CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="mt" dir="ltr"> <head> <meta charset="UTF-8"> <title>Kalkulu tal-varjazzjonijiet - Wikipedija</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )mtwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"dmy", "wgMonthNames":["","Jannar","Frar","Marzu","April","Mejju","Ġunju","Lulju","Awwissu","Settembru","Ottubru","Novembru","Diċembru"],"wgRequestId":"581843a9-c92f-4435-9066-e914fc7c7e24","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"Kalkulu_tal-varjazzjonijiet","wgTitle":"Kalkulu tal-varjazzjonijiet","wgCurRevisionId":298902,"wgRevisionId":298902,"wgArticleId":6802,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["Matematika","Analisi matematika"],"wgPageViewLanguage":"mt","wgPageContentLanguage":"mt","wgPageContentModel":"wikitext","wgRelevantPageName":"Kalkulu_tal-varjazzjonijiet","wgRelevantArticleId":6802,"wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0, "wgVisualEditor":{"pageLanguageCode":"mt","pageLanguageDir":"ltr","pageVariantFallbacks":"mt"},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":5000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q216861","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false,"wgSiteNoticeId":"2.0"};RLSTATE={"ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready" ,"user.options":"loading","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready","ext.dismissableSiteNotice.styles":"ready"};RLPAGEMODULES=["site","mediawiki.page.ready","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking","ext.dismissableSiteNotice"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=mt&modules=ext.dismissableSiteNotice.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=mt&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=mt&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="Kalkulu tal-varjazzjonijiet - Wikipedija"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//mt.m.wikipedia.org/wiki/Kalkulu_tal-varjazzjonijiet"> <link rel="alternate" type="application/x-wiki" title="Editja" href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedija (mt)"> <link rel="EditURI" type="application/rsd+xml" href="//mt.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://mt.wikipedia.org/wiki/Kalkulu_tal-varjazzjonijiet"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.mt"> <link rel="alternate" type="application/atom+xml" title="Feed Atom ta' Wikipedija" href="/w/index.php?title=Spe%C4%8Bjali:TibdilRi%C4%8Benti&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-Kalkulu_tal-varjazzjonijiet rootpage-Kalkulu_tal-varjazzjonijiet skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">Aqbeż għall-kontentut</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="Sit"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="Menu prinċipali" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-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-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Menu prinċipali</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Menu prinċipali</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">mexxi għall-ġenb</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">aħbi</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigazzjoni </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Il-Pa%C4%A1na_prin%C4%8Bipali" title="Żur il-paġna prinċipali [z]" accesskey="z"><span>Il-Paġna prinċipali</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Spe%C4%8Bjali:TibdilRi%C4%8Benti" title="Lista tal-bidliet riċenti fil-wiki [r]" accesskey="r"><span>Bidliet riċenti</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Spe%C4%8Bjali:Pa%C4%A1naKwalunkwe" title="Uri paġna kwalunkwe [x]" accesskey="x"><span>Paġna kwalunkwe</span></a></li> </ul> </div> </div> <div id="p-community" class="vector-menu mw-portlet mw-portlet-community" > <div class="vector-menu-heading"> Komunità </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-aboutsite" class="mw-list-item"><a href="/wiki/About-url" title="Kun af aktar fuq il-Wikipedija"><span>Dwar il-Wikipedija</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedija:Kuntatt" title="Kif tagħmel kuntatt mal-Wikipedija"><span>Kuntatt</span></a></li><li id="n-Avvenimenti-riċenti" class="mw-list-item"><a href="/wiki/Wikipedija:L-a%C4%A7%C4%A7ar_a%C4%A7barijiet"><span>Avvenimenti riċenti</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikipedija:Pjazza" title="Iddiskuti fuq il-Wikipedija"><span>Pjazza</span></a></li><li id="n-help" class="mw-list-item"><a href="https://www.mediawiki.org/wiki/Special:MyLanguage/Help:Contents" title="Gwida fuq kif tuża' u timmodifika 'l-Wikipedija"><span>Għajnuna</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Il-Pa%C4%A1na_prin%C4%8Bipali" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedija" src="/static/images/mobile/copyright/wikipedia-wordmark-mt.svg" style="width: 7.5em; height: 1.375em;"> <img class="mw-logo-tagline" alt="L-enċiklopedija l-ħielsa" src="/static/images/mobile/copyright/wikipedia-tagline-mt.