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דיברגנץ – ויקיפדיה
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user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o" class=""><span>כניסה לחשבון</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="אפשרויות נוספות" > <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="כלים אישיים" > <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">כלים אישיים</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="תפריט משתמש" > <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_he.wikipedia.org&uselang=he"><span>תרומה לוויקיפדיה</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5" title="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>יצירת חשבון</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>כניסה לחשבון</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"> דפים לעורכים שלא נכנסו לחשבון <a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A8%D7%95%D7%9B%D7%99%D7%9D_%D7%94%D7%91%D7%90%D7%99%D7%9D" aria-label="מידע נוסף על עריכה"><span>מידע נוסף</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/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%AA%D7%A8%D7%95%D7%9E%D7%95%D7%AA_%D7%A9%D7%9C%D7%99" title="רשימת העריכות שנעשו מכתובת IP זו [y]" accesskey="y"><span>תרומות</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A9%D7%99%D7%97%D7%94_%D7%A9%D7%9C%D7%99" title="דיון על העריכות שנעשו מכתובת IP זו [n]" accesskey="n"><span>שיחה</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\"\u003Eהסתרה\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"anonnotice\" lang=\"he\" dir=\"rtl\"\u003E\u003Cp\u003E\u003Cb\u003Eתמיד רציתם לכתוב בוויקיפדיה אבל לא ידעתם איך? אתם מוזמנים לסדנת עריכה בוויקיפדיה. הסדנה תתקיים בספרייה הלאומית (בבניינה החדש) בירושלים ביום שישי, 06.12.24, בשעה 09:00. להרשמה לחצו \u003Ca href=\"/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:%D7%9E%D7%99%D7%96%D7%9E%D7%99_%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94/%D7%92%D7%9C%D7%90%D7%9D/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA/%D7%90%D7%99%D7%A8%D7%95%D7%A2%D7%99%D7%9D/%D7%A1%D7%93%D7%A0%D7%AA_%D7%A2%D7%A8%D7%99%D7%9B%D7%94_%D7%93%D7%A6%D7%9E%D7%91%D7%A8_2024\" title=\"ויקיפדיה:מיזמי ויקיפדיה/גלאם/הספרייה הלאומית/אירועים/סדנת עריכה דצמבר 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class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">הסתרה</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">התחלה</div> </a> </li> <li id="toc-סימון" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#סימון"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>סימון</span> </div> </a> <ul id="toc-סימון-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-מבוא_אינטואיטיבי" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#מבוא_אינטואיטיבי"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>מבוא אינטואיטיבי</span> </div> </a> <ul id="toc-מבוא_אינטואיטיבי-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-הגדרה_פורמלית" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#הגדרה_פורמלית"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>הגדרה פורמלית</span> </div> </a> <ul id="toc-הגדרה_פורמלית-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-תכונות" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#תכונות"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>תכונות</span> </div> </a> <ul id="toc-תכונות-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-קישורים_חיצוניים" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#קישורים_חיצוניים"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>קישורים חיצוניים</span> </div> </a> <ul id="toc-קישורים_חיצוניים-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="תוכן עניינים" 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="מצב תוכן העניינים" > <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">מצב תוכן העניינים</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">דיברגנץ</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="מעבר לערך בשפה אחרת. זמין ב־50 שפות" > <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-50" 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">50 שפות</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Divergence" title="Divergence – אנגלית" lang="en" hreflang="en" data-title="Divergence" data-language-autonym="English" data-language-local-name="אנגלית" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%A8%D8%A7%D8%B9%D8%AF_(%D9%85%D8%AA%D8%AC%D9%87%D8%A7%D8%AA)" title="تباعد (متجهات) – ערבית" lang="ar" hreflang="ar" data-title="تباعد (متجهات)" data-language-autonym="العربية" data-language-local-name="ערבית" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D0%B2%D0%B5%D1%80%D0%B3%D0%B5%D0%BD%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Дивергенция (математика) – בולגרית" lang="bg" hreflang="bg" data-title="Дивергенция (математика)" data-language-autonym="Български" data-language-local-name="בולגרית" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A1%E0%A6%BE%E0%A6%87%E0%A6%AD%E0%A6%BE%E0%A6%B0%E0%A6%9C%E0%A7%87%E0%A6%A8%E0%A7%8D%E0%A6%B8" title="ডাইভারজেন্স – בנגלית" lang="bn" hreflang="bn" data-title="ডাইভারজেন্স" data-language-autonym="বাংলা" data-language-local-name="בנגלית" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Divergencija" title="Divergencija – בוסנית" lang="bs" hreflang="bs" data-title="Divergencija" data-language-autonym="Bosanski" data-language-local-name="בוסנית" 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/Diverg%C3%A8ncia" title="Divergència – קטלאנית" lang="ca" hreflang="ca" data-title="Divergència" data-language-autonym="Català" data-language-local-name="קטלאנית" 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/Divergence_(oper%C3%A1tor)" title="Divergence (operátor) – צ׳כית" lang="cs" hreflang="cs" data-title="Divergence (operátor)" data-language-autonym="Čeština" data-language-local-name="צ׳כית" 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%94%D0%B8%D0%B2%D0%B5%D1%80%D0%B3%D0%B5%D0%BD%D1%86%D0%B8" title="Дивергенци – צ׳ובשית" lang="cv" hreflang="cv" data-title="Дивергенци" data-language-autonym="Чӑвашла" data-language-local-name="צ׳ובשית" 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/Divergenz_eines_Vektorfeldes" title="Divergenz eines Vektorfeldes – גרמנית" lang="de" hreflang="de" data-title="Divergenz eines Vektorfeldes" data-language-autonym="Deutsch" data-language-local-name="גרמנית" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Diver%C4%9Denco" title="Diverĝenco – אספרנטו" lang="eo" hreflang="eo" data-title="Diverĝenco" data-language-autonym="Esperanto" data-language-local-name="אספרנטו" 