang="ar" hreflang="ar" data-title="تحليل رياضي" data-language-autonym="العربية" data-language-local-name="arabisk" 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/Anal%C3%ADs_matematica" title="Analís matematica – aragonsk" lang="an" hreflang="an" data-title="Analís matematica" data-language-autonym="Aragonés" data-language-local-name="aragonsk" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%97%E0%A6%BE%E0%A6%A3%E0%A6%BF%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%AC%E0%A6%BF%E0%A6%B6%E0%A7%8D%E0%A6%B2%E0%A7%87%E0%A6%B7%E0%A6%A3" title="গাণিতিক বিশ্লেষণ – assamesisk" lang="as" hreflang="as" data-title="গাণিতিক বিশ্লেষণ" data-language-autonym="অসমীয়া" data-language-local-name="assamesisk" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Anal%C3%ADs_matem%C3%A1ticu" title="Analís matemáticu – asturisk" lang="ast" hreflang="ast" data-title="Analís matemáticu" data-language-autonym="Asturianu" data-language-local-name="asturisk" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Riyazi_analiz" title="Riyazi analiz – aserbajdsjansk" lang="az" hreflang="az" data-title="Riyazi analiz" data-language-autonym="Azərbaycanca" data-language-local-name="aserbajdsjansk" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%BE%E0%A6%A3%E0%A6%BF%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%AC%E0%A6%BF%E0%A6%B6%E0%A7%8D%E0%A6%B2%E0%A7%87%E0%A6%B7%E0%A6%A3" title="গাণিতিক বিশ্লেষণ – bengali" lang="bn" hreflang="bn" data-title="গাণিতিক বিশ্লেষণ" data-language-autonym="বাংলা" data-language-local-name="bengali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%B1%D2%AF%D0%BB%D0%B5%D0%B3%D0%B5)" title="Анализ (математика бүлеге) – basjkirsk" lang="ba" hreflang="ba" data-title="Анализ (математика бүлеге)" data-language-autonym="Башҡортса" data-language-local-name="basjkirsk" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Матэматычны аналіз – belarusisk" lang="be" hreflang="be" data-title="Матэматычны аналіз" data-language-autonym="Беларуская" data-language-local-name="belarusisk" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Матэматычны аналіз – belarusisk (klassisk ortografi)" lang="be-tarask" hreflang="be-tarask" data-title="Матэматычны аналіз" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusisk (klassisk ortografi)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A5%80%E0%A4%AF_%E0%A4%AC%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%B2%E0%A5%87%E0%A4%B7%E0%A4%A3" title="गणितीय बिस्लेषण – bihari" lang="bh" hreflang="bh" data-title="गणितीय बिस्लेषण" data-language-autonym="भोजपुरी" data-language-local-name="bihari" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.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%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математически анализ – bulgarsk" lang="bg" hreflang="bg" data-title="Математически анализ" data-language-autonym="Български" data-language-local-name="bulgarsk" 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/Matemati%C4%8Dka_analiza" title="Matematička analiza – bosnisk" lang="bs" hreflang="bs" data-title="Matematička analiza" data-language-autonym="Bosanski" data-language-local-name="bosnisk" 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/An%C3%A0lisi_matem%C3%A0tica" title="Anàlisi matemàtica – katalansk" lang="ca" hreflang="ca" data-title="Anàlisi matemàtica" data-language-autonym="Català" data-language-local-name="katalansk" 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%90%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0_%D0%BF%D0%B0%D0%B9%C4%95)" title="Анализ (математика пайĕ) – tsjuvansk" lang="cv" hreflang="cv" data-title="Анализ (математика пайĕ)" data-language-autonym="Чӑвашла" data-language-local-name="tsjuvansk" 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/Matematick%C3%A1_anal%C3%BDza" title="Matematická analýza – tsjekkisk" lang="cs" hreflang="cs" data-title="Matematická analýza" data-language-autonym="Čeština" data-language-local-name="tsjekkisk" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Analisa" title="Analisa – korsikansk" lang="co" hreflang="co" data-title="Analisa" data-language-autonym="Corsu" data-language-local-name="korsikansk" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Dadansoddiad_mathemategol" title="Dadansoddiad mathemategol – walisisk" lang="cy" hreflang="cy" data-title="Dadansoddiad mathemategol" data-language-autonym="Cymraeg" data-language-local-name="walisisk" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Analysis" title="Analysis – tysk" lang="de" hreflang="de" data-title="Analysis" data-language-autonym="Deutsch" data-language-local-name="tysk" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Matemaatiline_anal%C3%BC%C3%BCs" title="Matemaatiline analüüs – estisk" lang="et" hreflang="et" data-title="Matemaatiline analüüs" data-language-autonym="Eesti" data-language-local-name="estisk" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AE_%CE%B1%CE%BD%CE%AC%CE%BB%CF%85%CF%83%CE%B7" title="Μαθηματική ανάλυση – gresk" lang="el" hreflang="el" data-title="Μαθηματική ανάλυση" data-language-autonym="Ελληνικά" data-language-local-name="gresk" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mathematical_analysis" title="Mathematical analysis – engelsk" lang="en" hreflang="en" data-title="Mathematical analysis" data-language-autonym="English" data-language-local-name="engelsk" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/An%C3%A1lisis_matem%C3%A1tico" title="Análisis matemático – spansk" lang="es" hreflang="es" data-title="Análisis matemático" data-language-autonym="Español" data-language-local-name="spansk" 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/Analitiko" title="Analitiko – esperanto" lang="eo" hreflang="eo" data-title="Analitiko" 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/Analisi_matematiko" title="Analisi