{"id":6728,"date":"2016-02-01T10:22:40","date_gmt":"2016-02-01T14:22:40","guid":{"rendered":"http:\/\/nycphantom.com\/journal\/?p=6728"},"modified":"2016-02-01T14:54:55","modified_gmt":"2016-02-01T18:54:55","slug":"the-city-college-cuny-class-math-39100-methods-of-differential-equations","status":"publish","type":"post","link":"http:\/\/nycphantom.com\/journal\/?p=6728","title":{"rendered":"The City College CUNY Class: MATH 39100 Methods of Differential Equations"},"content":{"rendered":"<p>Professor: Gennady Yassiyevich<\/p>\n<p>Variable of y will be t, not x, as standard notation.<\/p>\n<p>Ordinary Differential equation. y = y(t)<br \/>\nPartial Differential equation (later this semester, used in theoretical physics, e.g. laplace, etc.) u = u(x,y).<br \/>\nExample: <span class='MathJax_Preview'><img src='http:\/\/nycphantom.com\/journal\/wp-content\/plugins\/latex\/cache\/tex_4aefc7c8683f0616b8d159c0d67d08e7.gif' style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script>.<\/p>\n<p>Def: The \"order\" of a DE is the highest derivative that appears.<br \/>\nExample:<br \/>\nOrder 1:<br \/>\ny' + y = 0<br \/>\n<span class='MathJax_Preview'><img src='http:\/\/nycphantom.com\/journal\/wp-content\/plugins\/latex\/cache\/tex_731154c7e77ff54fa7e3cbcbc38f0c84.gif' style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script><\/p>\n<p>Order 2:<br \/>\n<span class='MathJax_Preview'><img src='http:\/\/nycphantom.com\/journal\/wp-content\/plugins\/latex\/cache\/tex_036638163e3a902b3d745e2bdc1ad387.gif' style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script><br \/>\n<span class='MathJax_Preview'><img src='http:\/\/nycphantom.com\/journal\/wp-content\/plugins\/latex\/cache\/tex_4871a9ca8e8c8906c90eb6d1dbc1c49d.gif' style='vertical-align: middle; border: none; ' class='tex' alt=\"\" \/><\/span><script type='math\/tex'><\/script> There can be many more solutions.<\/p>\n<p>We'll do mostly up to order 2, as most applications do.<\/p>\n<p>Numerical Analysis mentioned. City College supposed to offer this course: Solving problems without formulas.<\/p>\n<p>When <strong>initial<\/strong> condition is applied, the solution is called <strong>unique<\/strong> solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Professor: Gennady Yassiyevich Variable of y will be t, not x, as standard notation. Ordinary Differential equation. y = y(t) Partial Differential equation (later this semester, used in theoretical physics, e.g. laplace, etc.) u = u(x,y). Example: . Def: The &hellip; <a href=\"http:\/\/nycphantom.com\/journal\/?p=6728\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[27,10],"tags":[],"class_list":["post-6728","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-projects"],"_links":{"self":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/6728","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=6728"}],"version-history":[{"count":9,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/6728\/revisions"}],"predecessor-version":[{"id":6746,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=\/wp\/v2\/posts\/6728\/revisions\/6746"}],"wp:attachment":[{"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6728"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6728"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/nycphantom.com\/journal\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6728"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}