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/Divergencia_(matem%C3%A1tica)" title="Divergencia (matemática) – ספרדית" lang="es" hreflang="es" data-title="Divergencia (matemática)" data-language-autonym="Español" data-language-local-name="ספרדית" 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/Divergents_(matemaatika)" title="Divergents (matemaatika) – אסטונית" lang="et" hreflang="et" data-title="Divergents (matemaatika)" data-language-autonym="Eesti" data-language-local-name="אסטונית" 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/Dibergentzia_(matematika)" title="Dibergentzia (matematika) – בסקית" lang="eu" hreflang="eu" data-title="Dibergentzia (matematika)" data-language-autonym="Euskara" data-language-local-name="בסקית" 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%AF%DB%8C%D9%88%D8%B1%DA%98%D8%A7%D9%86%D8%B3" title="دیورژانس – פרסית" lang="fa" hreflang="fa" data-title="دیورژانس" data-language-autonym="فارسی" data-language-local-name="פרסית" 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/Divergenssi" title="Divergenssi – פינית" lang="fi" hreflang="fi" data-title="Divergenssi" data-language-autonym="Suomi" data-language-local-name="פינית" 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/Divergence_(analyse_vectorielle)" title="Divergence (analyse vectorielle) – צרפתית" lang="fr" hreflang="fr" data-title="Divergence (analyse vectorielle)" data-language-autonym="Français" data-language-local-name="צרפתית" class="interlanguage-link-target"><span>Français</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%B2%E0%A4%A8" title="विचलन – הינדי" lang="hi" hreflang="hi" data-title="विचलन" data-language-autonym="हिन्दी" data-language-local-name="הינדי" 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/Divergencija_polja" title="Divergencija polja – קרואטית" lang="hr" hreflang="hr" data-title="Divergencija polja" data-language-autonym="Hrvatski" data-language-local-name="קרואטית" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Divergencia_(vektoranal%C3%ADzis)" title="Divergencia (vektoranalízis) – הונגרית" lang="hu" hreflang="hu" data-title="Divergencia (vektoranalízis)" data-language-autonym="Magyar" data-language-local-name="הונגרית" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%A1%D6%80%D5%A1%D5%B4%D5%AB%D5%BF%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Տարամիտություն – ארמנית" lang="hy" hreflang="hy" data-title="Տարամիտություն" data-language-autonym="Հայերեն" data-language-local-name="ארמנית" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Sundurleitni" title="Sundurleitni – איסלנדית" lang="is" hreflang="is" data-title="Sundurleitni" data-language-autonym="Íslenska" data-language-local-name="איסלנדית" 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/Divergenza" title="Divergenza – איטלקית" lang="it" hreflang="it" data-title="Divergenza" data-language-autonym="Italiano" data-language-local-name="איטלקית" 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/%E7%99%BA%E6%95%A3_(%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E8%A7%A3%E6%9E%90)" title="発散 (ベクトル解析) – יפנית" lang="ja" hreflang="ja" data-title="発散 (ベクトル解析)" data-language-autonym="日本語" data-language-local-name="יפנית" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%98%E1%83%95%E1%83%94%E1%83%A0%E1%83%92%E1%83%94%E1%83%9C%E1%83%AA%E1%83%98%E1%83%90" title="დივერგენცია – גאורגית" lang="ka" hreflang="ka" data-title="დივერგენცია" data-language-autonym="ქართული" data-language-local-name="גאורגית" 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%94%D0%B8%D0%B2%D0%B5%D1%80%D0%B3%D0%B5%D0%BD%D1%86%D0%B8%D1%8F" title="Дивергенция – קזחית" lang="kk" hreflang="kk" data-title="Дивергенция" data-language-autonym="Қазақша" data-language-local-name="קזחית" 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%B0%9C%EC%82%B0_(%EB%B2%A1%ED%84%B0)" title="발산 (벡터) – קוריאנית" lang="ko" hreflang="ko" data-title="발산 (벡터)" data-language-autonym="한국어" data-language-local-name="קוריאנית" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Divergenza" title="Divergenza – לומברדית" lang="lmo" hreflang="lmo" data-title="Divergenza" data-language-autonym="Lombard" data-language-local-name="לומברדית" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Divergencija" title="Divergencija – ליטאית" lang="lt" hreflang="lt" data-title="Divergencija" data-language-autonym="Lietuvių" data-language-local-name="ליטאית" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Divergentie_(vectorveld)" title="Divergentie (vectorveld) – הולנדית" lang="nl" hreflang="nl" data-title="Divergentie (vectorveld)" data-language-autonym="Nederlands" data-language-local-name="הולנדית" 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/Divergens" title="Divergens – נורווגית חדשה" lang="nn" hreflang="nn" data-title="Divergens" data-language-autonym="Norsk nynorsk" data-language-local-name="נורווגית חדשה" 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/Divergens" title="Divergens – נורווגית ספרותית" lang="nb" hreflang="nb" data-title="Divergens" data-language-autonym="Norsk bokmål" data-language-local-name="נורווגית ספרותית" 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/Dywergencja" title="Dywergencja – פולנית" lang="pl" hreflang="pl" data-title="Dywergencja" data-language-autonym="Polski" data-language-local-name="פולנית" 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/Diverg%C3%AAncia" title="Divergência – פורטוגזית" lang="pt" hreflang="pt" data-title="Divergência" data-language-autonym="Português" data-language-local-name="פורטוגזית" 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/Divergen%C8%9B%C4%83" title="Divergență – רומנית" lang="ro" hreflang="ro" data-title="Divergență" data-language-autonym="Română" data-language-local-name="רומנית" 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%94%D0%B8%D0%B2%D0%B5%D1%80%D0%B3%D0%B5%D0%BD%D1%86%D0%B8%D1%8F" title="Дивергенция – רוסית" lang="ru" hreflang="ru" data-title="Дивергенция" data-language-autonym="Русский" data-language-local-name="רוסית" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Divergencija" title="Divergencija – סרבו-קרואטית" lang="sh" hreflang="sh" data-title="Divergencija" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="סרבו-קרואטית" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Divergence" title="Divergence – אנגלית פשוטה" lang="en-simple" hreflang="en-simple" data-title="Divergence" data-language-autonym="Simple English" data-language-local-name="אנגלית פשוטה" 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/Divergencia_(vektorov%C3%A9_pole)" title="Divergencia (vektorové pole) – סלובקית" lang="sk" hreflang="sk" data-title="Divergencia (vektorové pole)" data-language-autonym="Slovenčina" data-language-local-name="סלובקית" 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/Divergenca" title="Divergenca – סלובנית" lang="sl" hreflang="sl" data-title="Divergenca" data-language-autonym="Slovenščina" data-language-local-name="סלובנית" 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/Divergjenca" title="Divergjenca – אלבנית" lang="sq" hreflang="sq" data-title="Divergjenca" data-language-autonym="Shqip" data-language-local-name="אלבנית" 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/%D0%94%D0%B8%D0%B2%D0%B5%D1%80%D0%B3%D0%B5%D0%BD%D1%86%D0%B8%D1%98%D0%B0" title="Дивергенција – סרבית" lang="sr" hreflang="sr" data-title="Дивергенција" data-language-autonym="Српски / srpski" data-language-local-name="סרבית" 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/Divergens_(vektoranalys)" title="Divergens (vektoranalys) – שוודית" lang="sv" hreflang="sv" data-title="Divergens (vektoranalys)" data-language-autonym="Svenska" data-language-local-name="שוודית" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%BF%E0%AE%B0%E0%AE%BF%E0%AE%A4%E0%AE%B2%E0%AF%8D_(%E0%AE%A4%E0%AE%BF%E0%AE%9A%E0%AF%88%E0%AE%AF%E0%AE%A9%E0%AF%8D_%E0%AE%A8%E0%AF%81%E0%AE%A3%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="விரிதல் (திசையன் நுண்கணிதம்) – טמילית" lang="ta" hreflang="ta" data-title="விரிதல் (திசையன் நுண்கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="טמילית" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Diberhensiya_(matematika)" title="Diberhensiya (matematika) – טאגאלוג" lang="tl" hreflang="tl" data-title="Diberhensiya (matematika)" data-language-autonym="Tagalog" data-language-local-name="טאגאלוג" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Diverjans" title="Diverjans – טורקית" lang="tr" hreflang="tr" data-title="Diverjans" data-language-autonym="Türkçe" data-language-local-name="טורקית" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%94%D0%B8%D0%B2%D0%B5%D1%80%D0%B3%D0%B5%D0%BD%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Дивергенция (математика) – טטרית" lang="tt" hreflang="tt" data-title="Дивергенция (математика)" data-language-autonym="Татарча / tatarça" data-language-local-name="טטרית" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%94%D0%B8%D0%B2%D0%B5%D1%80%D0%B3%D0%B5%D0%BD%D1%86%D1%96%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Дивергенція (математика) – אוקראינית" lang="uk" hreflang="uk" data-title="Дивергенція (математика)" data-language-autonym="Українська" data-language-local-name="אוקראינית" 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/To%C3%A1n_t%E1%BB%AD_div" title="Toán tử div – וייטנאמית" lang="vi" hreflang="vi" data-title="Toán tử div" data-language-autonym="Tiếng Việt" data-language-local-name="וייטנאמית" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%A3%E5%BA%A6" title="散度 – סינית" lang="zh" hreflang="zh" data-title="散度" data-language-autonym="中文" data-language-local-name="סינית" 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/%E6%95%A3%E5%BA%A6" title="散度 – קנטונזית" lang="yue" hreflang="yue" data-title="散度" data-language-autonym="粵語" data-language-local-name="קנטונזית" 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/Q189000#sitelinks-wikipedia" title="עריכת קישורים בין־לשוניים" class="wbc-editpage">עריכת הקישורים</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="מרחבי שם"> <div 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class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">הסתרה</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="אפשרויות נוספות" > <div class="vector-menu-heading"> פעולות </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/%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5"><span>קריאה</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=edit" title="עריכת קוד המקור של הדף הזה [e]" accesskey="e"><span>עריכת קוד מקור</span></a></li><li id="ca-more-ve-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&veaction=edit" title="עריכת הדף הזה [v]" accesskey="v"><span>עריכה</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=history"><span>גרסאות קודמות</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> כללי </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%93%D7%A4%D7%99%D7%9D_%D7%94%D7%9E%D7%A7%D7%95%D7%A9%D7%A8%D7%99%D7%9D_%D7%9C%D7%9B%D7%90%D7%9F/%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5" title="רשימה של כל דפי הוויקי שמקשרים לדף הזה [j]" accesskey="j"><span>דפים המקושרים לכאן</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A9%D7%99%D7%A0%D7%95%D7%99%D7%99%D7%9D_%D7%91%D7%93%D7%A4%D7%99%D7%9D_%D7%94%D7%9E%D7%A7%D7%95%D7%A9%D7%A8%D7%99%D7%9D/%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5" rel="nofollow" title="השינויים האחרונים בדפים המקושרים מהדף הזה [k]" accesskey="k"><span>שינויים בדפים המקושרים</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%93%D7%A4%D7%99%D7%9D_%D7%9E%D7%99%D7%95%D7%97%D7%93%D7%99%D7%9D" title="רשימה של כל הדפים המיוחדים [q]" accesskey="q"><span>דפים מיוחדים</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&oldid=38793387" title="קישור קבוע לגרסה הזאת של הדף הזה"><span>קישור קבוע</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=info" title="מידע נוסף על הדף הזה"><span>מידע על הדף</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A6%D7%99%D7%98%D7%95%D7%98_%D7%93%D7%A3_%D7%96%D7%94&page=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&id=38793387&wpFormIdentifier=titleform" title="מידע איך לצטט את הדף הזה"><span>ציטוט הדף הזה</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9E%D7%A7%D7%A6%D7%A8_%D7%9B%D7%AA%D7%95%D7%91%D7%95%D7%AA&url=https%3A%2F%2Fhe.wikipedia.org%2Fwiki%2F%25D7%2593%25D7%2599%25D7%2591%25D7%25A8%25D7%2592%25D7%25A0%25D7%25A5"><span>קבלת כתובת מקוצרת</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:QrCode&url=https%3A%2F%2Fhe.wikipedia.org%2Fwiki%2F%25D7%2593%25D7%2599%25D7%2591%25D7%25A8%25D7%2592%25D7%25A0%25D7%25A5"><span>הורדת קוד QR</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"> הדפסה/יצוא </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=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A1%D7%A4%D7%A8&bookcmd=book_creator&referer=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5"><span>יצירת ספר</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:DownloadAsPdf&page=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=show-download-screen"><span>הורדה כ־PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&printable=yes" title="גרסה להדפסה של הדף הזה [p]" accesskey="p"><span>גרסה להדפסה</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"> במיזמים