matematiko – baskisk" lang="eu" hreflang="eu" data-title="Analisi matematiko" data-language-autonym="Euskara" data-language-local-name="baskisk" 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%A2%D9%86%D8%A7%D9%84%DB%8C%D8%B2_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="آنالیز ریاضی – persisk" lang="fa" hreflang="fa" data-title="آنالیز ریاضی" data-language-autonym="فارسی" data-language-local-name="persisk" 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/Mathematical_analysis" title="Mathematical analysis – fijiansk hindi" lang="hif" hreflang="hif" data-title="Mathematical analysis" data-language-autonym="Fiji Hindi" data-language-local-name="fijiansk 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/Analyse_(math%C3%A9matiques)" title="Analyse (mathématiques) – fransk" lang="fr" hreflang="fr" data-title="Analyse (mathématiques)" data-language-autonym="Français" data-language-local-name="fransk" 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/Anail%C3%ADs_mhatamaitici%C3%BAil" title="Anailís mhatamaiticiúil – irsk" lang="ga" hreflang="ga" data-title="Anailís mhatamaiticiúil" data-language-autonym="Gaeilge" data-language-local-name="irsk" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Anailis_mhatamataigeach" title="Anailis mhatamataigeach – skotsk-gælisk" lang="gd" hreflang="gd" data-title="Anailis mhatamataigeach" data-language-autonym="Gàidhlig" data-language-local-name="skotsk-gælisk" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/An%C3%A1lise_matem%C3%A1tica" title="Análise matemática – galisisk" lang="gl" hreflang="gl" data-title="Análise matemática" data-language-autonym="Galego" data-language-local-name="galisisk" 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/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析 – gan" lang="gan" hreflang="gan" data-title="數學分析" 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-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%95%B4%EC%84%9D%ED%95%99_(%EC%88%98%ED%95%99)" title="해석학 (수학) – koreansk" lang="ko" hreflang="ko" data-title="해석학 (수학)" data-language-autonym="한국어" data-language-local-name="koreansk" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A1%D5%B6%D5%A1%D5%AC%D5%AB%D5%A6" title="Մաթեմատիկական անալիզ – armensk" lang="hy" hreflang="hy" data-title="Մաթեմատիկական անալիզ" data-language-autonym="Հայերեն" data-language-local-name="armensk" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A5%80%E0%A4%AF_%E0%A4%B5%E0%A4%BF%E0%A4%B6%E0%A5%8D%E0%A4%B2%E0%A5%87%E0%A4%B7%E0%A4%A3" title="गणितीय विश्लेषण – hindi" lang="hi" hreflang="hi" data-title="गणितीय विश्लेषण" 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/Matemati%C4%8Dka_analiza" title="Matematička analiza – kroatisk" lang="hr" hreflang="hr" data-title="Matematička analiza" data-language-autonym="Hrvatski" data-language-local-name="kroatisk" 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/Analitiko" title="Analitiko – ido" lang="io" hreflang="io" data-title="Analitiko" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Analisis_matematis" title="Analisis matematis – indonesisk" lang="id" hreflang="id" data-title="Analisis matematis" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesisk" 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/Analyse_(mathematica)" title="Analyse (mathematica) – interlingua" lang="ia" hreflang="ia" data-title="Analyse (mathematica)" 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/St%C3%A6r%C3%B0fr%C3%A6%C3%B0igreining" title="Stærðfræðigreining – islandsk" lang="is" hreflang="is" data-title="Stærðfræðigreining" data-language-autonym="Íslenska" data-language-local-name="islandsk" 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/Analisi_matematica" title="Analisi matematica – italiensk" lang="it" hreflang="it" data-title="Analisi matematica" data-language-autonym="Italiano" data-language-local-name="italiensk" 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%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%AA" title="אנליזה מתמטית – hebraisk" lang="he" hreflang="he" data-title="אנליזה מתמטית" data-language-autonym="עברית" data-language-local-name="hebraisk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B5%E0%B2%BF%E0%B2%B6%E0%B3%8D%E0%B2%B2%E0%B3%87%E0%B2%B7%E0%B2%A3_%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ವಿಶ್ಲೇಷಣ ಗಣಿತ – kannada" lang="kn" hreflang="kn" data-title="ವಿಶ್ಲೇಷಣ ಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%90%E1%83%9C%E1%83%90%E1%83%9A%E1%83%98%E1%83%96%E1%83%98" title="მათემატიკური ანალიზი – georgisk" lang="ka" hreflang="ka" data-title="მათემატიკური ანალიზი" data-language-autonym="ქართული" data-language-local-name="georgisk" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D1%82%D0%B0%D0%BB%D0%B4%D0%B0%D1%83" title="Математикалық талдау – kasakhisk" lang="kk" hreflang="kk" data-title="Математикалық талдау" data-language-autonym="Қазақша" data-language-local-name="kasakhisk" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Uchambuzi_wa_kihisabati" title="Uchambuzi wa kihisabati – swahili" lang="sw" hreflang="sw" data-title="Uchambuzi wa kihisabati" data-language-autonym="Kiswahili" data-language-local-name="swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Analiz_(mat%C3%A9matik)" title="Analiz (matématik) – franskguyansk kreol" lang="gcr" hreflang="gcr" data-title="Analiz (matématik)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="franskguyansk kreol" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D0%BA_%D1%82%D0%B0%D0%BB%D0%B4%D0%BE%D0%BE" title="Математикалык талдоо – kirgisisk" lang="ky" hreflang="ky" data-title="Математикалык талдоо" data-language-autonym="Кыргызча" data-language-local-name="kirgisisk" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%81%E0%BA%B2%E0%BA%99%E0%BA%A7%E0%BA%B4%E0%BB%80%E0%BA%84%E0%BA%B2%E0%BA%B0%E0%BA%97%E0%BA%B2%E0%BA%87%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94%E0%BA%AA%E0%BA%B2%E0%BA%94" title="ການວິເຄາະທາງຄະນິດສາດ – laotisk" lang="lo" hreflang="lo" data-title="ການວິເຄາະທາງຄະນິດສາດ" data-language-autonym="ລາວ" data-language-local-name="laotisk" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Analysis_mathematica" title="Analysis mathematica – latin" lang="la" hreflang="la" data-title="Analysis mathematica" 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/Matem%C4%81tisk%C4%81_anal%C4%ABze" title="Matemātiskā analīze – latvisk" lang="lv" hreflang="lv" data-title="Matemātiskā analīze" data-language-autonym="Latviešu" data-language-local-name="latvisk" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Analys_(Mathematik)" title="Analys (Mathematik) – luxemburgsk" lang="lb" hreflang="lb" data-title="Analys (Mathematik)" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxemburgsk" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Matematin%C4%97_analiz%C4%97" title="Matematinė analizė – litauisk" lang="lt" hreflang="lt" data-title="Matematinė analizė" data-language-autonym="Lietuvių" data-language-local-name="litauisk" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Analixi_matematica" title="Analixi matematica – ligurisk" lang="lij" hreflang="lij" data-title="Analixi matematica" data-language-autonym="Ligure" data-language-local-name="ligurisk" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Analise_matematical" title="Analise matematical – lingua franca nova" lang="lfn" hreflang="lfn" data-title="Analise matematical" 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-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Analisi_matematega" title="Analisi matematega – lombardisk" lang="lmo" hreflang="lmo" data-title="Analisi matematega" data-language-autonym="Lombard" data-language-local-name="lombardisk" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Matematikai_anal%C3%ADzis" title="Matematikai analízis – ungarsk" lang="hu" hreflang="hu" data-title="Matematikai analízis" data-language-autonym="Magyar" data-language-local-name="ungarsk" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0" title="Математичка анализа – makedonsk" lang="mk" hreflang="mk" data-title="Математичка анализа" data-language-autonym="Македонски" data-language-local-name="makedonsk" 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%85%E0%B4%A8%E0%B4%BE%E0%B4%B2%E0%B4%BF%E0%B4%B8%E0%B4%BF%E0%B4%B8%E0%B5%8D_(%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82)" title="അനാലിസിസ് (ഗണിതം) – malayalam" lang="ml" hreflang="ml" data-title="അനാലിസിസ് (ഗണിതം)" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Analisi_matematika" title="Analisi matematika – maltesisk" lang="mt" hreflang="mt" data-title="Analisi matematika" data-language-autonym="Malti" data-language-local-name="maltesisk" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Analisis_matematik" title="Analisis matematik – malayisk" lang="ms" hreflang="ms" data-title="Analisis matematik" data-language-autonym="Bahasa Melayu" data-language-local-name="malayisk" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/An%C3%A1leze_matem%C3%A1tica" title="Análeze matemática – mirandesisk" lang="mwl" hreflang="mwl" data-title="Análeze matemática" data-language-autonym="Mirandés" data-language-local-name="mirandesisk" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%81%E1%80%BD%E1%80%B2%E1%80%81%E1%80%BC%E1%80%99%E1%80%BA%E1%80%B8%E1%80%85%E1%80%AD%E1%80%90%E1%80%BA%E1%80%96%E1%80%BC%E1%80%AC%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="ခွဲခြမ်းစိတ်ဖြာသင်္ချာ – burmesisk" lang="my" hreflang="my" data-title="ခွဲခြမ်းစိတ်ဖြာသင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="burmesisk" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Analyse_(wiskunde)" title="Analyse (wiskunde) – nederlandsk" lang="nl" hreflang="nl" data-title="Analyse (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="nederlandsk" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%A7%A3%E6%9E%90%E5%AD%A6" title="解析学 – japansk" lang="ja" hreflang="ja" data-title="解析学" data-language-autonym="日本語" data-language-local-name="japansk" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Analysis" title="Analysis – nordfrisisk" lang="frr" hreflang="frr" data-title="Analysis" data-language-autonym="Nordfriisk" data-language-local-name="nordfrisisk" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Analisi_matematica" title="Analisi matematica – oksitansk" lang="oc" hreflang="oc" data-title="Analisi matematica" data-language-autonym="Occitan" data-language-local-name="oksitansk" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Matematik_analiz" title="Matematik analiz – usbekisk" lang="uz" hreflang="uz" data-title="Matematik analiz" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="usbekisk" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4_%E0%A8%B5%E0%A8%BF%E0%A8%B8%E0%A8%BC%E0%A8%B2%E0%A9%87%E0%A8%B8%E0%A8%BC%E0%A8%A3" title="ਗਣਿਤ ਵਿਸ਼ਲੇਸ਼ਣ – panjabi" lang="pa" hreflang="pa" data-title="ਗਣਿਤ ਵਿਸ਼ਲੇਸ਼ਣ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="panjabi" 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/%D9%85%DB%8C%D8%AA%DA%BE%D9%85%DB%8C%D9%B9%DB%8C%DA%A9%D9%84_%D8%A7%D9%86%DB%8C%D9%84%DB%8C%D8%B3%D8%B2" title="میتھمیٹیکل انیلیسز – vestpunjabi" lang="pnb" hreflang="pnb" data-title="میتھمیٹیکل انیلیسز" data-language-autonym="پنجابی" data-language-local-name="vestpunjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Matimatikal_analisis" title="Matimatikal analisis – jamaicansk kreolengelsk" lang="jam" hreflang="jam" data-title="Matimatikal analisis" data-language-autonym="Patois" data-language-local-name="jamaicansk kreolengelsk" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/An%C3%A0lisi_matem%C3%A0tica" title="Anàlisi