{"id":1628,"date":"2019-02-07T08:16:07","date_gmt":"2019-02-07T13:16:07","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2019\/?p=1628"},"modified":"2019-02-13T10:55:16","modified_gmt":"2019-02-13T15:55:16","slug":"reading-4-exterior-calculus","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2019\/2019\/02\/07\/reading-4-exterior-calculus\/","title":{"rendered":"Reading 4: Exterior Calculus \u2014 due 2\/14"},"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&ndash;83).  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, February 14 at 10am<\/b>.  See the <a href=\"http:\/\/brickisland.net\/DDGSpring2019\/assignments\/\">assignments page<\/em> for handin instructions.<\/p>\n<p><a href=\"http:\/\/www.cs.cmu.edu\/~kmcrane\/Projects\/DDG\/paper.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2019\/wp-content\/uploads\/2019\/02\/CMU_DDG_Spring2019_R4_ExteriorCalculus.jpg\" alt=\"\" width=\"287\" height=\"362\" class=\"alignnone size-full wp-image-1629\" srcset=\"https:\/\/brickisland.net\/DDGSpring2019\/wp-content\/uploads\/2019\/02\/CMU_DDG_Spring2019_R4_ExteriorCalculus.jpg 574w, https:\/\/brickisland.net\/DDGSpring2019\/wp-content\/uploads\/2019\/02\/CMU_DDG_Spring2019_R4_ExteriorCalculus-238x300.jpg 238w\" sizes=\"auto, (max-width: 287px) 85vw, 287px\" \/><\/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\/DDGSpring2019\/2019\/02\/07\/reading-4-exterior-calculus\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Reading 4: Exterior Calculus \u2014 due 2\/14&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-1628","post","type-post","status-publish","format-standard","hentry","category-readings"],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1628","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/comments?post=1628"}],"version-history":[{"count":3,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1628\/revisions"}],"predecessor-version":[{"id":1648,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1628\/revisions\/1648"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/media?parent=1628"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/categories?post=1628"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/tags?post=1628"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}