אחרים </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:Divergence" hreflang="en"><span>ויקישיתוף</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/Q189000" title="קישור לפריט המשויך במאגר הנתונים [g]" accesskey="g"><span>פריט ויקינתונים</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="כלי דף"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="מראה"> <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">מראה</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">הסתרה</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">מתוך ויקיפדיה, האנציקלופדיה החופשית</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-rtl mw-parser-output" lang="he" dir="rtl"><p>ב<a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%AA" title="אנליזה וקטורית">אנליזה וקטורית</a>, ה<b>דיברגנץ</b> (ב<a href="/wiki/%D7%90%D7%A0%D7%92%D7%9C%D7%99%D7%AA" title="אנגלית">אנגלית</a>: <b>Divergence</b>) הוא <a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8" title="אופרטור">אופרטור</a> המופעל על <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="שדה וקטורי">שדה וקטורי</a>. הדיברגנץ משייך לכל <a href="/wiki/%D7%A0%D7%A7%D7%95%D7%93%D7%94_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="נקודה (גאומטריה)">נקודה</a> במרחב ערך מספרי המתאר את צפיפות המקורות של השדה הווקטורי שעליו הוא מופעל. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="סימון"><span id=".D7.A1.D7.99.D7.9E.D7.95.D7.9F"></span>סימון</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=edit&section=1" title="עריכת קוד המקור של הפרק: סימון"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&veaction=edit&section=1" title="עריכת פסקה: "סימון"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>אם <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 {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94" title="פונקציה">פונקציה</a> וקטורית שהדיברגנץ שלה הוא הפונקציה הסקלרית <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span>, מסמנים <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=\operatorname {div} {\vec {F}}={\vec {\nabla }}\cdot {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mi>div</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=\operatorname {div} {\vec {F}}={\vec {\nabla }}\cdot {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/934cf32dfb3210b0096ce3a8b52bfa3b4ea25951" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.186ex; height:3.176ex;" alt="{\displaystyle f=\operatorname {div} {\vec {F}}={\vec {\nabla }}\cdot {\vec {F}}}"></span>, כאשר <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 {\vec {\nabla }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\nabla }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65eeb56775c5bb9a9645ca773c8b8f744ca6ce0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.843ex;" alt="{\displaystyle {\vec {\nabla }}}"></span>הוא <a href="/wiki/%D7%A0%D7%91%D7%9C%D7%94_(%D7%A1%D7%99%D7%9E%D7%9F)" title="נבלה (סימן)">הנבלה</a>. </p><p>ניתן לראות מהסימון כי הדיברגנץ הוא סקלר, מכיוון ש<a href="/wiki/%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A1%D7%A7%D7%9C%D7%A8%D7%99%D7%AA" title="מכפלה סקלרית">מכפלה סקלרית</a> של ווקטור (<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 {\vec {\nabla }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\nabla }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65eeb56775c5bb9a9645ca773c8b8f744ca6ce0a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.936ex; height:2.843ex;" alt="{\displaystyle {\vec {\nabla }}}"></span>) בווקטור (<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 {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span>) מחזירה סקלר. </p> <div class="mw-heading mw-heading2"><h2 id="מבוא_אינטואיטיבי"><span id=".D7.9E.D7.91.D7.95.D7.90_.D7.90.D7.99.D7.A0.D7.98.D7.95.D7.90.D7.99.D7.98.D7.99.D7.91.D7.99"></span>מבוא אינטואיטיבי</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=edit&section=2" title="עריכת קוד המקור של הפרק: מבוא אינטואיטיבי"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&veaction=edit&section=2" title="עריכת פסקה: "מבוא אינטואיטיבי"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>הדיברגנץ מאפשר לכמת את צפיפות המקורות של שדה. באנלוגיה מתחום ה<a href="/wiki/%D7%A0%D7%95%D7%96%D7%9C" title="נוזל">נוזלים</a> והזרימה, אם מחזיקים בתוך זורם שלד של קובייה (רק המקצועות, ללא הפאות), ומבקשים לדעת כמה מים נטו יוצאים או נכנסים לתוך הקובייה, מודדים כמה מים זורמים דרך כל פאה ובאיזה כיוון (מים שיוצאים החוצה נספרים בסימן חיובי ואילו מים שנכנסים לקובייה נספרים בסימן שלילי), אם בסך הכל יוצאים מים מהקובייה, ניתן לספור את השטף שנפלט ממנה, ואילו אם בסך הכל נכנסים מים לקובייה, ניתן לכמת את השטף שנבלע מתוכה (מנוקז דרכה). </p><p>כלומר, באמצעות מדידת השטף דרך שטח מסוים, יודעים כמה "ברזים" או "חורי ניקוז" יש בתוך הנפח הכלוא בתוכו. כדי לחשב את צפיפות ה"ברזים"/"חורי ניקוז", מחלקים בנפח הקובייה. הדיברגנץ מודד בדיוק את אותו דבר - את צפיפות ה"ברזים" או "חורי ניקוז" - ב<a href="/wiki/%D7%A0%D7%A7%D7%95%D7%93%D7%94_(%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94)" title="נקודה (גאומטריה)">נקודה</a> במרחב. כדי לחשב את הגודל הזה, "בונים" סביב הנקודה קובייה <a href="/wiki/%D7%90%D7%99%D7%A0%D7%A4%D7%99%D7%A0%D7%99%D7%98%D7%A1%D7%99%D7%9E%D7%9C" title="אינפיניטסימל">אינפיניטסימלית</a>, ואז לוקחים את ה<a href="/wiki/%D7%92%D7%91%D7%95%D7%9C_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="גבול (מתמטיקה)">גבול</a> כאשר הנפח שלה שואף ל-0, ומקבלים את הדיברגנץ. </p><p>תופעה זו, שכמות המקורות בנפח נתון שווה לשטף הכולל היוצא (או הנכנס) מדפנות אותו הנפח, היא עובדה בעלת חשיבות רבה ב<a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%AA" title="אנליזה וקטורית">אנליזה וקטורית</a>, ונקראת <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5" class="mw-redirect" title="משפט הדיברגנץ">משפט הדיברגנץ</a> (או משפט גאוס). </p> <div class="mw-heading mw-heading2"><h2 id="הגדרה_פורמלית"><span id=".D7.94.D7.92.D7.93.D7.A8.D7.94_.D7.A4.D7.95.D7.A8.D7.9E.D7.9C.D7.99.D7.AA"></span>הגדרה פורמלית</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=edit&section=3" title="עריכת קוד המקור של הפרק: הגדרה פורמלית"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&veaction=edit&section=3" title="עריכת פסקה: "הגדרה פורמלית"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>יהי <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 {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> שדה וקטורי גזיר ברציפות, ויהי <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 V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> תחום במרחב הכולל נקודה <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> אשר שפתו <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 \ \partial V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \partial V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ed443ae5a6e129fc480cb5b6a2e9aa48cd0ed5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.686ex; height:2.176ex;" alt="{\displaystyle \ \partial V}"></span>. </p><p>הדיברגנץ של השדה <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 {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> בנקודה <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span> הוא: </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 \nabla \cdot {\vec {F}}(p)=\lim _{V\to 0}{\frac {\oiint _{\partial V}{\vec {F}}\cdot d{\vec {a}}}{V}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>V</mi> <mo stretchy="false">→<!