{"id":1562,"date":"2024-01-29T10:20:53","date_gmt":"2024-01-29T15:20:53","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2024\/?p=1562"},"modified":"2024-02-21T18:43:09","modified_gmt":"2024-02-21T23:43:09","slug":"slides-k-forms","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2024\/2024\/01\/29\/slides-k-forms\/","title":{"rendered":"Slides\u2014\\(k\\)-Forms"},"content":{"rendered":"<p>Today we continue our journey toward building up (discrete) exterior calculus by talking about how to <em>measure<\/em> little k-dimensional volumes. Just like rulers measure length, and cups measure volume, <em>k-forms<\/em> will be used to take measurements of the little <em>k<\/em>-dimensional volumes or <em>k-vectors<\/em> that we built up using exterior algebra in our previous lecture. Such measurements will ultimately allow us to talk about integration over curved spaces; in the discrete setting, these measurements will be the basic data we associate with the elements of mesh.<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/01\/DDG_458_SP19_Lecture04_kForms.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2024\/wp-content\/uploads\/2019\/01\/DDG_458_SP19_Lecture04_kForms_icon.jpg\" alt=\"\" width=\"419\" height=\"243\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today we continue our journey toward building up (discrete) exterior calculus by talking about how to measure little k-dimensional volumes. Just like rulers measure length, and cups measure volume, k-forms will be used to take measurements of the little k-dimensional volumes or k-vectors that we built up using exterior algebra in our previous lecture. Such &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2024\/2024\/01\/29\/slides-k-forms\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Slides\u2014\\(k\\)-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":{"inline_featured_image":false,"footnotes":"","_links_to":"","_links_to_target":""},"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1562"}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/comments?post=1562"}],"version-history":[{"count":4,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1562\/revisions"}],"predecessor-version":[{"id":2365,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/posts\/1562\/revisions\/2365"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/media?parent=1562"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/categories?post=1562"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2024\/wp-json\/wp\/v2\/tags?post=1562"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}