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Spe%C4%8Bjali:Fittex" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Fittex fis-sit: Wikipedija [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Fittex</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Fittex fis-sit: Wikipedija" aria-label="Fittex fis-sit: Wikipedija" autocapitalize="sentences" title="Fittex fis-sit: Wikipedija [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Speċjali:Fittex"> </div> <button class="cdx-button cdx-search-input__end-button">Fittex</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Għodda personali"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Dehra"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Dehra" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Dehra</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_mt.wikipedia.org&uselang=mt" class=""><span>Donazzjonijiet</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spe%C4%8Bjali:O%C4%A7loqKont&returnto=Kalkulu+tal-varjazzjonijiet" title="Nagħtuk parir toħloq kont u tidħol fih; però dan mhux obligatorju." class=""><span>Oħloq kont</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Spe%C4%8Bjali:UtentD%C4%A7ul&returnto=Kalkulu+tal-varjazzjonijiet" title="Inħeġġuk tidħol fil-kont tiegħek, għalkemm dan mhux obbligatorju [o]" accesskey="o" class=""><span>Idħol</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Aktar għażliet" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Għodda personali" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Għodda personali</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_mt.wikipedia.org&uselang=mt"><span>Donazzjonijiet</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spe%C4%8Bjali:O%C4%A7loqKont&returnto=Kalkulu+tal-varjazzjonijiet" title="Nagħtuk parir toħloq kont u tidħol fih; però dan mhux obligatorju."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Oħloq kont</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Spe%C4%8Bjali:UtentD%C4%A7ul&returnto=Kalkulu+tal-varjazzjonijiet" title="Inħeġġuk tidħol fil-kont tiegħek, għalkemm dan mhux obbligatorju [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Idħol</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Il-paġni għal edituri anonimi <a href="/wiki/G%C4%A7ajnuna:Introduction" aria-label="Tgħallem iktar dwar kif timmodifika"><span>kun af aktar</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Spe%C4%8Bjali:KontribuzzjonijietTieg%C4%A7i" title="A list of edits made from this IP address [y]" accesskey="y"><span>Kontribuzzjonijiet</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spe%C4%8Bjali:DiskussjonijietTieg%C4%A7i" title="Diskussjoni dwar il-modifiki magħmula minn dan l-indirizz tal-IP [n]" accesskey="n"><span>Diskussjoni</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><div id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eaħbi\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"sitenotice\" lang=\"mt\" dir=\"ltr\"\u003E\u003Cdiv class=\"plainlinks\" style=\"background:white;width:100%; padding: 0.5ex; margin: 0 0 5px;font-family: -apple-system, BlinkMacSystemFont, \u0026#39;Segoe UI\u0026#39;, Roboto, Helvetica, Arial, sans-serif, \u0026#39;Apple Color Emoji\u0026#39;, \u0026#39;Segoe UI Emoji\u0026#39;, \u0026#39;Segoe UI Symbol\u0026#39;; text-align: center; font-size: 16pt; color: grey\"\u003E\u003Cp style=\"font-size: 10.5pt\"\u003EŻomm ruħek aġġornat mal-attivitajiet ta' \u003Ca rel=\"nofollow\" class=\"external text\" href=\"http://www.wikimalta.org\"\u003E\u003Cspan style=\"color:#3b5998; font-weight:bolder;\"\u003EWikimedia Community Malta\u003C/span\u003E\u003C/a\u003E, għaqda bl-għan li tgħin fit-titjib tal-Wikipedija Maltija.\u003C/p\u003E\n\u003Cdiv style=\"clear: both;\"\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E\u003C/div\u003E";}}());</script></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Sit"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Kontenut" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Kontenut</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mexxi għall-ġenb</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">aħbi</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Bidu</div> </a> </li> <li id="toc-Paġni_li_għandhom_x’jaqsmu" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Paġni_li_għandhom_x’jaqsmu"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Paġni li għandhom x’jaqsmu</span> </div> </a> <ul id="toc-Paġni_li_għandhom_x’jaqsmu-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ħoloq_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ħoloq_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Ħoloq esterni</span> </div> </a> <ul id="toc-Ħoloq_esterni-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibljografija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibljografija"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Bibljografija</span> </div> </a> <ul id="toc-Bibljografija-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="Kontenut" 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="Aħbi jew uri l-werrej" > <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">Aħbi jew uri