{"id":1289,"date":"2021-03-08T20:30:26","date_gmt":"2021-03-09T02:30:26","guid":{"rendered":"https:\/\/charles-oneill.com\/blog\/?p=1289"},"modified":"2021-03-27T11:09:41","modified_gmt":"2021-03-27T16:09:41","slug":"classical-partial-differential-equations-pde-cheatsheet","status":"publish","type":"post","link":"https:\/\/charles-oneill.com\/blog\/classical-partial-differential-equations-pde-cheatsheet\/","title":{"rendered":"Classical Partial Differential Equations (PDE) Cheatsheet"},"content":{"rendered":"\n<p>The study of classical PDEs is a useful and typical course for engineers and scientists to both appreciate and understand the behavior of physical systems.<\/p>\n\n\n\n<p>As the (former) instructor of a course in PDEs, I reviewed classical solution techniques in a lecture titled <a href=\"https:\/\/charles-oneill.com\/ges554\/misc\/Final-Review.pdf\">A brief history of GES 554 PDE<\/a> to prepare students for their final exam. This lecture makes an excellent refresher or rapid introduction.<\/p>\n\n\n\n<p>If you want to review the entire 50 lecture course, visit <a href=\"https:\/\/charles-oneill.com\/blog\/ges-554-partial-differential-equations\/\">here<\/a>. Feel free to call it <em>The Brief History of the World of PDEs in 50 Parts<\/em>.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/charles-oneill.com\/ges554\/misc\/Final-Review.pdf\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2021\/03\/Toolbox.png\" alt=\"\" class=\"wp-image-1290\" width=\"286\" height=\"316\" srcset=\"https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2021\/03\/Toolbox.png 571w, https:\/\/charles-oneill.com\/blog\/wp-content\/uploads\/2021\/03\/Toolbox-271x300.png 271w\" sizes=\"(max-width: 286px) 100vw, 286px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>Topics covered are:<\/p>\n\n\n\n<ul><li>Motivation, classification &amp; canonical forms<\/li><li>Diffusion, Elliptic, Hyperbolic, and Transport PDEs<\/li><li>Solution methods: Series, Separation of variables, Monte Carlo, finite difference, Ritz \/ Galerkin and Transforms<\/li><li>1 page PDE toolbox<\/li><li>Laplace vs Fourier transforms for PDEs<\/li><li>Sturm Liouville Theory<\/li><li>Wave Equations<\/li><li>Strings, Beams, and Drums<\/li><li>Characteristics in transport equations<\/li><li>Systems of PDEs: eigenvalues &amp; eigenvectors<\/li><li>Green&#8217;s Functions<\/li><li>Calculus of Variations for PDEs<\/li><\/ul>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The study of classical PDEs is a useful and typical course for engineers and scientists to both appreciate and understand the behavior of physical systems. As the (former) instructor of a course in PDEs, I reviewed classical solution techniques in a lecture titled A brief history of GES 554 PDE to prepare students for their [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/1289"}],"collection":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/comments?post=1289"}],"version-history":[{"count":8,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/1289\/revisions"}],"predecessor-version":[{"id":1330,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/posts\/1289\/revisions\/1330"}],"wp:attachment":[{"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/media?parent=1289"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/categories?post=1289"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/charles-oneill.com\/blog\/wp-json\/wp\/v2\/tags?post=1289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}