{"id":1628,"date":"2022-02-03T01:05:07","date_gmt":"2022-02-03T06:05:07","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2022\/?p=1628"},"modified":"2022-01-17T16:49:58","modified_gmt":"2022-01-17T21:49:58","slug":"reading-4-exterior-calculus","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2022\/2022\/02\/03\/reading-4-exterior-calculus\/","title":{"rendered":"Reading 4: Exterior Calculus (due 2\/17)"},"content":{"rendered":"<p>The next reading assignment will wrap up our discussion of exterior calculus, both smooth and discrete. In particular, it will explore how to differentiate and integrate \\(k\\)-forms, and how an important relationship between differentiation and integration (<em>Stokes&#8217; theorem<\/em>) enables us to turn derivatives into discrete operations on meshes. In particular, the basic data we will work with in the computational setting are &#8220;integrals of derivatives,&#8221; which amount to simple scalar quantities we can associate with the vertices, edges, faces, <em>etc.<\/em> of a simplicial mesh. These tools will provide the basis for the algorithms we&#8217;ll explore throughout the rest of the semester.<\/p>\n<p>The reading is the remainder of Chapter 4 from the <a href=\"http:\/\/www.cs.cmu.edu\/~kmcrane\/Projects\/DDG\/paper.pdf\">course notes<\/a>, &#8220;A Quick and Dirty Introduction to Exterior Calculus&#8221;, Sections 4.6 through 4.8 (pages 67\u201383). Note that you just have to read these sections; you do <strong>not<\/strong> have to do the written exercises; a different set of written problems will be posted later on. The reading is due <b>Thursday, March 11 at 10am<\/b>. See the <a href=\"http:\/\/brickisland.net\/DDGSpring2022\/assignments\/\">assignments page for handin instructions.<\/a><\/p>\n<p><a href=\"http:\/\/www.cs.cmu.edu\/~kmcrane\/Projects\/DDG\/paper.pdf\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-1629\" src=\"http:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/CMU_DDG_Spring2019_R4_ExteriorCalculus.jpg\" alt=\"\" width=\"287\" height=\"362\" srcset=\"https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/CMU_DDG_Spring2019_R4_ExteriorCalculus.jpg 574w, https:\/\/brickisland.net\/DDGSpring2022\/wp-content\/uploads\/2019\/02\/CMU_DDG_Spring2019_R4_ExteriorCalculus-238x300.jpg 238w\" sizes=\"(max-width: 287px) 85vw, 287px\" \/><\/a><\/p>\n<p>Your short 2-3 sentence summary is due by <strong>10am Eastern on February 17, 2022.\u00a0<\/strong>\u00a0Handin instructions can be found on the <a href=\"http:\/\/brickisland.net\/DDGSpring2022\/assignments\/\">assignment page<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The next reading assignment will wrap up our discussion of exterior calculus, both smooth and discrete. In particular, it will explore how to differentiate and integrate \\(k\\)-forms, and how an important relationship between differentiation and integration (Stokes&#8217; theorem) enables us to turn derivatives into discrete operations on meshes. In particular, the basic data we will &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2022\/2022\/02\/03\/reading-4-exterior-calculus\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Reading 4: Exterior Calculus (due 2\/17)&#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":[2],"tags":[],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1628"}],"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=1628"}],"version-history":[{"count":7,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1628\/revisions"}],"predecessor-version":[{"id":3418,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/posts\/1628\/revisions\/3418"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/media?parent=1628"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/categories?post=1628"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2022\/wp-json\/wp\/v2\/tags?post=1628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}