l-werrej</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">Kalkulu tal-varjazzjonijiet</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="Żur artiklu f'lingwa differenti. Disponibbli fi 45 lingwi" > <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-45" 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">45 lingwi</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AD%D8%B3%D8%A7%D8%A8_%D8%A7%D9%84%D9%85%D8%AA%D8%BA%D9%8A%D8%B1%D8%A7%D8%AA" title="حساب المتغيرات – Għarbi" lang="ar" hreflang="ar" data-title="حساب المتغيرات" data-language-autonym="العربية" data-language-local-name="Għarbi" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/C%C3%A1lculu_de_variaciones" title="Cálculu de variaciones – Asturian" lang="ast" hreflang="ast" data-title="Cálculu de variaciones" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%92%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D0%B0%D0%BB%D1%8B_%D0%B8%D2%AB%D3%99%D0%BF%D0%BB%D3%99%D0%BC%D3%99" title="Вариациалы иҫәпләмә – Bashkir" lang="ba" hreflang="ba" data-title="Вариациалы иҫәпләмә" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" 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%92%D0%B0%D1%80%D1%8B%D1%8F%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D0%B5_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D0%B5" title="Варыяцыйнае злічэнне – Belarussu" lang="be" hreflang="be" data-title="Варыяцыйнае злічэнне" data-language-autonym="Беларуская" data-language-local-name="Belarussu" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%BE_%D1%81%D0%BC%D1%8F%D1%82%D0%B0%D0%BD%D0%B5" title="Вариационно смятане – Bulgaru" lang="bg" hreflang="bg" data-title="Вариационно смятане" data-language-autonym="Български" data-language-local-name="Bulgaru" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/C%C3%A0lcul_de_variacions" title="Càlcul de variacions – Katalan" lang="ca" hreflang="ca" data-title="Càlcul de variacions" data-language-autonym="Català" data-language-local-name="Katalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Varia%C4%8Dn%C3%AD_po%C4%8Det" title="Variační počet – Ċek" lang="cs" hreflang="cs" data-title="Variační počet" data-language-autonym="Čeština" data-language-local-name="Ċek" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%92%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D0%BB%D0%BB%D0%B5_%D1%88%D1%83%D1%82%D0%BB%D0%B0%D0%B2" title="Вариацилле шутлав – Chuvash" lang="cv" hreflang="cv" data-title="Вариацилле шутлав" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Variationsrechnung" title="Variationsrechnung – Ġermaniż" lang="de" hreflang="de" data-title="Variationsrechnung" data-language-autonym="Deutsch" data-language-local-name="Ġermaniż" 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_%CF%84%CF%89%CE%BD_%CE%BC%CE%B5%CF%84%CE%B1%CE%B2%CE%BF%CE%BB%CF%8E%CE%BD" title="Λογισμός των μεταβολών – Grieg" lang="el" hreflang="el" data-title="Λογισμός των μεταβολών" data-language-autonym="Ελληνικά" data-language-local-name="Grieg" 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/Calculus_of_variations" title="Calculus of variations – Ingliż" lang="en" hreflang="en" data-title="Calculus of variations" data-language-autonym="English" data-language-local-name="Ingliż" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Variada_kalkulo" title="Variada kalkulo – Esperanto" lang="eo" hreflang="eo" data-title="Variada kalkulo" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/C%C3%A1lculo_de_variaciones" title="Cálculo de variaciones – Spanjol" lang="es" hreflang="es" data-title="Cálculo de variaciones" data-language-autonym="Español" data-language-local-name="Spanjol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Variatsioonarvutus" title="Variatsioonarvutus – Estonjan" lang="et" hreflang="et" data-title="Variatsioonarvutus" data-language-autonym="Eesti" data-language-local-name="Estonjan" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Bariazioen_kalkulu" title="Bariazioen kalkulu – Bask" lang="eu" hreflang="eu" data-title="Bariazioen kalkulu" data-language-autonym="Euskara" data-language-local-name="Bask" 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%AA%D8%BA%DB%8C%DB%8C%D8%B1%D8%A7%D8%AA" title="حساب تغییرات – Persjan" lang="fa" hreflang="fa" data-title="حساب تغییرات" data-language-autonym="فارسی" data-language-local-name="Persjan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Variaatiolaskenta" title="Variaatiolaskenta – Finlandiż" lang="fi" hreflang="fi" data-title="Variaatiolaskenta" data-language-autonym="Suomi" data-language-local-name="Finlandiż" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Calcul_des_variations" title="Calcul des variations – Franċiż" lang="fr" hreflang="fr" data-title="Calcul des variations" data-language-autonym="Français" data-language-local-name="Franċiż" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/C%C3%A1lculo_de_variaci%C3%B3ns" title="Cálculo de variacións – Galiċjan" lang="gl" hreflang="gl" data-title="Cálculo de variacións" data-language-autonym="Galego" data-language-local-name="Galiċjan" class="interlanguage-link-target"><span>Galego</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%95%D7%A8%D7%99%D7%90%D7%A6%D7%99%D7%95%D7%AA" title="חשבון