-- → --></mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mrow class="MJX-TeXAtom-OP MJX-fixedlimits"> <mrow class="MJX-TeXAtom-VCENTER"> <mtext>∯<!-- ∯ --></mtext> </mrow> <mspace width="thinmathspace" /> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>V</mi> </mrow> </msub> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>⋅<!-- ⋅ --></mo> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>a</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mrow> <mi>V</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot {\vec {F}}(p)=\lim _{V\to 0}{\frac {\oiint _{\partial V}{\vec {F}}\cdot d{\vec {a}}}{V}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d06ecce3c0a768a9cb55408f931fa27c81c9e4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.93ex; height:6.509ex;" alt="{\displaystyle \nabla \cdot {\vec {F}}(p)=\lim _{V\to 0}{\frac {\oiint _{\partial V}{\vec {F}}\cdot d{\vec {a}}}{V}}}"></span></dd></dl> <p>ב<a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%99" title="מרחב אוקלידי">מרחב אוקלידי</a> תלת־ממדי המתואר על ידי <a href="/wiki/%D7%9E%D7%A2%D7%A8%D7%9B%D7%AA_%D7%A6%D7%99%D7%A8%D7%99%D7%9D_%D7%A7%D7%A8%D7%98%D7%96%D7%99%D7%AA" title="מערכת צירים קרטזית">קואורדינטות קרטזיות</a>, הדיברגנץ הוא: </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 \nabla \cdot {\vec {F}}(x,y,z)={\frac {\partial {F}_{x}}{\partial x}}+{\frac {\partial {F}_{y}}{\partial y}}+{\frac {\partial {F}_{z}}{\partial z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>y</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot {\vec {F}}(x,y,z)={\frac {\partial {F}_{x}}{\partial x}}+{\frac {\partial {F}_{y}}{\partial y}}+{\frac {\partial {F}_{z}}{\partial z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f520756fed96f769c1a3fc10834b194bc5fefb16" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:35.785ex; height:6.343ex;" alt="{\displaystyle \nabla \cdot {\vec {F}}(x,y,z)={\frac {\partial {F}_{x}}{\partial x}}+{\frac {\partial {F}_{y}}{\partial y}}+{\frac {\partial {F}_{z}}{\partial z}}}"></span></dd></dl> <p>כאשר <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 {\vec {F}}=\{{\ F}_{x},{\ F}_{y},{\ F}_{z}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mo fence="false" stretchy="false">{</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext> </mtext> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}=\{{\ F}_{x},{\ F}_{y},{\ F}_{z}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6bcbd5ebc98d1f7f5ad5825f44bb5cefa844bb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.711ex; height:3.509ex;" alt="{\displaystyle {\vec {F}}=\{{\ F}_{x},{\ F}_{y},{\ F}_{z}\}}"></span>, כלומר <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}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {F}_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2fa3ad5025035b0a39769c70be58ddba4e4cc4d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.667ex; height:2.509ex;" alt="{\displaystyle {F}_{x}}"></span>, ‏<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}_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {F}_{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e7ef9c3514dd576ce5209bc5e86dae0833fefc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.544ex; height:2.843ex;" alt="{\displaystyle {F}_{y}}"></span> ו־<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}_{z}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>F</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {F}_{z}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3cbbd22f475b60412ad5d9175c42d3e70a8e980b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.496ex; height:2.509ex;" alt="{\displaystyle {F}_{z}}"></span> הם רכיביו הקרטזיים של <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 {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span>. </p><p>הכללה למערכת <a href="/wiki/%D7%A7%D7%95%D7%90%D7%95%D7%A8%D7%93%D7%99%D7%A0%D7%98%D7%94" class="mw-redirect" title="קואורדינטה">קואורדינטות</a> <a href="/wiki/%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%92%D7%95%D7%A0%D7%9C%D7%99%D7%95%D7%AA" title="אורתוגונליות">אורתוגונלית</a> כלשהי: </p><p><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 \nabla \cdot {\vec {F}}={\frac {1}{h_{1}h_{2}h_{3}}}\left[{\frac {\partial }{\partial q_{1}}}\left(F_{1}h_{2}h_{3}\right)+{\frac {\partial }{\partial q_{2}}}\left(F_{2}h_{3}h_{1}\right)+{\frac {\partial }{\partial q_{3}}}\left(F_{3}h_{1}h_{2}\right)\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>[</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot {\vec {F}}={\frac {1}{h_{1}h_{2}h_{3}}}\left[{\frac {\partial }{\partial q_{1}}}\left(F_{1}h_{2}h_{3}\right)+{\frac {\partial }{\partial q_{2}}}\left(F_{2}h_{3}h_{1}\right)+{\frac {\partial }{\partial q_{3}}}\left(F_{3}h_{1}h_{2}\right)\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/071509c7bb005cf397696cb0621413ed5abdca22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:66.354ex; height:6.176ex;" alt="{\displaystyle \nabla \cdot {\vec {F}}={\frac {1}{h_{1}h_{2}h_{3}}}\left[{\frac {\partial }{\partial q_{1}}}\left(F_{1}h_{2}h_{3}\right)+{\frac {\partial }{\partial q_{2}}}\left(F_{2}h_{3}h_{1}\right)+{\frac {\partial }{\partial q_{3}}}\left(F_{3}h_{1}h_{2}\right)\right]}"></span> </p><p>כאשר: </p> <ul><li><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 h_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d535f210cbd9b9fe6689e61427b3e213e5b2d547" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.139ex; height:2.509ex;" alt="{\displaystyle h_{i}}"></span> הוא גודל הווקטור <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial {\vec {r}}}{\partial q_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial {\vec {r}}}{\partial q_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f379d303c9bdbd72e7c133933b33a506eb7e0691" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:3.991ex; height:5.843ex;" alt="{\displaystyle {\frac {\partial {\vec {r}}}{\partial q_{i}}}}"></span></li> <li><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_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18f9a5ed62f131c8ad9acdf7f8539f103f1e0ec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.294ex; height:2.509ex;" alt="{\displaystyle F_{i}}"></span> הוא רכיב הווקטור בכיוון <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 q_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle q_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2752dcbff884354069fe332b8e51eb0a70a531b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.837ex; height:2.009ex;" alt="{\displaystyle q_{i}}"></span></li></ul> <p>נקבל אם כן עבור <a href="/wiki/%D7%A7%D7%95%D7%90%D7%95%D7%A8%D7%93%D7%99%D7%A0%D7%98%D7%95%D7%AA_%D7%92%D7%9C%D7%99%D7%9C%D7%99%D7%95%D7%AA" title="קואורדינטות גליליות">קואורדינטות גליליות</a>: </p><p><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 \nabla \cdot {\vec {F}}={\frac {1}{r}}{\frac {\partial }{\partial r}}\left(rF_{r}\right)+{\frac {1}{r}}{\frac {\partial F_{\theta }}{\partial \theta }}+{\frac {\partial F_{z}}{\partial z}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>r</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>r</mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>θ<!-- θ --></mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>θ<!-- θ --></mi> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>z</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>z</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot {\vec {F}}={\frac {1}{r}}{\frac {\partial }{\partial r}}\left(rF_{r}\right)+{\frac {1}{r}}{\frac {\partial F_{\theta }}{\partial \theta }}+{\frac {\partial F_{z}}{\partial z}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bec0120b5129ff62ca8cba3ae66ff199334a8567" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:36.381ex; height:5.509ex;" alt="{\displaystyle \nabla \cdot {\vec {F}}={\frac {1}{r}}{\frac {\partial }{\partial r}}\left(rF_{r}\right)+{\frac {1}{r}}{\frac {\partial F_{\theta }}{\partial \theta }}+{\frac {\partial F_{z}}{\partial z}}}"></span> </p><p>ועבור <a href="/wiki/%D7%A7%D7%95%D7%90%D7%95%D7%A8%D7%93%D7%99%D7%A0%D7%98%D7%95%D7%AA_%D7%9B%D7%93%D7%95%D7%A8%D7%99%D7%95%D7%AA" title="קואורדינטות כדוריות"> קואורדינטות כדוריות</a>: </p><p><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 \nabla \cdot {\vec {F}}={\frac {1}{r^{2}}}{\frac {\partial }{\partial r}}\left(r^{2}F_{r}\right)+{\frac {1}{r\sin \theta }}{\frac {\partial }{\partial \theta }}(\sin \theta \,F_{\theta })+{\frac {1}{r\sin \theta }}{\frac {\partial F_{\varphi }}{\partial \varphi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>r</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>r</mi> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>θ<!-- θ --></mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> <mspace width="thinmathspace" /> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>θ<!-- θ --></mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mi>r</mi> <mi>sin</mi> <mo>⁡<!-- --></mo> <mi>θ<!-- θ --></mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>φ<!-- φ --></mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>φ<!-- φ --></mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot {\vec {F}}={\frac {1}{r^{2}}}{\frac {\partial }{\partial r}}\left(r^{2}F_{r}\right)+{\frac {1}{r\sin \theta }}{\frac {\partial }{\partial \theta }}(\sin \theta \,F_{\theta })+{\frac {1}{r\sin \theta }}{\frac {\partial F_{\varphi }}{\partial \varphi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e733950b716ad9d19cb716131910c88e058bb5d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:57.833ex; height:6.343ex;" alt="{\displaystyle \nabla \cdot {\vec {F}}={\frac {1}{r^{2}}}{\frac {\partial }{\partial r}}\left(r^{2}F_{r}\right)+{\frac {1}{r\sin \theta }}{\frac {\partial }{\partial \theta }}(\sin \theta \,F_{\theta })+{\frac {1}{r\sin \theta }}{\frac {\partial F_{\varphi }}{\partial \varphi }}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="תכונות"><span id=".D7.AA.D7.9B.D7.95.D7.A0.D7.95.D7.AA"></span>תכונות</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=edit&section=4" title="עריכת קוד המקור של הפרק: תכונות"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&veaction=edit&section=4" title="עריכת פסקה: "תכונות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>ערכי הדיברגנץ: <ol><li>אם <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 {\vec {\nabla }}\cdot {\vec {F}}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {\nabla }}\cdot {\vec {F}}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/96b6f8a52260fb63ec9474009fc7ab8eed523f61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.647ex; height:2.843ex;" alt="{\displaystyle {\vec {\nabla }}\cdot {\vec {F}}=0}"></span>, אז <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 {\vec {F}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>F</mi> <mo stretchy="false">→<!-- → --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {F}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef40edff397a115ecdce7d3518001dfcc7f37d9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.771ex; height:2.843ex;" alt="{\displaystyle {\vec {F}}}"></span> ייקרא "שדה חסר מקורות", כלומר שמספר "החלקיקים" שנכנסים לנפח אינפיניטסימלי (בהשפעת השדה הווקטורי) שווה למספר החלקיקים היוצאים מהנפח.</li> <li>דיברגנץ חיובי – מספר "החלקיקים" שנכנסים לנפח אינפיניטסימלי (בהשפעת השדה הווקטורי) קטן ממספר החלקיקים שיוצאים – הנפח משמש "ברז" (מקור).</li> <li>דיברגנץ שלילי – מספר "החלקיקים" שנכנסים לנפח אינפיניטסימלי (בהשפעת השדה הווקטורי) גדול ממספר החלקיקים שיוצאים – הנפח משמש "חור ניקוז" (מִבלע).</li></ol></li> <li>יהיו <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 \mathbf {F} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {F} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da18bef8c979f3548bb0d8976f5844012d7b8256" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.683ex; height:2.176ex;" alt="{\displaystyle \mathbf {F} }"></span> ו-<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 \mathbf {G} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {G} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6d9c60d3cf462a9812e9a9d021d17c7bc272a5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.101ex; height:2.176ex;" alt="{\displaystyle \mathbf {G} }"></span> שדות וקטוריים כלשהם, ויהי <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 \varphi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>φ<!