{"id":11295,"date":"2025-02-23T07:30:56","date_gmt":"2025-02-23T07:30:56","guid":{"rendered":"https:\/\/mathsuop.orizel.com\/?page_id=11295"},"modified":"2026-03-24T05:00:48","modified_gmt":"2026-03-24T05:00:48","slug":"em-1030-differential-equations","status":"publish","type":"page","link":"https:\/\/eng.pdn.ac.lk\/maths\/em-1030-differential-equations\/","title":{"rendered":"EM 1030: Differential Equations"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"11295\" class=\"elementor elementor-11295\">\n\t\t\t\t<div class=\"elementor-element elementor-element-084a54d e-flex e-con-boxed e-con e-parent\" data-id=\"084a54d\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-4f13400 e-con-full e-flex e-con e-child\" data-id=\"4f13400\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-de1f885 elementor-widget elementor-widget-heading\" data-id=\"de1f885\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Basic Details:<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f8c48b7 elementor-widget elementor-widget-text-editor\" data-id=\"f8c48b7\" data-element_type=\"widget\" data-settings=\"{&quot;thim_ekit_motion_fx_mouse&quot;:&quot;yes&quot;,&quot;thim_ekit_motion_fx_tilt_effect&quot;:&quot;yes&quot;,&quot;thim_ekit_motion_fx_tilt_speed&quot;:{&quot;unit&quot;:&quot;px&quot;,&quot;size&quot;:1,&quot;sizes&quot;:[]}}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<ul><li><strong>Course Code<\/strong>: EM 1030<\/li><li><strong>Credits<\/strong>: 2<\/li><li><strong>Compulsory\/Optional<\/strong>: Chemical, Computer, Civil, Mechanical, Manufacturing<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7d06cbe elementor-widget elementor-widget-spacer\" data-id=\"7d06cbe\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-b88759f e-con-full e-flex e-con e-child\" data-id=\"b88759f\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-86cea8d elementor-widget elementor-widget-heading\" data-id=\"86cea8d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Aim :<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1cf13df elementor-widget elementor-widget-text-editor\" data-id=\"1cf13df\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>To introduce analytical solving techniques for differential equations with constant coefficients and interpret the solutions.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5ff70c7 e-flex e-con-boxed e-con e-parent\" data-id=\"5ff70c7\" data-element_type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d8f921a elementor-widget elementor-widget-heading\" data-id=\"d8f921a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Intended Learning Outcomes:<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-723b881 elementor-widget elementor-widget-text-editor\" data-id=\"723b881\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>On successful completion of the course, the students should be able to;<\/p><ul><li>Solve higher order ordinary differential equations with constant coefficients.<\/li><li>Analyze the solution of a second-order ordinary differential equation with constant coefficients.<\/li><li>Apply matrix methods and Laplace transform in solving systems of ordinary differential equations with constant coefficients.<\/li><li>Obtain analytical solutions of first order linear partial differential equations using method of characteristics.<\/li><li>Classify second order linear partial differential equations and solve the wave equation, the Laplace equation and the heat equation.<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cc9874c elementor-widget elementor-widget-spacer\" data-id=\"cc9874c\" data-element_type=\"widget\" data-widget_type=\"spacer.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-spacer\">\n\t\t\t<div class=\"elementor-spacer-inner\"><\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-239eeeb e-con-full e-flex e-con e-child\" data-id=\"239eeeb\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-346e150 elementor-widget elementor-widget-heading\" data-id=\"346e150\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Course Content:<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-dd16f39 elementor-widget elementor-widget-thim-accordion\" data-id=\"dd16f39\" data-element_type=\"widget\" data-widget_type=\"thim-accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"thim-widget-accordion accordion-new-style\"><div