וריאציות – Ebrajk" lang="he" hreflang="he" data-title="חשבון וריאציות" data-language-autonym="עברית" data-language-local-name="Ebrajk" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%9A%E0%A4%B0%E0%A4%A3-%E0%A4%95%E0%A4%B2%E0%A4%A8" title="विचरण-कलन – Hindi" lang="hi" hreflang="hi" data-title="विचरण-कलन" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Vari%C3%A1ci%C3%B3sz%C3%A1m%C3%ADt%C3%A1s" title="Variációszámítás – Ungeriż" lang="hu" hreflang="hu" data-title="Variációszámítás" data-language-autonym="Magyar" data-language-local-name="Ungeriż" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Calcolo_delle_variazioni" title="Calcolo delle variazioni – Taljan" lang="it" hreflang="it" data-title="Calcolo delle variazioni" data-language-autonym="Italiano" data-language-local-name="Taljan" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%A4%89%E5%88%86%E6%B3%95" title="変分法 – Ġappuniż" lang="ja" hreflang="ja" data-title="変分法" data-language-autonym="日本語" data-language-local-name="Ġappuniż" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%92%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D0%B5%D1%81%D0%B5%D0%BF%D1%82%D0%B5%D1%83" title="Вариациялық есептеу – Każak" lang="kk" hreflang="kk" data-title="Вариациялық есептеу" data-language-autonym="Қазақша" data-language-local-name="Każak" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%80%EB%B6%84%EB%B2%95" title="변분법 – Korean" lang="ko" hreflang="ko" data-title="변분법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Variatierekening" title="Variatierekening – Olandiż" lang="nl" hreflang="nl" data-title="Variatierekening" data-language-autonym="Nederlands" data-language-local-name="Olandiż" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Variasjonsrekning" title="Variasjonsrekning – Ninorsk Norveġiż" lang="nn" hreflang="nn" data-title="Variasjonsrekning" data-language-autonym="Norsk nynorsk" data-language-local-name="Ninorsk Norveġiż" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Variasjonsregning" title="Variasjonsregning – Bokmal Norveġiż" lang="nb" hreflang="nb" data-title="Variasjonsregning" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmal Norveġiż" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rachunek_wariacyjny" title="Rachunek wariacyjny – Pollakk" lang="pl" hreflang="pl" data-title="Rachunek wariacyjny" data-language-autonym="Polski" data-language-local-name="Pollakk" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/C%C3%A0lcol_dle_variassion" title="Càlcol dle variassion – Piedmontese" lang="pms" hreflang="pms" data-title="Càlcol dle variassion" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/C%C3%A1lculo_variacional" title="Cálculo variacional – Portugiż" lang="pt" hreflang="pt" data-title="Cálculo variacional" data-language-autonym="Português" data-language-local-name="Portugiż" 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_varia%C8%9Bional" title="Calcul variațional – Rumen" lang="ro" hreflang="ro" data-title="Calcul variațional" data-language-autonym="Română" data-language-local-name="Rumen" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%92%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%BD%D0%BE%D0%B5_%D0%B8%D1%81%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Вариационное исчисление – Russu" lang="ru" hreflang="ru" data-title="Вариационное исчисление" data-language-autonym="Русский" data-language-local-name="Russu" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Calculus_of_variations" title="Calculus of variations – Simple English" lang="en-simple" hreflang="en-simple" data-title="Calculus of variations" 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-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Varia%C4%8Dn%C3%BD_po%C4%8Det" title="Variačný počet – Slovakk" lang="sk" hreflang="sk" data-title="Variačný počet" data-language-autonym="Slovenčina" data-language-local-name="Slovakk" 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/Variacijski_ra%C4%8Dun" title="Variacijski račun – Sloven" lang="sl" hreflang="sl" data-title="Variacijski račun" data-language-autonym="Slovenščina" data-language-local-name="Sloven" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Analiza_e_variacionit" title="Analiza e variacionit – Albaniż" lang="sq" hreflang="sq" data-title="Analiza e variacionit" data-language-autonym="Shqip" data-language-local-name="Albaniż" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/Varijacijski_ra%C4%8Dun" title="Varijacijski račun – Serb" lang="sr" hreflang="sr" data-title="Varijacijski račun" data-language-autonym="Српски / srpski" data-language-local-name="Serb" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Variationskalkyl" title="Variationskalkyl – Żvediż" lang="sv" hreflang="sv" data-title="Variationskalkyl" data-language-autonym="Svenska" data-language-local-name="Żvediż" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D0%B0%D1%80%D1%96%D0%B0%D1%86%D1%96%D0%B9%D0%BD%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F" title="Варіаційне