-- φ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33ee699558d09cf9d653f6351f9fda0b2f4aaa3e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.52ex; height:2.176ex;" alt="{\displaystyle \varphi }"></span> <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%A1%D7%A7%D7%9C%D7%A8%D7%99" title="שדה סקלרי">שדה סקלרי</a> כלשהו. מתקיימות התכונות הבאות:</li></ul> <ol><li>הדיברגנץ הוא <a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99" class="mw-redirect" title="אופרטור ליניארי">אופרטור ליניארי</a>, קרי: <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 \nabla \cdot (\alpha \mathbf {F} +\beta \mathbf {G} )=\alpha (\nabla \cdot \mathbf {F} )+\beta (\nabla \cdot \mathbf {G} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mi>α<!-- α --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>+</mo> <mi>β<!-- β --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>α<!-- α --></mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mi>β<!-- β --></mi> <mo stretchy="false">(</mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot (\alpha \mathbf {F} +\beta \mathbf {G} )=\alpha (\nabla \cdot \mathbf {F} )+\beta (\nabla \cdot \mathbf {G} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9791af17353141e173ea83064fbf18da51f5e397" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.258ex; height:2.843ex;" alt="{\displaystyle \nabla \cdot (\alpha \mathbf {F} +\beta \mathbf {G} )=\alpha (\nabla \cdot \mathbf {F} )+\beta (\nabla \cdot \mathbf {G} )}"></span></li> <li>בכלל מכפלה אחד נעשה שימוש גם באופרטור <a href="/wiki/%D7%92%D7%A8%D7%93%D7%99%D7%90%D7%A0%D7%98" title="גרדיאנט">גרדיאנט</a>:</li></ol> <dl><dd><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 \nabla \cdot (\varphi \mathbf {F} )=(\nabla \varphi )\cdot \mathbf {F} +\varphi \;(\nabla \cdot \mathbf {F} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mi>φ<!-- φ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mi>φ<!-- φ --></mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>+</mo> <mi>φ<!-- φ --></mi> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot (\varphi \mathbf {F} )=(\nabla \varphi )\cdot \mathbf {F} +\varphi \;(\nabla \cdot \mathbf {F} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d80a927a2079ce2aad6cba6483018f113c462bae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.465ex; height:2.843ex;" alt="{\displaystyle \nabla \cdot (\varphi \mathbf {F} )=(\nabla \varphi )\cdot \mathbf {F} +\varphi \;(\nabla \cdot \mathbf {F} )}"></span></dd></dl></dd> <dd>או ברישום אחר: <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 \operatorname {div} (\varphi \mathbf {F} )=\operatorname {grad} (\varphi )\cdot \mathbf {F} +\varphi \;\operatorname {div} (\mathbf {F} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>div</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>φ<!-- φ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>grad</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mi>φ<!-- φ --></mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>+</mo> <mi>φ<!-- φ --></mi> <mspace width="thickmathspace" /> <mi>div</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {div} (\varphi \mathbf {F} )=\operatorname {grad} (\varphi )\cdot \mathbf {F} +\varphi \;\operatorname {div} (\mathbf {F} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3fc8f3568c0c9e6bb99d9eb7fb9c14ab310f85f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.549ex; height:2.843ex;" alt="{\displaystyle \operatorname {div} (\varphi \mathbf {F} )=\operatorname {grad} (\varphi )\cdot \mathbf {F} +\varphi \;\operatorname {div} (\mathbf {F} )}"></span></dd></dl></dd> <dd>3. כלל מכפלה עבור <a href="/wiki/%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%AA" title="מכפלה וקטורית">מכפלה וקטורית</a> עושה שימוש גם באופרטור <a href="/wiki/%D7%A8%D7%95%D7%98%D7%95%D7%A8_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="רוטור (מתמטיקה)">קרל</a>: <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 \nabla \cdot (\mathbf {F} \times \mathbf {G} )=(\nabla \times \mathbf {F} )\cdot \mathbf {G} -\mathbf {F} \cdot (\nabla \times \mathbf {G} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∇<!-- ∇ --></mi> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nabla \cdot (\mathbf {F} \times \mathbf {G} )=(\nabla \times \mathbf {F} )\cdot \mathbf {G} -\mathbf {F} \cdot (\nabla \times \mathbf {G} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/479e495af7f9ac7ac421f7724cdd493d61a1facf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:42.083ex; height:2.843ex;" alt="{\displaystyle \nabla \cdot (\mathbf {F} \times \mathbf {G} )=(\nabla \times \mathbf {F} )\cdot \mathbf {G} -\mathbf {F} \cdot (\nabla \times \mathbf {G} )}"></span></dd></dl></dd> <dd>או ברישום אחר: <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 \operatorname {div} (\mathbf {F} \times \mathbf {G} )=\operatorname {curl} (\mathbf {F} )\cdot \mathbf {G} \;-\;\mathbf {F} \cdot \operatorname {curl} (\mathbf {G} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>div</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>×<!-- × --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>curl</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mspace width="thickmathspace" /> <mo>−<!-- − --></mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">F</mi> </mrow> <mo>⋅<!-- ⋅ --></mo> <mi>curl</mi> <mo>⁡<!-- --></mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">G</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {div} (\mathbf {F} \times \mathbf {G} )=\operatorname {curl} (\mathbf {F} )\cdot \mathbf {G} \;-\;\mathbf {F} \cdot \operatorname {curl} (\mathbf {G} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/668ce8920c2213e442caea1ff02bbe521747eec3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.14ex; height:2.843ex;" alt="{\displaystyle \operatorname {div} (\mathbf {F} \times \mathbf {G} )=\operatorname {curl} (\mathbf {F} )\cdot \mathbf {G} \;-\;\mathbf {F} \cdot \operatorname {curl} (\mathbf {G} )}"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading2"><h2 id="קישורים_חיצוניים"><span id=".D7.A7.D7.99.D7.A9.D7.95.D7.A8.D7.99.D7.9D_.D7.97.D7.99.D7.A6.D7.95.D7.A0.D7.99.D7.99.D7.9D"></span>קישורים חיצוניים</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&action=edit&section=5" title="עריכת קוד המקור של הפרק: קישורים חיצוניים"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%93%D7%99%D7%91%D7%A8%D7%92%D7%A0%D7%A5&veaction=edit&section=5" title="עריכת פסקה: "קישורים חיצוניים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="sisterwikilinkT"><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/" title="ויקישיתוף"><img alt="ויקישיתוף" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> מדיה וקבצים בנושא <b><a