{"id":1637,"date":"2023-02-07T10:27:57","date_gmt":"2023-02-07T15:27:57","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2023\/?p=1637"},"modified":"2023-03-13T12:07:52","modified_gmt":"2023-03-13T16:07:52","slug":"slides-exterior-calculus-ii-integration","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2023\/2023\/02\/07\/slides-exterior-calculus-ii-integration\/","title":{"rendered":"Slides\u2014Exterior Calculus II: Integration"},"content":{"rendered":"<p>Our first lecture on exterior calculus covered differentiation; our second lecture completes the picture by discussing integration of differential forms. The relationship between integration and differentiation is encapsulated by <em>Stokes&#8217; theorem<\/em>, which generalizes the fundamental theorem of calculus, as well as many other important theorems from vector calculus and complex analysis (divergence theorem, Green&#8217;s theorem, Cauchy&#8217;s integral formula, <em>etc.<\/em>). Stokes&#8217; theorem also plays a key role in numerical discretization of geometric problems, appearing for instance in finite volume methods and boundary element methods; for us it will be the essential tool for developing a discrete version of differential forms that we can actually compute with.<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2023\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture07_ExteriorIntegration.pdf\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-1638\" src=\"http:\/\/brickisland.net\/DDGSpring2023\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture07_ExteriorIntegration.jpg\" alt=\"\" width=\"419\" height=\"243\" srcset=\"https:\/\/brickisland.net\/DDGSpring2023\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture07_ExteriorIntegration.jpg 838w, https:\/\/brickisland.net\/DDGSpring2023\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture07_ExteriorIntegration-300x174.jpg 300w, https:\/\/brickisland.net\/DDGSpring2023\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture07_ExteriorIntegration-768x445.jpg 768w\" sizes=\"(max-width: 419px) 85vw, 419px\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Our first lecture on exterior calculus covered differentiation; our second lecture completes the picture by discussing integration of differential forms. The relationship between integration and differentiation is encapsulated by Stokes&#8217; theorem, which generalizes the fundamental theorem of calculus, as well as many other important theorems from vector calculus and complex analysis (divergence theorem, Green&#8217;s theorem, &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2023\/2023\/02\/07\/slides-exterior-calculus-ii-integration\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Slides\u2014Exterior Calculus II: Integration&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"_links_to":"","_links_to_target":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts\/1637"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/comments?post=1637"}],"version-history":[{"count":2,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts\/1637\/revisions"}],"predecessor-version":[{"id":2264,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/posts\/1637\/revisions\/2264"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/media?parent=1637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/categories?post=1637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2023\/wp-json\/wp\/v2\/tags?post=1637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}