числення – Ukren" lang="uk" hreflang="uk" data-title="Варіаційне числення" data-language-autonym="Українська" data-language-local-name="Ukren" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A9p_t%C3%ADnh_bi%E1%BA%BFn_ph%C3%A2n" title="Phép tính biến phân – Vjetnamiż" lang="vi" hreflang="vi" data-title="Phép tính biến phân" data-language-autonym="Tiếng Việt" data-language-local-name="Vjetnamiż" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%8F%98%E5%88%86%E6%B3%95" title="变分法 – Wu" lang="wuu" hreflang="wuu" data-title="变分法" 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-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%8F%98%E5%88%86%E6%B3%95" title="变分法 – Ċiniż" lang="zh" hreflang="zh" data-title="变分法" data-language-autonym="中文" data-language-local-name="Ċiniż" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%AE%8A%E5%88%86%E6%B3%95" title="變分法 – Kantoniż" lang="yue" hreflang="yue" data-title="變分法" data-language-autonym="粵語" data-language-local-name="Kantoniż" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q216861#sitelinks-wikipedia" title="Immodifika l-ħoloq interlingwi" class="wbc-editpage">Immodifika l-ħoloq</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Spazji tal-isem"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Kalkulu_tal-varjazzjonijiet" title="Uri l-paġna ta' kontenut [c]" accesskey="c"><span>Paġna</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskussjoni:Kalkulu_tal-varjazzjonijiet&action=edit&redlink=1" rel="discussion" class="new" title="Diskussjoni dwar il-paġna ta' kontenut (il-paġna ma teżistix) [t]" accesskey="t"><span>Diskussjoni</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Biddel il-varjant tal-lingwa" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Malti</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Visti"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Kalkulu_tal-varjazzjonijiet"><span>Aqra</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&veaction=edit" title="Immodifika din il-paġna [v]" accesskey="v"><span>Editja</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=edit" title="Edit the source code of this page [e]" accesskey="e"><span>Immodifika s-sors</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=history" title="Verżjonijiet preċedenti ta' din il-paġna [h]" accesskey="h"><span>Ara l-kronoloġija</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Għodda tal-paġna"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Għodda" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Għodda</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Għodda</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">mexxi għall-ġenb</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">aħbi</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="More options" > <div class="vector-menu-heading"> Azzjonijiet </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Kalkulu_tal-varjazzjonijiet"><span>Aqra</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&veaction=edit" title="Immodifika din il-paġna [v]" accesskey="v"><span>Editja</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=edit" title="Edit the source code of this page [e]" accesskey="e"><span>Immodifika s-sors</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=history"><span>Ara l-kronoloġija</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Ġenerali </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Spe%C4%8Bjali:XiJwassalHawn/Kalkulu_tal-varjazzjonijiet" title="Lista tal-paġni tal-wiki kollha li jwasslu hawn [j]" accesskey="j"><span>Li jwasslu 'l hawn</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Spe%C4%8Bjali:TibdilRelatat/Kalkulu_tal-varjazzjonijiet" rel="nofollow" title="Modifiki riċenti f'paġni b'ħolqa minn din il-paġna [k]" accesskey="k"><span>Tibdil relatat</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=mt" title="Tella' fajls [u]" accesskey="u"><span>Tella' fajl</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Spe%C4%8Bjali:Pa%C4%A1niSpe%C4%8Bjali" title="Lista tal-paġni speċjali kollha [q]" accesskey="q"><span>Paġni speċjali</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&oldid=298902" title="Ħolqa permanenti għal din il-verżjoni tal-paġna"><span>Ħolqa permanenti</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=info" title="Aktar informazzjoni fuq din il-paġna"><span>Informazzjoni fuq il-paġna</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Spe%C4%8Bjali:I%C4%8B%C4%8Bita&page=Kalkulu_tal-varjazzjonijiet&id=298902&wpFormIdentifier=titleform" title="Informazzjoni fuq kif tiċċita din il-paġna"><span>Iċċita dan l-artiklu</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Spe%C4%8Bjali:UrlShortener&url=https%3A%2F%2Fmt.wikipedia.org%2Fwiki%2FKalkulu_tal-varjazzjonijiet"><span>Get shortened URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Spe%C4%8Bjali:QrCode&url=https%3A%2F%2Fmt.wikipedia.org%2Fwiki%2FKalkulu_tal-varjazzjonijiet"><span>Download QR code</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Ipprintja/esporta </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Spe%C4%8Bjali:Ktieb&bookcmd=book_creator&referer=Kalkulu+tal-varjazzjonijiet"><span>Oħloq ktieb</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Spe%C4%8Bjali:DownloadAsPdf&page=Kalkulu_tal-varjazzjonijiet&action=show-download-screen"><span>Niżżel bħala PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&printable=yes" title="Verżjoni tal-ipprintjar ta' din il-paġna [p]" accesskey="p"><span>Verżjoni għall-ipprintjar</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Fi proġetti oħra </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Calculus_of_variations" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q216861" title="Ħolqa għall-element konness tal-arkivju tad-dejta [g]" accesskey="g"><span>Element ta' Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Għodda tal-paġna"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Dehra"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Dehra</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mexxi għall-ġenb</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">aħbi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Minn Wikipedija, l-enċiklopedija l-ħielsa</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="mt" dir="ltr"><p>Il-<b>kalkulu tal-varjazzjonijiet</b> hu qasam tal-<a href="/wiki/Matematika" title="Matematika">matematika</a> li jittratta <a href="/wiki/Funzjonijiet_(matematika)" title="Funzjonijiet (matematika)">funzjonijiet</a> ta’ funzjonijiet, differenti mill-<a href="/wiki/Analisi_matematika" title="Analisi matematika">analisi</a> ordinarja li tittratta funzjonijiet tan-numri. Dawn il-<i><a href="/w/index.php?title=Funzjonal&action=edit&redlink=1" class="new" title="Funzjonal (il-paġna ma teżistix)">funzjonali</a></i> jistgħu jkunu formulati, pereżempju, bħala integrali li jinvolvu funzjoni mhux magħrufa u d-derivati tagħha. L-interess hu fil-funzjonijiet <i>estremali</i>, jew dawk li jagħmlu l-valur tal-funzjonali massimu jew minimu. Xi problemi klassiċi fuq il-kurvi nistgħu inqegħduhom f’din il-forma: fost l-eżempji hemm il-kurva <a href="/w/index.php?title=Brakistokrona&action=edit&redlink=1" class="new" title="Brakistokrona (il-paġna ma teżistix)">brakistokrona</a>, il-mogħdija minn punt A għal punt B, mhux fl-istess linja vertikali, li matulha partiċella tinżel fl-inqas ħin taħt il-<a href="/w/index.php?title=Forza_ta%E2%80%99_gravit%C3%A0&action=edit&redlink=1" class="new" title="Forza ta’ gravità (il-paġna ma teżistix)">forza ta’ gravità</a>. Mela rridu nimminimizzaw il-funzjoni li tirrappreżenta l-ħin fuq il-kurvi kollha minn A għal B. </p><p>It-teorema tal-qofol tal-kalkulu tal-varjazzjonijiet hu l-<a href="/w/index.php?title=Ekwazzjonijiet_ta%E2%80%99_Euler-Lagrange&action=edit&redlink=1" class="new" title="Ekwazzjonijiet ta’ Euler-Lagrange (il-paġna ma teżistix)">ekwazzjoni ta’ Euler-Lagrange</a>. Din tikkorrispondi ma kondizzjoni ta’ stazzjonarjetà għall-funzjonal. Bħal fil-każ meta nfittxu l-massimi u l-minimi ta’ funzjoni, l-analisi tal-varjazzjonijiet żgħar madwar soluzzjoni tagħti kondizzjoni ta’ l-ewwel ordni. Ma nistgħux ngħidu direttament jekk inkunux sibna massimu, minimu, jew l-ebda wieħed. </p><p>Il-metodi varjazzjonali huma importanti fil-<a href="/w/index.php?title=Fi%C5%BCika_teorika&action=edit&redlink=1" class="new" title="Fiżika teorika (il-paġna ma teżistix)">fiżika teorika</a>: fil-<a href="/w/index.php?title=Mekkanika_lagran%C4%A1jana&action=edit&redlink=1" class="new" title="Mekkanika lagranġjana (il-paġna ma teżistix)">mekkanika lagranġjana</a> u fl-applikazzjoni tal-<a href="/w/index.php?title=Prin%C4%8Bipju_ta%E2%80%99_minima_azzjoni&action=edit&redlink=1" class="new" title="Prinċipju ta’ minima azzjoni (il-paġna ma teżistix)">prinċipju ta’ minima azzjoni</a> għall-<a href="/wiki/Mekkanika_kwantistika" title="Mekkanika kwantistika">fiżika kwantistika</a>. Il-metodi varjazzjonali jipprovdu l-bażi matematika għall-<a href="/w/index.php?title=Metodu_ta%E2%80%99_l-elementi_finiti&action=edit&redlink=1" class="new" title="Metodu ta’ l-elementi finiti (il-paġna ma teżistix)">metodu ta’ l-elementi finiti</a>, li hu biċċa għodda qawwija għar-riżoluzzjoni tal-<a href="/w/index.php?title=Problema_tax-xifer&action=edit&redlink=1" class="new" title="Problema tax-xifer (il-paġna ma teżistix)">problemi tax-xifer</a>. Huma użati ħafna wkoll fl-istudju ta’ l-ekwilibri statiċi fix-<a href="/wiki/Xjenza_tal-materjali" title="Xjenza tal-materjali">xjenza tal-materjali</a>, u fil-matematika pura, pereżempju fl-użu tal-<i><a href="/w/index.php?title=Prin%C4%8Bipju_ta%E2%80%99_Dirichlet&action=edit&redlink=1" class="new" title="Prinċipju ta’ Dirichlet (il-paġna ma teżistix)">prinċipju ta’ Dirichlet</a></i> għall-funzjonijiet armoniċi mill-lat ta’ <a href="/w/index.php?title=Bernhard_Riemann&action=edit&redlink=1" class="new" title="Bernhard Riemann (il-paġna ma teżistix)">Bernhard Riemann</a>. </p><p>L-istessi konċetti jidhru f’suriet oħra, pereżempju, bħala metodi fl-i<a href="/w/index.php?title=Spazju_ta%E2%80%99_Hilbert&action=edit&redlink=1" class="new" title="Spazju ta’ Hilbert (il-paġna ma teżistix)">spazji ta’ Hilbert</a>, fit-<a