{"id":4836,"date":"2024-12-19T05:58:50","date_gmt":"2024-12-19T05:58:50","guid":{"rendered":"https:\/\/science.sjp.ac.lk\/mat\/?page_id=4836"},"modified":"2024-12-19T05:59:23","modified_gmt":"2024-12-19T05:59:23","slug":"amt-453-2-0-applied-mathematical-techniques","status":"publish","type":"page","link":"https:\/\/science.sjp.ac.lk\/mat\/amt-453-2-0-applied-mathematical-techniques\/","title":{"rendered":"AMT 453 2.0 Applied Mathematical Techniques"},"content":{"rendered":"<section class=\"wpb-content-wrapper\"><p>[vc_row][vc_column][vc_column_text]<\/p>\n<p><strong>Course:\u00a0<\/strong><strong>AMT 111 2.0\u00a0<\/strong><strong>Analytical Geometry<\/strong>\u00a0<strong>(Compulsory)<\/strong><\/p>\n\n<p><strong>Course content:<\/strong><\/p>\n\n<p style=\"text-align: justify;\">First Order partial Differential Equations, Classification,\u00a0 General first order equation, system of semi-linear first order equations, Quasi-linear equations, Non-linear first order PDEs; Linear Second Order Equations, Classification and reduction to canonical form of linear second order equations; Solution of Cauchy problems for hyperbolic equations by reduction to canonical form,\u00a0 Well posed problems for partial differential equations;\u00a0 The wave equation, Energy method and uniqueness; Well posedness\u00a0 of initial value problem;\u00a0 The heat equation,\u00a0 Solutions using Gaussian kernel; uniqueness; maximum principle for heat equation; Laplace\u2019s equation,\u00a0 Basic properties of harmonic functions; maximum principle for boundary value problem; Existence of solution and well-posedness of boundary value problems for Laplace\u2019s equation; Green\u2019s function ; Duhamel\u2019s Principle;\u00a0 Nonlinear conservation laws,\u00a0 Discontinuous solutions of conservation laws; jump condition; model of a traffic flow, uniqueness and the entropy condition.<\/p>\n\n<p><strong>Recommended Readings:<\/strong><\/p>\n\n\n<ol type=\"1\">\n<li style=\"list-style-type: none;\">\n<ol type=\"1\"><\/p>\n<li>Courant,R., &amp; Hilbert,D. (2008). <em>Methods of Mathematical Physics. <\/em>John Wiley &amp; Sons.<\/li>\n\n\n<li>Strauss,W.A. (2007). <em>Partial Differential Equations: An Introduction. <\/em>John Wiley &amp; Sons.<\/li>\n\n\n<li>Amaranath,T. (2009). <em>An Elementary Course in Partial Differential Equations <\/em>(2<sup>nd<\/sup> ed). Jones and Bartlett Publishers.<\/li>\n\n\n<li>Sneddon,I. (2006). <em>Elements of Partial Differential Equations. <\/em>Dover Publications.<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n\n\n<p>&nbsp;<\/p>\n<p>[\/vc_column_text][\/vc_column][\/vc_row]<\/p>\n<\/section>","protected":false},"excerpt":{"rendered":"<p>[vc_row][vc_column][vc_column_text] Course:\u00a0AMT 111 2.0\u00a0Analytical Geometry\u00a0(Compulsory) Course content: First Order partial Differential Equations, Classification,\u00a0 General first order equation, system of semi-linear first order equations, Quasi-linear equations, Non-linear first order PDEs; Linear Second Order Equations, Classification and reduction to canonical form of linear second order equations; Solution of Cauchy problems for hyperbolic equations by reduction to canonical &hellip; <a href=\"https:\/\/science.sjp.ac.lk\/mat\/amt-453-2-0-applied-mathematical-techniques\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">AMT 453 2.0 Applied Mathematical Techniques<\/span><\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_ti_tpc_template_sync":false,"_ti_tpc_template_id":"","footnotes":""},"_links":{"self":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/4836"}],"collection":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/comments?post=4836"}],"version-history":[{"count":2,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/4836\/revisions"}],"predecessor-version":[{"id":4839,"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/pages\/4836\/revisions\/4839"}],"wp:attachment":[{"href":"https:\/\/science.sjp.ac.lk\/mat\/wp-json\/wp\/v2\/media?parent=4836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}