{"id":1651,"date":"2022-02-15T01:00:32","date_gmt":"2022-02-15T06:00:32","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=1651"},"modified":"2022-01-17T15:45:53","modified_gmt":"2022-01-17T20:45:53","slug":"slides-discrete-differential-forms","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/02\/15\/slides-discrete-differential-forms\/","title":{"rendered":"Lecture 8: Discrete Differential Forms"},"content":{"rendered":"<p><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture08_DiscreteDifferentialForms-1.pdf\"><img loading=\"lazy\" src=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture09_DiscreteDifferentialForms_icon.jpg\" alt=\"\" width=\"419\" height=\"243\" class=\"alignnone size-full wp-image-1652\" srcset=\"https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture09_DiscreteDifferentialForms_icon.jpg 838w, https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture09_DiscreteDifferentialForms_icon-300x174.jpg 300w, https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/DDG_458_SP19_Lecture09_DiscreteDifferentialForms_icon-768x445.jpg 768w\" sizes=\"(max-width: 419px) 85vw, 419px\" \/><\/a><\/p>\n<p>In this lecture, we turn smooth differential \\(k\\)-forms into discrete objects that we can actually compute with.  The basic idea is actually quite simple: to capture some information about a differential \\(k\\)-form, we integrate it over each oriented \\(k\\)-simplex of a mesh.  The resulting values are just ordinary numbers that give us some sense of what the original \\(k\\)-form must have looked like.<\/p>\n<ul>\n<li><a href=\"https:\/\/www.youtube.com\/watch?v=PGzgE5fqPUo\">Video<\/a><\/li>\n<li><a href=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2020\/02\/DDG_08_DiscreteDifferentialForms.pdf\">Slides<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>In this lecture, we turn smooth differential \\(k\\)-forms into discrete objects that we can actually compute with. The basic idea is actually quite simple: to capture some information about a differential \\(k\\)-form, we integrate it over each oriented \\(k\\)-simplex of a mesh. The resulting values are just ordinary numbers that give us some sense of &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/02\/15\/slides-discrete-differential-forms\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Lecture 8: Discrete Differential Forms&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_links_to":"","_links_to_target":""},"categories":[7,3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1651"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/comments?post=1651"}],"version-history":[{"count":5,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1651\/revisions"}],"predecessor-version":[{"id":3238,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1651\/revisions\/3238"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=1651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=1651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=1651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}