href="/w/index.php?title=Teorija_ta%E2%80%99_Morse&action=edit&redlink=1" class="new" title="Teorija ta’ Morse (il-paġna ma teżistix)">teorija ta’ Morse</a>, jew fil-<a href="/w/index.php?title=%C4%A0ometrija_simplettika&action=edit&redlink=1" class="new" title="Ġometrija simplettika (il-paġna ma teżistix)">ġometrija simplettika</a>. Il termini <i>varjazzjonali</i> tintuża fil-każi kollha ta’ funzjonali estremali. L-istudju tal-<a href="/w/index.php?title=%C4%A0eodetika&action=edit&redlink=1" class="new" title="Ġeodetika (il-paġna ma teżistix)">ġeodetiċi</a> fil-<a href="/w/index.php?title=%C4%A0ometrija_differenzjali&action=edit&redlink=1" class="new" title="Ġometrija differenzjali (il-paġna ma teżistix)">ġometrija differenzjali</a> hu qasam li ovvjament għandu kontenut varjazzjonali. Sar ħafna xogħol fuq il-problema tas-<i><a href="/w/index.php?title=Superfi%C4%8Bju_minimu&action=edit&redlink=1" class="new" title="Superfiċju minimu (il-paġna ma teżistix)">superfiċju minimu</a></i> (problema tal- <a href="/w/index.php?title=Bu%C5%BC%C5%BCieqa_tas-sapun&action=edit&redlink=1" class="new" title="Bużżieqa tas-sapun (il-paġna ma teżistix)">bużżieqa tas-sapun</a>), magħrufa wkoll bħala l-<a href="/w/index.php?title=Problema_ta%E2%80%99_Plateau&action=edit&redlink=1" class="new" title="Problema ta’ Plateau (il-paġna ma teżistix)">problema ta’ Plateau</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Paġni_li_għandhom_x’jaqsmu"><span id="Pa.C4.A1ni_li_g.C4.A7andhom_x.E2.80.99jaqsmu"></span>Paġni li għandhom x’jaqsmu</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&veaction=edit&section=1" title="Editja s-sezzjoni: Paġni li għandhom x’jaqsmu" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=edit&section=1" title="Edit section's source code: Paġni li għandhom x’jaqsmu"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Di%C5%BCugwaljanza_isoperimetrika&action=edit&redlink=1" class="new" title="Diżugwaljanza isoperimetrika (il-paġna ma teżistix)">Diżugwaljanza isoperimetrika</a></li> <li><a href="/w/index.php?title=Prin%C4%8Bipju_varjazzjonali_ta%E2%80%99_Hamilton&action=edit&redlink=1" class="new" title="Prinċipju varjazzjonali ta’ Hamilton (il-paġna ma teżistix)">Prinċipju varjazzjonali ta’ Hamilton</a></li> <li><a href="/w/index.php?title=Prin%C4%8Bipju_ta%E2%80%99_minima_azzjoni&action=edit&redlink=1" class="new" title="Prinċipju ta’ minima azzjoni (il-paġna ma teżistix)">Prinċipju ta’ Maupertuis</a></li> <li><a href="/w/index.php?title=Prin%C4%8Bipju_ta%E2%80%99_Fermat&action=edit&redlink=1" class="new" title="Prinċipju ta’ Fermat (il-paġna ma teżistix)">Prinċipju ta’ Fermat</a></li> <li><a href="/w/index.php?title=Prin%C4%8Bipju_ta%E2%80%99_minima_azzjoni&action=edit&redlink=1" class="new" title="Prinċipju ta’ minima azzjoni (il-paġna ma teżistix)">Prinċipju ta’ minima azzjoni</a></li> <li><a href="/w/index.php?title=Ottimizzazzjoni_infinito-dimensjonali&action=edit&redlink=1" class="new" title="Ottimizzazzjoni infinito-dimensjonali (il-paġna ma teżistix)">Ottimizzazzjoni infinito-dimensjonali</a></li> <li><a href="/w/index.php?title=Analisi_funzjonali&action=edit&redlink=1" class="new" title="Analisi funzjonali (il-paġna ma teżistix)">Analisi funzjonali</a></li> <li><a href="/w/index.php?title=Metodi_perturbattivi&action=edit&redlink=1" class="new" title="Metodi perturbattivi (il-paġna ma teżistix)">Metodi perturbattivi</a></li> <li><a href="/w/index.php?title=Metodi_diretti_fil-Kalkulu_Varjazzjonali&action=edit&redlink=1" class="new" title="Metodi diretti fil-Kalkulu Varjazzjonali (il-paġna ma teżistix)">Metodi diretti fil-Kalkulu Varjazzjonali</a></li></ul> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Ħoloq_esterni"><span id=".C4.A6oloq_esterni"></span>Ħoloq esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&veaction=edit&section=2" title="Editja s-sezzjoni: Ħoloq esterni" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=edit&section=2" title="Edit section's source code: Ħoloq esterni"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060311033849/http://www.sm.luth.se/~johanb/applmath/chap3en/index.htm">Chapter III: Introduction to the calculus of variations</a> ta' Johan Byström, Lars-Erik Persson, and Fredrik Strömberg</li></ul> <div class="mw-heading mw-heading2"><h2 id="Bibljografija">Bibljografija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&veaction=edit&section=3" title="Editja s-sezzjoni: Bibljografija" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Kalkulu_tal-varjazzjonijiet&action=edit&section=3" title="Edit section's source code: Bibljografija"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Leonida_Tonelli&action=edit&redlink=1" class="new" title="Leonida Tonelli (il-paġna ma teżistix)">Tonelli, L.