id=\"accordion_dd16f39\" class=\"panel-group\" role=\"tablist\" aria-multiselectable=\"true\">\n\t\t\t<div class=\"panel panel-default\">\n\t\t\t\t<div class=\"panel-heading\" role=\"tab\"\n\t\t\t\t\t id=\"heading_accordion_dd16f39_0\">\n\t\t\t\t\t<h4 class=\"panel-title\">\n\t\t\t\t\t\t<a role=\"button\" class=\"collapsed\" data-toggle=\"collapse\"\n\t\t\t\t\t\t   data-parent=\"#accordion_dd16f39\"\n\t\t\t\t\t\t   href=\"#collapse_accordion_dd16f39_0\" aria-expanded=\"false\"\n\t\t\t\t\t\t   aria-controls=\"collapse_accordion_dd16f39_0\">\n\t\t\t\t\t\t\tSecond Order Ordinary Differential Equations: \t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t<\/div>\n\t\t\t\t<div id=\"collapse_accordion_dd16f39_0\"\n\t\t\t\t\t class=\"panel-collapse collapse\"\n\t\t\t\t\t role=\"tabpanel\" aria-labelledby=\"heading_accordion_dd16f39_0\">\n\t\t\t\t\t<div class=\"panel-body\">\n\t\t\t\t\t\t<p>Spring mass damper equation: forced oscillations and resonance.<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\n\t\t\n\t\t\t<div class=\"panel panel-default\">\n\t\t\t\t<div class=\"panel-heading\" role=\"tab\"\n\t\t\t\t\t id=\"heading_accordion_dd16f39_1\">\n\t\t\t\t\t<h4 class=\"panel-title\">\n\t\t\t\t\t\t<a role=\"button\" class=\"collapsed\" data-toggle=\"collapse\"\n\t\t\t\t\t\t   data-parent=\"#accordion_dd16f39\"\n\t\t\t\t\t\t   href=\"#collapse_accordion_dd16f39_1\" aria-expanded=\"false\"\n\t\t\t\t\t\t   aria-controls=\"collapse_accordion_dd16f39_1\">\n\t\t\t\t\t\t\tLaplace Transform: \t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t<\/div>\n\t\t\t\t<div id=\"collapse_accordion_dd16f39_1\"\n\t\t\t\t\t class=\"panel-collapse collapse\"\n\t\t\t\t\t role=\"tabpanel\" aria-labelledby=\"heading_accordion_dd16f39_1\">\n\t\t\t\t\t<div class=\"panel-body\">\n\t\t\t\t\t\t<p>Definition, existence and properties; Laplace transform of standard functions, derivatives and integrals; solve ordinary differential equations with constant coefficients; discontinuous forcing functions; convolution.<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\n\t\t\n\t\t\t<div class=\"panel panel-default\">\n\t\t\t\t<div class=\"panel-heading\" role=\"tab\"\n\t\t\t\t\t id=\"heading_accordion_dd16f39_2\">\n\t\t\t\t\t<h4 class=\"panel-title\">\n\t\t\t\t\t\t<a role=\"button\" class=\"collapsed\" data-toggle=\"collapse\"\n\t\t\t\t\t\t   data-parent=\"#accordion_dd16f39\"\n\t\t\t\t\t\t   href=\"#collapse_accordion_dd16f39_2\" aria-expanded=\"false\"\n\t\t\t\t\t\t   aria-controls=\"collapse_accordion_dd16f39_2\">\n\t\t\t\t\t\t\tBoundary Value Problems: \t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t<\/div>\n\t\t\t\t<div id=\"collapse_accordion_dd16f39_2\"\n\t\t\t\t\t class=\"panel-collapse collapse\"\n\t\t\t\t\t role=\"tabpanel\" aria-labelledby=\"heading_accordion_dd16f39_2\">\n\t\t\t\t\t<div class=\"panel-body\">\n\t\t\t\t\t\t<p>Boundary value problem of a second order differential equation with constant coefficients using direct calculation; Euler Bernoulli equation and Macaulay\u2019s Bracket method.<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\n\t\t\n\t\t\t<div class=\"panel panel-default\">\n\t\t\t\t<div class=\"panel-heading\" role=\"tab\"\n\t\t\t\t\t id=\"heading_accordion_dd16f39_3\">\n\t\t\t\t\t<h4 class=\"panel-title\">\n\t\t\t\t\t\t<a role=\"button\" class=\"collapsed\" data-toggle=\"collapse\"\n\t\t\t\t\t\t   data-parent=\"#accordion_dd16f39\"\n\t\t\t\t\t\t   href=\"#collapse_accordion_dd16f39_3\" aria-expanded=\"false\"\n\t\t\t\t\t\t   aria-controls=\"collapse_accordion_dd16f39_3\">\n\t\t\t\t\t\t\tSystems of ODEs: \t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t<\/div>\n\t\t\t\t<div id=\"collapse_accordion_dd16f39_3\"\n\t\t\t\t\t class=\"panel-collapse collapse\"\n\t\t\t\t\t role=\"tabpanel\" aria-labelledby=\"heading_accordion_dd16f39_3\">\n\t\t\t\t\t<div class=\"panel-body\">\n\t\t\t\t\t\t<p>Converting higher-order differential equations to a system of first-order differential equations; eigenvalue eigenvector method; matrix exponential method.