matemàtica – piemontesisk" lang="pms" hreflang="pms" data-title="Anàlisi matemàtica" data-language-autonym="Piemontèis" data-language-local-name="piemontesisk" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Analysis" title="Analysis – lågtysk" lang="nds" hreflang="nds" data-title="Analysis" data-language-autonym="Plattdüütsch" data-language-local-name="lågtysk" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Analiza_matematyczna" title="Analiza matematyczna – polsk" lang="pl" hreflang="pl" data-title="Analiza matematyczna" data-language-autonym="Polski" data-language-local-name="polsk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/An%C3%A1lise_matem%C3%A1tica" title="Análise matemática – portugisisk" lang="pt" hreflang="pt" data-title="Análise matemática" data-language-autonym="Português" data-language-local-name="portugisisk" 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/Analiza_matematic%C4%83" title="Analiza matematică – rumensk" lang="ro" hreflang="ro" data-title="Analiza matematică" data-language-autonym="Română" data-language-local-name="rumensk" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D1%96%D1%87%D0%BD%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7%D0%B0" title="Математічна аналіза – rusinsk" lang="rue" hreflang="rue" data-title="Математічна аналіза" data-language-autonym="Русиньскый" data-language-local-name="rusinsk" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_(%D1%80%D0%B0%D0%B7%D0%B4%D0%B5%D0%BB_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B8)" title="Анализ (раздел математики) – russisk" lang="ru" hreflang="ru" data-title="Анализ (раздел математики)" data-language-autonym="Русский" data-language-local-name="russisk" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Mathematical_analysis" title="Mathematical analysis – skotsk" lang="sco" hreflang="sco" data-title="Mathematical analysis" data-language-autonym="Scots" data-language-local-name="skotsk" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Analiza_matematikore" title="Analiza matematikore – albansk" lang="sq" hreflang="sq" data-title="Analiza matematikore" data-language-autonym="Shqip" data-language-local-name="albansk" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/An%C3%A0lisi_(matim%C3%A0tica)" title="Anàlisi (matimàtica) – siciliansk" lang="scn" hreflang="scn" data-title="Anàlisi (matimàtica)" data-language-autonym="Sicilianu" data-language-local-name="siciliansk" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%B8%E0%B6%BA_%E0%B7%80%E0%B7%92%E0%B7%81%E0%B7%8A%E0%B6%BD%E0%B7%9A%E0%B7%82%E0%B6%AB%E0%B6%BA" title="ගණිතමය විශ්ලේෂණය – singalesisk" lang="si" hreflang="si" data-title="ගණිතමය විශ්ලේෂණය" data-language-autonym="සිංහල" data-language-local-name="singalesisk" 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/Mathematical_analysis" title="Mathematical analysis – enkel engelsk" lang="en-simple" hreflang="en-simple" data-title="Mathematical analysis" data-language-autonym="Simple English" data-language-local-name="enkel engelsk" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Matematick%C3%A1_anal%C3%BDza" title="Matematická analýza – slovakisk" lang="sk" hreflang="sk" data-title="Matematická analýza" data-language-autonym="Slovenčina" data-language-local-name="slovakisk" 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/Matemati%C4%8Dna_analiza" title="Matematična analiza – slovensk" lang="sl" hreflang="sl" data-title="Matematična analiza" data-language-autonym="Slovenščina" data-language-local-name="slovensk" 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%B4%DB%8C%DA%A9%D8%A7%D8%B1%DB%8C%DB%8C_%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9%DB%8C" title="شیکاریی ماتماتیکی – sorani" lang="ckb" hreflang="ckb" data-title="شیکاریی ماتماتیکی" data-language-autonym="کوردی" data-language-local-name="sorani" 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/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7%D0%B0" title="Математичка анализа – serbisk" lang="sr" hreflang="sr" data-title="Математичка анализа" data-language-autonym="Српски / srpski" data-language-local-name="serbisk" 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/Matemati%C4%8Dka_analiza" title="Matematička analiza – serbokroatisk" lang="sh" hreflang="sh" data-title="Matematička analiza" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroatisk" 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/Analyysi_(matematiikka)" title="Analyysi (matematiikka) – finsk" lang="fi" hreflang="fi" data-title="Analyysi (matematiikka)" data-language-autonym="Suomi" data-language-local-name="finsk" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Pagsusuring_matematikal" title="Pagsusuring matematikal – tagalog" lang="tl" hreflang="tl" data-title="Pagsusuring matematikal" 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%AA%E0%AE%95%E0%AF%81%E0%AE%B5%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="பகுவியல் (கணிதம்) – tamil" lang="ta" hreflang="ta" data-title="பகுவியல் (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Математик анализ – tatarisk" lang="tt" hreflang="tt" data-title="Математик анализ" data-language-autonym="Татарча / tatarça" data-language-local-name="tatarisk" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A7%E0%B8%B4%E0%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B2%E0%B8%B0%E0%B8%AB%E0%B9%8C" title="คณิตวิเคราะห์ – thai" lang="th" hreflang="th" data-title="คณิตวิเคราะห์" data-language-autonym="ไทย" data-language-local-name="thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Analiz_(matematik)" title="Analiz (matematik) – tyrkisk" lang="tr" hreflang="tr" data-title="Analiz (matematik)" data-language-autonym="Türkçe" data-language-local-name="tyrkisk" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Analiz" title="Analiz – turkmensk" lang="tk" hreflang="tk" data-title="Analiz" data-language-autonym="Türkmençe" data-language-local-name="turkmensk" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Математичний аналіз – ukrainsk" lang="uk" hreflang="uk" data-title="Математичний аналіз" data-language-autonym="Українська" data-language-local-name="ukrainsk" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA%DB%8C_%D8%AA%D8%AD%D9%84%DB%8C%D9%84" title="ریاضیاتی تحلیل – urdu" lang="ur" hreflang="ur" data-title="ریاضیاتی تحلیل" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/An%C3%A0%C5%82ixi_matem%C3%A0tica" title="Anàłixi matemàtica – venetiansk" lang="vec" hreflang="vec" data-title="Anàłixi matemàtica" data-language-autonym="Vèneto" data-language-local-name="venetiansk" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Analiz_(matematikan_jaguz)" title="Analiz (matematikan jaguz) – vepsisk" lang="vep" hreflang="vep" data-title="Analiz (matematikan jaguz)" data-language-autonym="Vepsän kel’" data-language-local-name="vepsisk" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Gi%E1%BA%A3i_t%C3%ADch_to%C3%A1n_h%E1%BB%8Dc" title="Giải tích toán học – vietnamesisk" lang="vi" hreflang="vi" data-title="Giải tích toán học" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesisk" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%88%86%E6%9E%90%E5%AD%B8" title="分析學 – klassisk kinesisk" lang="lzh" hreflang="lzh" data-title="分析學" data-language-autonym="文言" data-language-local-name="klassisk kinesisk" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Analisis_matematikal" title="Analisis matematikal – waray" lang="war" hreflang="war" data-title="Analisis matematikal" data-language-autonym="Winaray" data-language-local-name="waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90" title="数学分析 – wu" lang="wuu" hreflang="wuu" data-title="数学分析" data-language-autonym="吴语" data-language-local-name="wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Vukambisisi_bya_Dyondzo-Tinhlayo" title="Vukambisisi bya Dyondzo-Tinhlayo – tsonga" lang="ts" hreflang="ts" data-title="Vukambisisi bya Dyondzo-Tinhlayo" data-language-autonym="Xitsonga" data-language-local-name="tsonga" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%9E%D7%90%D7%98%D7%A2%D7%9E%D7%90%D7%98%D7%99%D7%A9%D7%A2%D7%A8_%D7%90%D7%A0%D7%90%D7%9C%D7%99%D7%96" title="מאטעמאטישער אנאליז – jiddisk" lang="yi" hreflang="yi" data-title="מאטעמאטישער אנאליז" data-language-autonym="ייִדיש" data-language-local-name="jiddisk" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/%C3%8Ct%C3%BAw%C3%B2_Mathim%C3%A1t%C3%AD%C3%ACk%C3%AC" title="Ìtúwò Mathimátíìkì – joruba" lang="yo" hreflang="yo" data-title="Ìtúwò Mathimátíìkì" data-language-autonym="Yorùbá" data-language-local-name="joruba" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析 – kantonesisk" lang="yue" hreflang="yue" data-title="數學分析" data-language-autonym="粵語" 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<b>analyse</b>) er eit av hovudområda i <a href="/wiki/Matematikk" title="Matematikk">matematikken</a> og omfattar i den vidaste forstanden heile den matematiske utviklinga som har utgangspunktet i oppdaginga til <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> og <a href="/wiki/Gottfried_Wilhelm_Leibniz" class="mw-redirect" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a> av <a href="/wiki/Differensialrekning" title="Differensialrekning">differensial</a>- og <a href="/wiki/Integral" title="Integral">integralrekninga</a> mot slutten av 1600-talet. Sidan den gong har det voks fram fleire meir eller mindre fråskilde felt innanfor matematisk analyse. Desse omfattar mellom andre <a href="/w/index.php?title=Uendeleg_rekkje&action=edit&redlink=1" class="new" title="Uendeleg rekkje (sida finst ikkje)">uendelege rekkjer</a>, <a href="/wiki/Variasjonsrekning" title="Variasjonsrekning">variasjonsrekning</a>, <a href="/wiki/Differensiallikning" title="Differensiallikning">differensiallikningar</a>, <a href="/w/index.php?title=Fourieranalyse&action=edit&redlink=1" class="new" title="Fourieranalyse (sida finst ikkje)">Fourieranalyse</a>, <a href="/w/index.php?title=Kompleks_analyse&action=edit&redlink=1" class="new" title="Kompleks analyse (sida finst ikkje)">kompleks analyse</a>, <a href="/wiki/Vektor" title="Vektor">vektor</a>- og <a href="/wiki/Tensor" title="Tensor">tensoranalyse</a>, <a href="/wiki/M%C3%A5lteori" title="Målteori">mål-</a> og <a href="/wiki/Integrasjon" class="mw-disambig" title="Integrasjon">integrasjonsteori</a> og <a href="/wiki/Funksjonalanalyse" title="Funksjonalanalyse">funksjonalanalyse</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historia_til_analysen">Historia til analysen</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_analyse&veaction=edit&section=1" title="Endre bolk: Historia til analysen" class="mw-editsection-visualeditor"><span>endre</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_analyse&action=edit&section=1" title="Rediger kildekoden til seksjonen Historia til analysen"><span>endre wikiteksten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Historikarar reknar med at matematisk analyse har røtene sine heilt tilbake til matematikarane i <a href="/wiki/Den_greske_antikken" class="mw-redirect" title="Den greske antikken">den greske antikken</a>. Den <a href="/wiki/Hellenismen" class="mw-redirect" title="Hellenismen">hellenistiske</a> matematikaren <a href="/w/index.php?title=Eudoksos_fr%C3%A5_Knidos&action=edit&redlink=1" class="new" title="Eudoksos frå Knidos (sida finst ikkje)">Eudoxos</a> hadde blant anna ein metode for å rekne ut areal av flater og volum av lekamar, som blir rekna som ein tidleg forløpar for integrasjon. <a href="/wiki/Arkimedes" title="Arkimedes">Arkimedes</a> utvikla desse ideane vidare til ein <a href="/wiki/Heuristikk" title="Heuristikk">heuristikk</a> som minner om integralrekning. Etter Arkimedes skjedde ikkje noko viktig med utviklinga av analysen på nærare 500 år.