{"id":83,"date":"2017-02-17T14:09:52","date_gmt":"2017-02-17T14:09:52","guid":{"rendered":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/?page_id=83"},"modified":"2024-03-04T23:40:27","modified_gmt":"2024-03-04T23:40:27","slug":"tema-2-integrales-multiples-curvilineas-y-de-superficie","status":"publish","type":"page","link":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/?page_id=83","title":{"rendered":"Tema 2: Integrales m\u00faltiples, curvilineas y de superficie"},"content":{"rendered":"<h4 align=\"left\"><strong>TEMA 2.1.\u00a0\u00a0<em>INTEGRALES M\u00daLTIPLES<\/em><\/strong><\/h4>\n<p align=\"left\"><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/04\/03.Integrales_m\u00faltiples.pdf\"><strong>GU\u00cdA TE\u00d3RICA<\/strong><\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Practica_2_Multiples.pdf\"><strong>GU\u00cdA PR\u00c1CTICA\u00a02022<\/strong><\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/A6sEt2n6t3KL7gC\"><strong>GU\u00cdA PR\u00c1CTICA\u00a02021<\/strong><\/a><\/p>\n<p align=\"left\"><strong>GRABACIONES DE CLASES TE\u00d3RICAS 2022<\/strong><\/p>\n<p id=\"sites-page-title-header\" align=\"left\"><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1650365545777\/\">10. Integrales m\u00faltiples &#8211; Dominio de integraci\u00f3n &#8211; Integrales iteradas<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1650538541835\/\">11. Integrales m\u00faltiples &#8211; Cambio de coordenadas &#8211; Aplicaciones<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1650970955379\/\">12. Integrales triples &#8211; Cambio de coordenadas &#8211; Aplicaciones<\/a><\/p>\n<p align=\"left\"><strong>RESOLUCI\u00d3N DE EJERCICIOS DE GU\u00cdA PR\u00c1CTICA (GU\u00cdA 2022)<\/strong><\/p>\n<p align=\"left\"><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Ejercicios_Guia_2_1int_multiple.pdf\">01. Pr\u00e1ctica 2.1<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Ejercicios_Guia_2_2int_multiple.pdf\">02. Pr\u00e1ctica 2.2<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Ejercicios_Guia_2_3int_multiple.pdf\">03. Pr\u00e1ctica 2.3<\/a><\/p>\n<p align=\"left\"><strong>GRABACIONES DE CLASES\u00a0PR\u00c1CTICAS\u00a0(GU\u00cdA 2021)<\/strong><\/p>\n<p align=\"left\"><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1619184036945\/?meetingId=6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1619184036945\/\">Clase Pr\u00e1ctica (5)<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1619695561349\/?meetingId=6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1619695561349\/\">Clase Pr\u00e1ctica (6)<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1619789215361\/?meetingId=6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1619789215361\/\">Clase Pr\u00e1ctica (7)<\/a><\/p>\n<p align=\"left\"><b>V\u00cdDEOS<\/b><strong>\u00a0RESOLUCI\u00d3N DE EJERCICIOS DE LA GU\u00cdA (GU\u00cdA 2021)<\/strong><\/p>\n<p align=\"left\"><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/HTpc27HX3qwPHtW\">Ejercicio 2b<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/T4sGE8Jqo5S35sb\">Ejercicio 4b<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/7bqWLyd37ZSn36x\">Ejercicio 7d<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/b7fkxdiqNPX4XGM\">Ejercicio 12b<\/a><\/p>\n<p align=\"left\"><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/bEEwXciZiaeGiHQ\">Ejercicio 15b<\/a><\/p>\n<h4 align=\"left\"><strong>TEMA\u00a02.2.\u00a0\u00a0<em>INTEGRALES DE L\u00cdNEA<\/em><\/strong><\/h4>\n<p><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/04\/03.Integrales_de_linea.pdf\"><strong>GU\u00cdA TE\u00d3RICA<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Practica_2_Linea.pdf\"><strong>GU\u00cdA PR\u00c1CTICA\u00a02022<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/MftPmemk753ef3n\"><strong>GU\u00cdA PR\u00c1CTICA\u00a02021<\/strong><\/a><\/p>\n<p><strong>GRABACIONES DE CLASES TE\u00d3RICAS 2022<\/strong><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1651576143565\/\">13. Integrales de l\u00ednea &#8211; Diferencial de arco &#8211; Integrales sobre campos escalares y vectoriales<\/a><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1651749374632\/\">14. Integrales de l\u00ednea &#8211; Circulaci\u00f3n &#8211; Primer y Segundo Teorema Fundamental &#8211; Teorema de la Funci\u00f3n Potencial &#8211; Teorema de Green<\/a><\/p>\n<p><strong>RESOLUCI\u00d3N DE EJERCICIOS DE GU\u00cdA PR\u00c1CTICA (GU\u00cdA 2022)<\/strong><\/p>\n<p><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Ejercicios_Guia_2_4int_linea.pdf\">04. Pr\u00e1ctica 2.4<\/a><\/p>\n<p><strong>GRABACIONES DE CLASES\u00a0PR\u00c1CTICAS\u00a0(GU\u00cdA 2021)<\/strong><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1620393365708\/?meetingId=6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1620393365708\/\">Clase Pr\u00e1ctica (8)<\/a><\/p>\n<p><b>V\u00cdDEOS<\/b><strong>\u00a0RESOLUCI\u00d3N DE EJERCICIOS DE LA GU\u00cdA (GU\u00cdA 2021)<\/strong><\/p>\n<p><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/BTPSH5fCrZjytZ6\">Ejercicio 3b<\/a><\/p>\n<p><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/9GLMbDMbF3P2ZTr\">Ejercicios 9 y 10<\/a><\/p>\n<h4><strong>TEMA\u00a02.3.