{"id":16528,"date":"2025-04-02T11:37:52","date_gmt":"2025-04-02T06:07:52","guid":{"rendered":"https:\/\/civileng.helashop.lk\/?page_id=16528"},"modified":"2025-04-02T11:38:50","modified_gmt":"2025-04-02T06:08:50","slug":"em1020","status":"publish","type":"page","link":"https:\/\/eng.pdn.ac.lk\/civileng\/em1020\/","title":{"rendered":"EM1020"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"16528\" class=\"elementor elementor-16528\" data-elementor-post-type=\"page\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2fd3d978 e-flex e-con-boxed e-con e-parent\" data-id=\"2fd3d978\" data-element_type=\"container\" data-e-type=\"container\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-21ecb18f elementor-widget elementor-widget-html\" data-id=\"21ecb18f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<style>\r\n    table {\r\n        border: 1px solid black;\r\n        font-family: Verdana;\r\n        font-size: 12pt;\r\n        border-collapse: collapse;\r\n        width: 100%;\r\n    }\r\n    td, th {\r\n        border: 1px solid black;\r\n        padding: 5px;\r\n        text-align: left;\r\n    }\r\n    @media screen and (max-width: 600px) {\r\n        table {\r\n            display: block;\r\n            overflow-x: auto;\r\n            white-space: nowrap;\r\n        }\r\n    }\r\n<\/style>\r\n<table>\r\n<tbody style=\"vertical-align: top; overflow: visible;\">\r\n\r\n<tr>\r\n<td style=\"width: 260px;\">\r\n<p><strong>Semester:<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 536px;\" colspan=\"6\">\r\n<p>2<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\">\r\n<p><strong>Course Code<\/strong>:<\/p>\r\n<\/td>\r\n<td style=\"width: 536px;\" colspan=\"6\">\r\n<p>EM1020<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\">\r\n<p><strong>Course Name<\/strong>:<\/p>\r\n<\/td>\r\n<td style=\"width: 536px;\" colspan=\"6\">\r\n<p>Linear Algebra<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\">\r\n<p><strong>Credit Value:<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 536px;\" colspan=\"6\">\r\n<p>3 (Notional hours: 150)<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\">\r\n<p><strong>Prerequisites:<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 536px;\" colspan=\"6\">\r\n<p>None<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\">\r\n<p><strong>Core\/Optional<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 536px;\" colspan=\"6\">\r\n<p>Core<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 260px;\" rowspan=\"2\">\r\n<p><strong>Hourly Breakdown<\/strong><\/p>\r\n<\/td>\r\n<td style=\"width: 97px;\" colspan=\"2\">\r\n<p>Lecture hrs.<\/p>\r\n<\/td>\r\n<td style=\"width: 114.625px;\">\r\n<p>Tutorial hrs.<\/p>\r\n<\/td>\r\n<td style=\"width: 134.375px;\">\r\n<p>Assignment hrs.<\/p>\r\n<\/td>\r\n<td style=\"width: 190px;\" colspan=\"2\">\r\n<p>Independent Learning &amp; Assessment hrs.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 97px;\" colspan=\"2\">\r\n<p>35<\/p>\r\n<\/td>\r\n<td style=\"width: 114.625px;\">\r\n<p>10<\/p>\r\n<\/td>\r\n<td style=\"width: 134.375px;\">\r\n<p>-<\/p>\r\n<\/td>\r\n<td style=\"width: 190px;\" colspan=\"2\">\r\n<p>105<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 796px;\" colspan=\"7\">\r\n<p><strong>Course Aim: <\/strong>To encourage students to develop a working knowledge of the central ideas of linear algebra: vector spaces, linear transformations, orthogonality, eigenvalues, eigenvectors and canonical forms and the applications of these ideas in science and engineering.<\/p>\r\n\r\n<p><strong>Intended Learning Outcomes<\/strong>:<\/p>\r\n<p>On successful completion of the course, the students should be able to;<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>apply <\/strong>the knowledge of matrices, Gaussian reduction and determinants to solve systems of linear equations.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>apply <\/strong>the properties of vector spaces and to generalize the concepts of Euclidean geometry to arbitrary vector spaces.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>identify <\/strong>linear transformations, represent them in terms of matrices, and interpret their geometric aspects.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>calculate <\/strong>eigenvalues and Eigenvectors of matrices and linear transformations and apply the concepts in physical situations.