</a>: <a rel="nofollow" class="external text" href="http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath&idno=ACQ6956">Fondamenti di calcolo delle variazioni</a>, N. Zanichelli, 1921-23</li> <li>Todhunter, I. <a rel="nofollow" class="external text" href="http://www.archive.org/details/histroyofthecalc033379mbp">A history of the calculus of variations</a>, Chelsea, 1861</li> <li>Carll, L. B. <a rel="nofollow" class="external text" href="http://www.archive.org/details/treatiseonthecal032865mbp">A Treatise On The Calculus Of Variations</a> John Wiley & sons, 1881</li> <li>Hancock, H. <a rel="nofollow" class="external text" href="http://www.archive.org/details/151181775">Lectures on the calculus of variations (the Weierstrassian theory)</a> Cincinnati University Press, 1904</li> <li>Bolza, O <a rel="nofollow" class="external text" href="http://name.umdl.umich.edu/ACM2513.0001.001">Lectures on the calculus of variations</a>, Chicago University Press, 1904</li> <li>Byerly, W. E. <a rel="nofollow" class="external text" href="http://name.umdl.umich.edu/ACQ6938.0001.001">Introduction to the calculus of variations</a> Harvard University Press, 1917</li> <li>Weinstock, R. <a rel="nofollow" class="external text" href="http://www.archive.org/details/calculusofvariat033563mbp">Calculus Of Variations With Applications To Physics And Engineering</a>, McGrawHill, 1952</li> <li>Hadamard J. e Fréchet, M. <a rel="nofollow" class="external text" href="http://www.archive.org/details/leconssurlecalcu00hadarich">Leçons sur le calcul des variations</a> (francese) Hermann, 1910</li> <li>Fomin, S.V. and Gelfand, I.M.: Calculus of Variations, Dover Publ., 2000</li> <li>Lebedev, L.P. and Cloud, M.J.: The Calculus of Variations and Functional Analysis with Optimal Control and Applications in Mechanics, World Scientific, 2003, pages 1-98</li> <li>Charles Fox: An Introduction to the Calculus of Variations, Dover Publ., 1987</li></ul> <p><br /> </p> <div class="tright portal" style="border:solid #aaa 1px;margin:0.5em 0 0.5em 0.5em;"> <table style="background:#f9f9f9; font-size:85%; line-height:110%;"> <tbody><tr> <td><span class="mw-default-size" typeof="mw:File"><a href="/wiki/Stampa:P_math.png" class="mw-file-description" title="1pxx28px"><img alt="1pxx28px" src="//upload.wikimedia.org/wikipedia/commons/b/b7/P_math.png" decoding="async" width="77" height="68" class="mw-file-element" data-file-width="77" data-file-height="68" /></a></span> </td> <td style="padding:0 0.2em;"><i><b><a href="/wiki/Portal:Matematika" title="Portal:Matematika">Portal Matematika </a></b></i> </td></tr></tbody></table> </div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Miksub minn "<a dir="ltr" href="https://mt.wikipedia.org/w/index.php?title=Kalkulu_tal-varjazzjonijiet&oldid=298902">https://mt.wikipedia.org/w/index.php?title=Kalkulu_tal-varjazzjonijiet&oldid=298902</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Spe%C4%8Bjali:Kategoriji" title="Speċjali:Kategoriji">Kategoriji</a>: <ul><li><a href="/wiki/Kategorija:Matematika" title="Kategorija:Matematika">Matematika</a></li><li><a href="/wiki/Kategorija:Analisi_matematika" title="Kategorija:Analisi matematika">Analisi matematika</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> L-aħħar bidla fuq il-paġna: 02:04, 23 Diċembru 2023.</li> <li id="footer-info-copyright">It-test huwa disponibbli taħt il-<a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">Liċenzja Creative Commons Attribution-ShareAlike</a>; jistgħu japplikaw xi kundizzjonijiet oħra. Ara l-<a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">kundizzjonijiet tal-użu</a> għal aktar dettalji.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">Politika dwar il-privatezza</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedija:Dwar">Dwar il-Wikipedija</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedija:%C4%8Aa%C4%A7da_%C4%A1enerali">Ċaħdiet</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">Code of Conduct</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">Żviluppaturi</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/mt.wikipedia.org">Statistika</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Stqarrija dwar il-cookies</a></li> <li id="footer-places-mobileview"><a href="//mt.m.wikipedia.org/w/index.php?title=Kalkulu_tal-varjazzjonijiet&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">Verżjoni għall-mowbajl</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-f69cdc8f6-5w7wd","wgBackendResponseTime":136,"wgPageParseReport":{"limitreport":{"cputime":"0.017","walltime":"0.021","ppvisitednodes":{"value":74,"limit":1000000},"postexpandincludesize":{"value":325,"limit":2097152},"templateargumentsize":{"value":33,"limit":2097152},"expansiondepth":{"value":5,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":0,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 2.180 1 Mudell:Portal","100.00% 2.180 1 -total"]},"cachereport":{"origin":"mw-api-int.codfw.main-7858d788f6-rct2x","timestamp":"20241101235254","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"Kalkulu tal-varjazzjonijiet","url":"https:\/\/mt.wikipedia.org\/wiki\/Kalkulu_tal-varjazzjonijiet","sameAs":"http:\/\/www.wikidata.org\/entity\/Q216861","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q216861","author":{"@type":"Organization","name":"Contributors to Wikimedia projects"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2007-11-20T19:54:04Z","dateModified":"2023-12-23T02:04:45Z"}</script> </body> </html>