href="https://commons.wikimedia.org/wiki/Category:Divergence" class="extiw" title="commons:Category:Divergence">דיברגנץ</a></b> ב<a href="/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A9%D7%99%D7%AA%D7%95%D7%A3" title="ויקישיתוף">וויקישיתוף</a></div> <ul><li><a rel="nofollow" class="external text" href="https://youtu.be/bWJLPsKhhak?list=PLW6KNQoisKdsaND4eIPz3Ye9cA4ShlOy8&t=2562">HIT משפט הדיברגנץ</a> - הסבר אינטואיטיבי על משפט הדיברגנץ בעברית</li> <li><a rel="nofollow" class="external text" href="https://www.encyclopediaofmath.org/index.php/Divergence">דיברגנץ</a>, באתר <a href="/wiki/%D7%90%D7%A0%D7%A6%D7%99%D7%A7%D7%9C%D7%95%D7%A4%D7%93%D7%99%D7%94_%D7%9C%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94" title="אנציקלופדיה למתמטיקה">אנציקלופדיה למתמטיקה</a> <span dir="rtl" class="languageicon">(באנגלית)</span><style data-mw-deduplicate="TemplateStyles:r36549940">.mw-parser-output .languageicon{font-size:0.95em;font-weight:bold;color:#555}</style></li> <li><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/divergence-mathematics">דיברגנץ</a>, באתר <a href="/wiki/%D7%90%D7%A0%D7%A6%D7%99%D7%A7%D7%9C%D7%95%D7%A4%D7%93%D7%99%D7%94_%D7%91%D7%A8%D7%99%D7%98%D7%A0%D7%99%D7%A7%D7%94" title="אנציקלופדיה בריטניקה">אנציקלופדיה בריטניקה</a> <span dir="rtl" class="languageicon">(באנגלית)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36549940"></li> <li><a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Divergence.html">דיברגנץ</a>, באתר <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> <span dir="rtl" class="languageicon">(באנגלית)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36549940"></li></ul> <p><br /> </p> <table class="navbox nowraplinks mw-collapsible autocollapse" style="width: 90%; clear: both; margin: 0.5em auto; margin-top: 0.5em; margin-bottom: 0.5em; padding: 0.2em; text-align: right;"> <tbody><tr> <th colspan="3" style="text-align: center; padding-top: 0.1em; padding-bottom: 0.1em; color: black; background:#d1eeee; font-weight: bold;"><a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%AA" title="אנליזה וקטורית">אנליזה וקטורית</a> </th></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">מושגים </td> <td style="padding-right: 5px; text-align: right;"><a href="/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_-_%D7%9E%D7%95%D7%A0%D7%97%D7%99%D7%9D" title="אנליזה מתמטית - מונחים">אנליזה מתמטית - מונחים</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב וקטורי</a> • <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%A1%D7%A7%D7%9C%D7%A8%D7%99" title="שדה סקלרי">שדה סקלרי</a> • <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="שדה וקטורי">שדה וקטורי</a> • <a href="/wiki/%D7%92%D7%A8%D7%93%D7%99%D7%90%D7%A0%D7%98" title="גרדיאנט">גרדיאנט</a> • <a href="/wiki/%D7%A0%D7%92%D7%96%D7%A8%D7%AA_%D7%9B%D7%99%D7%95%D7%95%D7%A0%D7%99%D7%AA" title="נגזרת כיוונית">נגזרת כיוונית</a> • <a class="mw-selflink selflink">דיברגנץ</a> • <a href="/wiki/%D7%A8%D7%95%D7%98%D7%95%D7%A8_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="רוטור (מתמטיקה)">רוטור</a> • <a href="/wiki/%D7%9C%D7%A4%D7%9C%D7%A1%D7%99%D7%90%D7%9F" title="לפלסיאן">לפלסיאן</a> • <a href="/wiki/%D7%93%D7%9C_%D7%91%D7%9E%D7%A2%D7%A8%D7%9B%D7%95%D7%AA_%D7%A6%D7%99%D7%A8%D7%99%D7%9D_%D7%A9%D7%95%D7%A0%D7%95%D7%AA" title="דל במערכות צירים שונות">דל במערכות צירים שונות</a> • <a href="/wiki/%D7%93%27%D7%90%D7%9C%D7%9E%D7%91%D7%A8%D7%98%D7%99%D7%90%D7%9F" title="ד'אלמברטיאן">ד'אלמברטיאן</a> • <a href="/wiki/%D7%A4%D7%95%D7%98%D7%A0%D7%A6%D7%99%D7%90%D7%9C_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="פוטנציאל וקטורי (מתמטיקה)">פוטנציאל וקטורי</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">משפטים </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%92%D7%90%D7%95%D7%A1" title="משפט גאוס">משפט גאוס</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%92%D7%A8%D7%99%D7%9F" title="משפט גרין">משפט גרין</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%92%D7%A8%D7%93%D7%99%D7%90%D7%A0%D7%98" title="משפט הגרדיאנט">משפט הגרדיאנט</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%A1%D7%98%D7%95%D7%A7%D7%A1" title="משפט סטוקס">משפט סטוקס</a> </td></tr> <tr> <td colspan="3" style="background-color: #F2F3F4; text-align: center; font-weight: bold;"><a href="/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">אנליזה מתמטית</a> • <a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%AA" title="אנליזה וקטורית">אנליזה וקטורית</a> • <a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94" title="טופולוגיה">טופולוגיה</a> • <a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%9E%D7%A8%D7%95%D7%9B%D7%91%D7%AA" title="אנליזה מרוכבת">אנליזה מרוכבת</a> • <a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%A0%D7%9C%D7%99%D7%AA" title="אנליזה פונקציונלית">אנליזה פונקציונלית</a> • <a href="/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%9E%D7%99%D7%93%D7%94" title="תורת המידה">תורת המידה</a> • <a href="/wiki/%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94_%D7%93%D7%99%D7%A4%D7%A8%D7%A0%D7%A6%D7%99%D7%90%D7%9C%D7%99%D7%AA" title="גאומטריה דיפרנציאלית">גאומטריה דיפרנציאלית</a> </td></tr> </tbody></table> <div role="navigation" class="navbox authority-control" aria-labelledby="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q189000?uselang=he&#124;עריכת_הנתון_בוויקינתונים" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q189000?uselang=he&#124;עריכת_הנתון_בוויקינתונים" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A7%D7%A8%D7%AA_%D7%96%D7%94%D7%95%D7%99%D7%95%D7%AA" title="עזרה:בקרת זהויות">בקרת זהויות</a> <span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q189000?uselang=he" title="עריכת הנתון בוויקינתונים"><img alt="עריכת הנתון בוויקינתונים" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/15px-Blue_pencil_RTL.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/23px-Blue_pencil_RTL.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/30px-Blue_pencil_RTL.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></th><td class="navbox-list navbox-odd" style="text-align:left;border-right-width:2px;border-right-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><div dir="ltr"> <ul><li><span class="nowrap"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5_%D7%91%D7%A7%D7%A8%D7%94_%D7%9E%D7%A9%D7%95%D7%9C%D7%91" title="קובץ בקרה משולב">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4528420-9">4528420-9</a></span></span></li></ul> </div></div></td></tr></tbody></table></div> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐64476968cd‐5sqh8 Cached time: 20241102100924 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.161 seconds 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