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>prove <\/strong>eigenvalue properties of real symmetric matrices and apply them in quadratic forms.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 796px;\" colspan=\"7\">\r\n<p><strong>Course Content:<\/strong><\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Matrix Algebra: <\/strong>Operations, elementary matrices, inverse, partitioned matrices.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Determinants: <\/strong>Introduction and properties<strong>.<\/strong><\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Vector spaces: <\/strong>Definition, subspaces, linear independence and spanning, basis, change of basis, normed spaces, inner product spaces, Gram-Schmidt orthonormalization.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Linear Transformations: <\/strong>Introduction, matrix representation, operations of linear transformations, change of basis.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>System of linear equations: <\/strong>Gauss and Jordan elimination; LU factorization, least square approximations, ill-conditioned and overdetermined systems.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Characteristic value problem: <\/strong>Computing eigenvalues and eigenvectors, Eigen-basis, diagonalization, matrix exponentials.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Real Symmetric matrices<\/strong>: Properties, definiteness, quadratic forms, applications.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 796px;\" colspan=\"7\">\r\n<p><strong>Teaching \/Learning Methods:<\/strong><\/p>\r\n<p>Classroom lectures, tutorial discussions and in-class assignments<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 796px;\" colspan=\"7\">\r\n<p><strong>Assessment Strategy:<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 339px; text-align: center; vertical-align: middle;\" colspan=\"2\">\r\n<p>Continuous Assessment <br \/>50%<\/p>\r\n<\/td>\r\n<td style=\"width: 457px; text-align: center; vertical-align: middle;\" colspan=\"5\">\r\n<p>Final Assessment <br \/>50%<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 339px; text-align: left; vertical-align: top;\" colspan=\"2\">\r\n<p>Details: <br>Tutorials\/Assignments\/Quizzes 20% <br>Mid Semester Examination 30%<\/p>\r\n<\/td>\r\n<td style=\"width: 132.625px; text-align: left; vertical-align: top;\" colspan=\"2\">\r\n<p>Theory (%) <br \/> <br \/> 50%<\/p>\r\n<\/td>\r\n<td style=\"width: 166.375px; text-align: left; vertical-align: top;\" colspan=\"2\">\r\n<p>Practical (%)<\/p>\r\n<p>&nbsp;-<\/p>\r\n<\/td>\r\n<td style=\"width: 158px; text-align: left; vertical-align: top;\">\r\n<p>Other (%)<\/p>\r\n<p>&nbsp;-<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 796px;\" colspan=\"7\">\r\n<p><strong>Recommended Reading<\/strong>:<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Gilbert Strang, Introduction to Linear Algebra, 5th edition, (2010), Cambridge Press.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; David C. Lay, S. R. Lay &amp; J. Mcdonald, Linear Algebra and its Applications, 5th edition, (2012), Pearson.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; David Poole, Linear Algebra: A Modern introduction, 4th edition, (2005), Cengage.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Thomas. S. Shores, Applied Linear Algebra and Matrix Analysis, (2007), Springer.<\/p>\r\n<\/td>\r\n<\/tr>\r\n\r\n<\/tbody>\r\n<\/table>\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\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Semester: 2 Course Code: EM1020 Course Name: Linear Algebra Credit Value: 3 (Notional hours: 150) Prerequisites: None Core\/Optional Core Hourly Breakdown Lecture hrs. Tutorial hrs. Assignment hrs. Independent Learning &amp; Assessment hrs. 35 10 &#8211; 105 Course Aim: To encourage &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-16528","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages\/16528","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/comments?post=16528"}],"version-history":[{"count":0,"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages\/16528\/revisions"}],"wp:attachment":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/media?parent=16528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}