{"id":1529,"date":"2019-01-24T11:49:37","date_gmt":"2019-01-24T16:49:37","guid":{"rendered":"http:\/\/brickisland.net\/DDGSpring2019\/?p=1529"},"modified":"2019-01-24T11:49:37","modified_gmt":"2019-01-24T16:49:37","slug":"slides-exterior-algebra","status":"publish","type":"post","link":"https:\/\/brickisland.net\/DDGSpring2019\/2019\/01\/24\/slides-exterior-algebra\/","title":{"rendered":"Slides\u2014Exterior Algebra"},"content":{"rendered":"<p>Today&#8217;s lecture will cover one of the basic tools we&#8217;ll use throughout the rest of the course: <em>exterior algebra<\/em>. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about <em>volumes<\/em> rather than just vectors. If you felt ok working with things like the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Cross_product\">cross product<\/a> and the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Determinant\">determinant<\/a> in your linear algebra\/vector calculus courses, this shouldn&#8217;t be too big of a leap. (If not, could be a good moment for a <a href=\"http:\/\/brickisland.net\/DDGFall2017\/2017\/09\/03\/linear-algebra-and-vector-calculus-review\/\">review<\/a>!)<\/p>\n<p><a href=\"http:\/\/brickisland.net\/DDGSpring2019\/wp-content\/uploads\/2019\/01\/DDG_458_SP19_Lecture03_ExteriorAlgebra.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/brickisland.net\/DDGSpring2019\/wp-content\/uploads\/2019\/01\/DDG_458_SP19_Lecture03_ExteriorAlgebra_icon.jpg\" alt=\"\" width=\"419\" height=\"243\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today&#8217;s lecture will cover one of the basic tools we&#8217;ll use throughout the rest of the course: exterior algebra. The basic idea is to add a couple new operations to our usual list of vector operations (dot product, cross product, etc.) that make it easy to talk about volumes rather than just vectors. If you &hellip; <a href=\"https:\/\/brickisland.net\/DDGSpring2019\/2019\/01\/24\/slides-exterior-algebra\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Slides\u2014Exterior Algebra&#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":[3],"tags":[],"class_list":["post-1529","post","type-post","status-publish","format-standard","hentry","category-slides"],"_links":{"self":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1529","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=1529"}],"version-history":[{"count":2,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1529\/revisions"}],"predecessor-version":[{"id":1533,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/posts\/1529\/revisions\/1533"}],"wp:attachment":[{"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/media?parent=1529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/categories?post=1529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/brickisland.net\/DDGSpring2019\/wp-json\/wp\/v2\/tags?post=1529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}