<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\n\t\t\n\t\t\t<div class=\"panel panel-default\">\n\t\t\t\t<div class=\"panel-heading\" role=\"tab\"\n\t\t\t\t\t id=\"heading_accordion_dd16f39_4\">\n\t\t\t\t\t<h4 class=\"panel-title\">\n\t\t\t\t\t\t<a role=\"button\" class=\"collapsed\" data-toggle=\"collapse\"\n\t\t\t\t\t\t   data-parent=\"#accordion_dd16f39\"\n\t\t\t\t\t\t   href=\"#collapse_accordion_dd16f39_4\" aria-expanded=\"false\"\n\t\t\t\t\t\t   aria-controls=\"collapse_accordion_dd16f39_4\">\n\t\t\t\t\t\t\tFirst order linear partial differential equations:\t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t<\/div>\n\t\t\t\t<div id=\"collapse_accordion_dd16f39_4\"\n\t\t\t\t\t class=\"panel-collapse collapse\"\n\t\t\t\t\t role=\"tabpanel\" aria-labelledby=\"heading_accordion_dd16f39_4\">\n\t\t\t\t\t<div class=\"panel-body\">\n\t\t\t\t\t\t<p>Partial differential equations as a mathematical model and Classification; Method of characteristics.<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\n\t\t\n\t\t\t<div class=\"panel panel-default\">\n\t\t\t\t<div class=\"panel-heading\" role=\"tab\"\n\t\t\t\t\t id=\"heading_accordion_dd16f39_5\">\n\t\t\t\t\t<h4 class=\"panel-title\">\n\t\t\t\t\t\t<a role=\"button\" class=\"collapsed\" data-toggle=\"collapse\"\n\t\t\t\t\t\t   data-parent=\"#accordion_dd16f39\"\n\t\t\t\t\t\t   href=\"#collapse_accordion_dd16f39_5\" aria-expanded=\"false\"\n\t\t\t\t\t\t   aria-controls=\"collapse_accordion_dd16f39_5\">\n\t\t\t\t\t\t\tSecond order linear partial differential equations: \t\t\t\t\t\t<\/a>\n\t\t\t\t\t<\/h4>\n\t\t\t\t<\/div>\n\t\t\t\t<div id=\"collapse_accordion_dd16f39_5\"\n\t\t\t\t\t class=\"panel-collapse collapse\"\n\t\t\t\t\t role=\"tabpanel\" aria-labelledby=\"heading_accordion_dd16f39_5\">\n\t\t\t\t\t<div class=\"panel-body\">\n\t\t\t\t\t\t<p>Classification: hyperbolic, parabolic and elliptic equations; Fourier series; method of separation of variables: wave equation, heat equation, Laplace equation on rectangular domains with homogeneous boundary conditions.<\/p>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\n\t\t<\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-7133136 e-con-full e-flex e-con e-parent\" data-id=\"7133136\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-78cef1a elementor-widget elementor-widget-heading\" data-id=\"78cef1a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Time Allocation (Hours):<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-97b0fa9 e-grid e-con-full e-con e-child\" data-id=\"97b0fa9\" data-element_type=\"container\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1640844 elementor-widget elementor-widget-counter\" data-id=\"1640844\" data-element_type=\"widget\" data-widget_type=\"counter.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-counter\">\n\t\t\t<div class=\"elementor-counter-title\">Lectures<\/div>\t\t\t<div class=\"elementor-counter-number-wrapper\">\n\t\t\t\t<span class=\"elementor-counter-number-prefix\"><\/span>\n\t\t\t\t<span class=\"elementor-counter-number\" data-duration=\"1000\" data-to-value=\"25\" data-from-value=\"0\" data-delimiter=\",\">0<\/span>\n\t\t\t\t<span class=\"elementor-counter-number-suffix\"><\/span>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-808daa8 elementor-widget elementor-widget-counter\" data-id=\"808daa8\" data-element_type=\"widget\" data-widget_type=\"counter.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-counter\">\n\t\t\t<div class=\"elementor-counter-title\">Tutorials<\/div>\t\t\t<div class=\"elementor-counter-number-wrapper\">\n\t\t\t\t<span class=\"elementor-counter-number-prefix\"><\/span>\n\t\t\t\t<span class=\"elementor-counter-number\" data-duration=\"1000\" data-to-value=\"5\" data-from-value=\"0\" data-delimiter=\",\">0<\/span>\n\t\t\t\t<span class=\"elementor-counter-number-suffix\"><\/span>\n\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Basic Details: Course Code: EM 1030 Credits: 2 Compulsory\/Optional: Chemical, Computer, Civil, Mechanical, Manufacturing Aim : To introduce analytical solving techniques for differential equations with constant coefficients and interpret the solutions. Intended Learning Outcomes: On successful completion of the course, &hellip; <\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-11295","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/pages\/11295","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/comments?post=11295"}],"version-history":[{"count":13,"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/pages\/11295\/revisions"}],"predecessor-version":[{"id":12988,"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/pages\/11295\/revisions\/12988"}],"wp:attachment":[{"href":"https:\/\/eng.pdn.ac.lk\/maths\/wp-json\/wp\/v2\/media?parent=11295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}