\u00a0\u00a0<em>INTEGRALES DE SUPERFICIE<\/em><\/strong><\/h4>\n<p><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/04\/03.Integrales_de_superficie.pdf\"><strong>GU\u00cdA TE\u00d3RICA<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Practica_2_Superficie.pdf\"><strong>GU\u00cdA PR\u00c1CTICA 2022<\/strong><\/a><\/p>\n<p><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/p6qCsAW6rAgkTfw\"><strong>GU\u00cdA PR\u00c1CTICA\u00a02021<\/strong><\/a><\/p>\n<p><strong>GRABACIONES DE CLASES TE\u00d3RICAS 2022<\/strong><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1652180620583\/\">15. Integrales de superficie &#8211; Representaci\u00f3n param\u00e9trica de una superficie &#8211; Vector normal a una superficie &#8211; Diferencial de superficie<\/a><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1652353828086\/\">16. Integrales de superficie &#8211; Superficie orientable &#8211; Flujo &#8211; Divergencia y rotor de un campo vectorial<\/a><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/b32d0d86e493c177dcc4edd4d2b7f0a51d1cc6ba-1652784693355\/\">17. Integrales de superficie &#8211; Teorema de Gauss &#8211; Teorema de Stokes &#8211; Ejercicios<\/a><\/p>\n<p><strong>RESOLUCI\u00d3N DE EJERCICIOS DE GU\u00cdA PR\u00c1CTICA (GU\u00cdA 2022)<\/strong><\/p>\n<p><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Ejercicios_Guia_2_5int_sup.pdf\">05. Pr\u00e1ctica 2.5<\/a><\/p>\n<p><a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/wp-content\/uploads\/2022\/08\/Ejercicios_Guia_2_6int_sup.pdf\">06. Pr\u00e1ctica 2.6<\/a><\/p>\n<p><strong>GRABACIONES DE CLASES\u00a0PR\u00c1CTICAS\u00a0\u00a0(GU\u00cdA 2021)<\/strong><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1620998467273\/?meetingId=6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1620998467273\/\">Clase Pr\u00e1ctica (9)<\/a><\/p>\n<p><a href=\"https:\/\/scalelite.unsj.edu.ar\/playback\/presentation\/2.3\/6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1621509738694\/?meetingId=6f245df6d7e0aef1a23b48110b35a9a0a71ecb5e-1621509738694\/\">Clase Pr\u00e1ctica (10)<\/a><\/p>\n<p><strong><b>V\u00cdDEOS<\/b>\u00a0RESOLUCI\u00d3N DE EJERCICIOS DE LA GU\u00cdA (GU\u00cdA 2021) <\/strong><\/p>\n<p><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/aQ5HaXgdRpdDpQm\">Ejercicio\u00a0 3c<\/a><\/p>\n<p><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/cfA7Jyio5BrfeGK\">Ejercicio 5a<\/a><\/p>\n<p><a href=\"https:\/\/nextcloud.unsj.edu.ar\/index.php\/s\/LXSprSoYmZQP78E\">Ejercicio 10<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>TEMA 2.1.\u00a0\u00a0INTEGRALES M\u00daLTIPLES GU\u00cdA TE\u00d3RICA GU\u00cdA PR\u00c1CTICA\u00a02022 GU\u00cdA PR\u00c1CTICA\u00a02021 GRABACIONES DE CLASES TE\u00d3RICAS 2022 10. Integrales m\u00faltiples &#8211; Dominio de integraci\u00f3n &#8211; Integrales iteradas 11. Integrales m\u00faltiples &#8211; Cambio de coordenadas &#8211; Aplicaciones 12. Integrales triples &#8211; Cambio de coordenadas &#8211; Aplicaciones RESOLUCI\u00d3N DE EJERCICIOS DE GU\u00cdA PR\u00c1CTICA (GU\u00cdA 2022) 01. Pr\u00e1ctica 2.1 02. Pr\u00e1ctica &hellip; <a href=\"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/?page_id=83\" class=\"more-link\">Seguir leyendo <span class=\"screen-reader-text\">Tema 2: Integrales m\u00faltiples, curvilineas y de superficie<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":23,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-83","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=\/wp\/v2\/pages\/83","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=83"}],"version-history":[{"count":36,"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=\/wp\/v2\/pages\/83\/revisions"}],"predecessor-version":[{"id":982,"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=\/wp\/v2\/pages\/83\/revisions\/982"}],"up":[{"embeddable":true,"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=\/wp\/v2\/pages\/23"}],"wp:attachment":[{"href":"https:\/\/calculo2analisis2.fi.unsj.edu.ar\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=83"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}