<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>I <a href="/wiki/499" title="499">499</a> brukte den indiske matematikaren og astronomen <a href="/wiki/Aryabhata" title="Aryabhata">Aryabhata</a> <a href="/w/index.php?title=Infinitesimal&action=edit&redlink=1" class="new" title="Infinitesimal (sida finst ikkje)">infinitesimalar</a>, og han uttrykte òg eit astronomisk problem som ei <a href="/wiki/Differensiallikning" title="Differensiallikning">differensiallikning</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> Denne differensiallikninga vart utvikla vidare i ein kommentar av Manjula på <a href="/wiki/900-talet" title="900-talet">900-talet</a>, og til slutt leia denne differensiallikninga <a href="/wiki/Bhaskara" title="Bhaskara">Bhaskara</a> til å utvikle ei rekkje grunnleggjande idear i matematisk analyse på <a href="/wiki/1100-talet" title="1100-talet">1100-talet</a>. Bhaskara var òg den første som definerte den deriverte som ein grenseverdi. </p><p>Sjølv om den matematiske analysen altså har røtene sine heilt tilbake i oldtida, er det først på midten av <a href="/wiki/1600-talet" title="1600-talet">1600-talet</a> at dei meir generelle teknikkane knytte til grenser og infinitesimalar dukkar opp. Då <a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Fermat</a> og <a href="/wiki/Descartes" class="mw-redirect" title="Descartes">Descartes</a> grunnla den <a href="/wiki/Analytisk_geometri" title="Analytisk geometri">analytiske geometrien</a> i <a href="/wiki/1637" title="1637">1637</a> fekk ein òg eit verktøy for å gjere meir omfattande utrekningar for generelle kurvar. Desse oppdagingane leia både Fermat og Descartes til å utvikle reknemetodar for å studere maksimalverdiar og <a href="/w/index.php?title=Tangent_i_matematikk&action=edit&redlink=1" class="new" title="Tangent i matematikk (sida finst ikkje)">tangentar</a>.<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> </p><p>I åra etter var det fleire som jobba med problem knytte til tangentar, men fullstendige derivasjonsteoriar slik vi kjenner dei i dag vart først utvikla av <a href="/wiki/Isaac_Newton" title="Isaac Newton">Isaac Newton</a> og <a href="/wiki/Gottfried_Wilhelm_Leibniz" class="mw-redirect" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a>. Dei to oppdaga òg samanhengen mellom <a href="/wiki/Integrasjon" class="mw-disambig" title="Integrasjon">integrasjon</a> og <a href="/wiki/Derivasjon" title="Derivasjon">derivasjon</a>, og dei gjorde sine oppdaginga uavhengig av kvarandre og omtrent samstundes. Begge blir rekna som grunnleggjarar av den matematiske analysen.<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> <div class="mw-heading mw-heading2"><h2 id="Derivasjon">Derivasjon</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_analyse&veaction=edit&section=2" title="Endre bolk: Derivasjon" class="mw-editsection-visualeditor"><span>endre</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_analyse&action=edit&section=2" title="Rediger kildekoden til seksjonen Derivasjon"><span>endre wikiteksten</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="boilerplate seealso"> <dl><dd><i>For meir om dette emnet, sjå <a href="/wiki/Derivasjon" title="Derivasjon">derivasjon</a>.</i></dd></dl></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Derivative.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Derivative.svg/220px-Derivative.svg.png" decoding="async" width="220" height="244" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/18/Derivative.svg/330px-Derivative.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/18/Derivative.svg/440px-Derivative.svg.png 2x" data-file-width="1158" data-file-height="1282" /></a><figcaption>Den deriverte til ein kurve definert ved ein funksjon <i>f</i>(<i>x</i>) kan sjåast på som stigninga til sekanten mellom to punkt som skjer kurven i <i>x</i> og <i>x+h</i>, og så lét avstanden <i>h</i> mellom dei to punkta bli mindre og mindre.</figcaption></figure> <p>Den deriverte gjev den momentane endringa til ein <a href="/wiki/Funksjon_i_matematikk" class="mw-redirect" title="Funksjon i matematikk">funksjon</a> (<i>f</i>(<i>x</i>)) per endring av <a href="/w/index.php?title=Funksjonsargument&action=edit&redlink=1" class="new" title="Funksjonsargument (sida finst ikkje)">funksjonsargumentet</a> (<i>x</i>). For reelle funksjonar av ein variabel blir kalla dette verdien for stigningstalet til funksjonen. Stigningstalet er definert som stigninga til <a href="/w/index.php?title=Tangent_i_matematikk&action=edit&redlink=1" class="new" title="Tangent i matematikk (sida finst ikkje)">tangenten</a> til funksjonen i punktet og kan estimerast ved hjelp av <a href="/wiki/Sekant" title="Sekant">sekantar</a>. Ein viktig spurnad knytt til om ein funksjon er deriverbar eller ikkje er om han er kontinuerleg overalt. Ikkje alle funksjonar er deriverbare overalt. Til dømes kan ein funksjon vere diskontinuerleg eller ha ein <a href="/wiki/Loddrett" title="Loddrett">loddrett</a> tangent i eit punkt, og då vil den deriverte vere udefinert for dette punktet. </p><p>Dersom vi har ein funksjon <i>f</i> som kan definerast i ein omegn omkring punktet <i>x</i>, seier vi at <i>f</i> er deriverbar i <i>x</i> dersom følgjande grenseverdi eksisterer: </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\rightarrow 0}{\frac {f(x+h)-f(x)}{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>x</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>h</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/388ce6baa60ed9162895159b88c96ec129d61cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.49ex; height:5.843ex;" alt="{\displaystyle \lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}}}"></span></dd></dl> <p>Her er <i>h</i> avstanden mellom punktet x og eit anna punkt som vi vil ha nærmast mogleg x, ved å senke h mot 0. Vi skriv det slik: </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 f'(x)=\lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>f</mi> <mo>′</mo> </msup> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <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> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>+</mo> <mi>h</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mi>h</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f'(x)=\lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8021906a3114c8ac58b486ef744058c198fa2483" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:28.733ex; height:5.843ex;" alt="{\displaystyle f'(x)=\lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}}}"></span></dd></dl> <p>og vi kallar denne storleiken for den deriverte til <i>f</i> i punktet <i>x</i>.<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> </p><p>Derivasjon er eit sentralt emne i matematisk analyse, og det blir mykje brukt i samband med kurvedrøfting. Ved hjelp av ulike teknikkar knytte til derivasjon, kan vi blant anna finne maksimums- og minimumspunkt for kurvar. Vi skil mellom globalt maksimum og minimum, som er absolutte maksimums- og minimumspunkt på ein kurve, og lokale maksimum og minimum. Andre eigenskapar ved kurvar som vi kan analysere ved hjelp av derivasjon er i kva grad ei kurve er <a href="/wiki/Konveks" class="mw-disambig" title="Konveks">konveks</a> eller <a href="/wiki/Konkav" class="mw-disambig" title="Konkav">konkav</a> innanfor eit bestemt intervall, og vi kan òg bruke derivasjon til å avgjere eventuelle <a href="/wiki/Asymptote" title="Asymptote">asymptoter</a> til ein kurve. </p> <div class="mw-heading mw-heading2"><h2 id="Integrasjon">Integrasjon</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_analyse&veaction=edit&section=3" title="Endre bolk: Integrasjon" class="mw-editsection-visualeditor"><span>endre</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_analyse&action=edit&section=3" title="Rediger kildekoden til seksjonen Integrasjon"><span>endre wikiteksten</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="boilerplate seealso"> <dl><dd><i>For meir om dette emnet, sjå <a href="/wiki/Integrasjon" class="mw-disambig" title="Integrasjon">integrasjon</a>.</i></dd></dl></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fil:Integral_as_region_under_curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/220px-Integral_as_region_under_curve.svg.png" decoding="async" width="220" height="205" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/330px-Integral_as_region_under_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/440px-Integral_as_region_under_curve.svg.png 2x" data-file-width="750" data-file-height="700" /></a><figcaption>Integrasjon kan sjåast på som utrekning av arealet under ein kurve definert ved <i>f</i>(<i>x</i>), mellom to punkt (her <i>a</i> og <i>b</i>), ved å dele opp området i stadig mindre delar og såg summere desse delar.</figcaption></figure> <p>Heilt frå ganske tidleg i historia til menneskja har det knytte seg interesse i å finne storleiken til ulike geometriske objekt. Så lenge figurane har rette kantar og flatar kan slike problem løysast ganske lett, men når kantar og flater er krumme blir problema straks mykje vanskelegare. Integrasjon kan blant anna brukast til å gjere utrekningar av areal og volum. </p><p>Prosessen for å finne integralet kallast integrasjon, og i den enklaste forma si dreier det seg om å derivere baklengs. Nokre funksjonar er så uregelmessige at det ikkje er mogleg å definere arealet under grafen ved hjelp av integrasjonsteknikkar, men det finst òg ulike tilnærmingsteknikkar for å finne integralet til slike funksjonar. Ei setning i analysen seier at kvar og ein <b>monoton</b> funksjon er integrerbar.<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> <div class="mw-heading mw-heading3"><h3 id="Analysen_sitt_fundamentalteorem">Analysen sitt fundamentalteorem</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_analyse&veaction=edit&section=4" title="Endre bolk: Analysen sitt fundamentalteorem" class="mw-editsection-visualeditor"><span>endre</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_analyse&action=edit&section=4" title="Rediger kildekoden til seksjonen Analysen sitt fundamentalteorem"><span>endre wikiteksten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den grunnleggjande oppdaginga til Newton og Leibniz var at integrasjon og derivasjon var omvende rekningsartar. Dermed kunne ein løyse integrasjonsoppgåver ved å finne den antideriverte, i staden for å bruke arbeidskrevjande summasjonar, slik ein hadde gjort tidlegare. Det teoretiske grunnlaget for denne metoden finn vi i det som blir kalla <a href="/w/index.php?title=Analysen_sitt_fundamentalteorem&action=edit&redlink=1" class="new" title="Analysen sitt fundamentalteorem (sida finst ikkje)">analysen sitt fundamentalteorem</a>. </p><p>Kort fortalt går dette teoremet ut på at dersom funksjonen <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 f:[a,b]\rightarrow \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:[a,b]\rightarrow \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc0d2d0b70573525d149ab82948308455d1853d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.063ex; height:2.843ex;" alt="{\displaystyle f:[a,b]\rightarrow \mathbb {R} }"></span> er kontinuerleg, så er <i>f</i> integrerbar på eit kvart intervall innanfor dette området (frå og med a, til og med b). Då er følgjande funksjon deriverbar: </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 F(x)=\int _{a}^{x}f(t)\,dt}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <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> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F(x)=\int _{a}^{x}f(t)\,dt}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d4c32a77cf12a8000f39c3cbebc1acdf6ff7f5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.372ex; height:5.843ex;" alt="{\displaystyle F(x)=\int _{a}^{x}f(t)\,dt}"></span></dd></dl> <p>Og den deriverte til funksjonen <i>F(x)</i> blir då lik <i>f(x)</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Kjelder">Kjelder</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_analyse&veaction=edit&section=5" title="Endre bolk: Kjelder" class="mw-editsection-visualeditor"><span>endre</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_analyse&action=edit&section=5" title="Rediger kildekoden til seksjonen Kjelder"><span>endre wikiteksten</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small"> <ul><li><i>Denne artikkelen bygger på «<a href="https://no.wikipedia.org/wiki/Matematisk_analyse" class="extiw" title="nb:Matematisk analyse">Matematisk analyse</a>» frå <a href="https://no.wikipedia.org/wiki/Hovedside" class="extiw" title="nb:Hovedside">Wikipedia på bokmål</a>, den 28. oktober 2011.</i> <ul><li><i><a href="https://no.wikipedia.org/wiki/Hovedside" class="extiw" title="nb:Hovedside">Wikipedia på bokmål</a> oppgav desse kjeldene:</i></li></ul></li> <li><cite class="citation book">Katz, Victor J. (1998). <i>A history of mathematics: an introduction</i>. Reading, Mass.: Addison-Wesley Longman. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Spesial:Bokkjelder/0-321-01618-1" title="Spesial:Bokkjelder/0-321-01618-1">0-321-01618-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fnn.wikipedia.org%3AMatematisk+analyse&rft.au=Katz%2C+Victor+J.&rft.btitle=A+history+of+mathematics%3A+an+introduction.&rft.date=1998&rft.genre=book&rft.isbn=0-321-01618-1&rft.place=Reading%2C+Mass.&rft.pub=Addison-Wesley+Longman&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <ul><li><cite class="citation book">Lindstrøm, Tom (1995). <i>Kalkulus</i>. Oslo: Universitetsforlaget. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Spesial:Bokkjelder/82-00-22823-1" title="Spesial:Bokkjelder/82-00-22823-1">82-00-22823-1</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fnn.wikipedia.org%3AMatematisk+analyse&rft.au=Lindstr%C3%B8m%2C+Tom&rft.btitle=Kalkulus.&rft.date=1995&rft.genre=book&rft.isbn=82-00-22823-1&rft.place=Oslo&rft.pub=Universitetsforlaget&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <ul><li><cite class="citation book">Sydsæter, Knut (1994). <i>Matematisk analyse</i>. Oslo: Universitetsforlaget. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Spesial:Bokkjelder/82-00-21461-3" title="Spesial:Bokkjelder/82-00-21461-3">82-00-21461-3</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fnn.wikipedia.org%3AMatematisk+analyse&rft.au=Syds%C3%A6ter%2C+Knut&rft.btitle=Matematisk+analyse.&rft.date=1994&rft.genre=book&rft.isbn=82-00-21461-3&rft.place=Oslo&rft.pub=Universitetsforlaget&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r3318915">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.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"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Archimedes, <i>Method</i>, i The Works of Archimedes <a href="/wiki/Spesial:Bokkjelder/9780521661607" class="internal mw-magiclink-isbn">ISBN 978-0-521-66160-7</a></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www-history.mcs.st-andrews.ac.uk/Biographies/Aryabhata_i.html">Aryabhata den eldre</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Lindstrøm, 1995, s. 260</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Lindstrøm, 1995, s. 378</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Lindstrøm, 1995, s. 220</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Lindstrøm, 1995, s. 326</span> </li> </ol></div></div> </div> <div class="mw-heading mw-heading2"><h2 id="Bakgrunnsstoff">Bakgrunnsstoff</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematisk_analyse&veaction=edit&section=6" title="Endre bolk: Bakgrunnsstoff" class="mw-editsection-visualeditor"><span>endre</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematisk_analyse&action=edit&section=6" title="Rediger kildekoden til seksjonen Bakgrunnsstoff"><span>endre wikiteksten</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://home.hia.no/~cornelib/animasjon/matematikk/digivitalis/derivasjon-integrasjon.htm">Animasjonar knytte til derivasjon og integrasjon</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20061215000009/http://home.hia.no/%7Ecornelib/animasjon/matematikk/digivitalis/derivasjon-integrasjon.htm">Arkivert</a> 2006-12-15 ved <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</li> <li><a rel="nofollow" class="external text" href="http://www.matematikk.net/klassetrinn/2MX/anvendtderivasjon.php">Bruk av derivasjon</a></li> <li><a rel="nofollow" class="external text" href="http://www.uio.no/studier/emner/matnat/math/MAT-INF1100/h04/undervisningsmateriale/num-int-der.pdf"><i>Litt om numerisk integrasjon og derivasjon</i>, av Knut Mørken (UiO)</a></li></ul> <p><b>Bøker på nettet (engelsk)</b> </p> <ul><li><a rel="nofollow" class="external text" href="http://ocw.mit.edu/ans7870/resources/Strang/strangtext.htm">Calculus</a> av Gilbert Strang. (Publisert i 1991 av Wellesley-Cambridge Press)</li> <li><a rel="nofollow" class="external text" href="http://www.lightandmatter.com/calc/calc.pdf">Calculus (pdf)</a> av Benjamin Crowell</li> <li><a rel="nofollow" class="external text" href="http://www.understandingcalculus.com/">Understanding Calculus</a> av Faraz Hussain</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r3515230">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output 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