{"id":17044,"date":"2025-04-02T15:17:27","date_gmt":"2025-04-02T09:47:27","guid":{"rendered":"https:\/\/civileng.helashop.lk\/?page_id=17044"},"modified":"2025-04-02T15:19:41","modified_gmt":"2025-04-02T09:49:41","slug":"em1010","status":"publish","type":"page","link":"https:\/\/eng.pdn.ac.lk\/civileng\/em1010\/","title":{"rendered":"EM1010"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"17044\" class=\"elementor elementor-17044\" data-elementor-post-type=\"page\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f6edd87 e-flex e-con-boxed e-con e-parent\" data-id=\"f6edd87\" 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-52f9f6be elementor-widget elementor-widget-html\" data-id=\"52f9f6be\" 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   <table style=\"border-color: black; font-family: Verdana; font-size: 12pt; text-indent: 0; border-collapse:collapse; margin-left:5.25pt;\" border=\"solid\" cellspacing=\"6\" cellpadding=\"5\">\r\n<tbody style=\"vertical-align: top; overflow: visible;\">\r\n\r\n<tbody>\r\n<tr style=\"height:18.9pt\">\r\n<td style=\"width:203.05pt; border-style:solid; border-width:0.75pt; vertical-align:top\">\r\n\t\t\t\t\t\t<p style=\"margin-top:2.05pt; margin-left:5.5pt; margin-bottom:0pt; font-size:12pt\">\r\n\t\t\t\t\t\t\t<strong><span style=\"font-family:Verdana; letter-spacing:-0.1pt\">Semester:<\/span><\/strong>\r\n\t\t\t\t\t\t<\/p>\r\n\t\t\t\t\t<\/td>\r\n<td colspan=\"6\" style=\"width:442.9pt; border-style:solid; border-width:0.75pt; vertical-align:top\">\r\n<p style=\"margin-top:0pt; margin-left:5.5pt; margin-bottom:0pt; line-height:14.5pt\">\r\n <span style=\"font-family:Verdana; font-size:12pt; letter-spacing:-0.5pt\">1<\/span>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height:18.9pt\">\r\n<td style=\"width:203.05pt; border-style:solid; border-width:0.75pt; vertical-align:top\">\r\n\t\t\t\t\t\t<p style=\"margin-top:2.05pt; margin-left:5.5pt; margin-bottom:0pt; font-size:12pt\">\r\n\t\t\t\t\t\t\t<strong><span style=\"font-family:Verdana; letter-spacing:-0.1pt\">Course Code<\/span><\/strong>\r\n\t\t\t\t\t\t<\/p>\r\n\t\t\t\t\t<\/td>\r\n<td style=\"height: 25px; width: 531px;\" colspan=\"6\">\r\n<p style=\"margin-top:0pt; margin-left:5.5pt; margin-bottom:0pt; line-height:14.5pt\">\r\n <span style=\"font-family:Verdana; font-size:12pt; letter-spacing:-0.5pt\">EM1010<\/span>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height:18.9pt\">\r\n<td style=\"width:203.05pt; border-style:solid; border-width:0.75pt; vertical-align:top\">\r\n\t\t\t\t\t\t<p style=\"margin-top:2.05pt; margin-left:5.5pt; margin-bottom:0pt; font-size:12pt\">\r\n\t\t\t\t\t\t\t<strong><span style=\"font-family:Verdana; letter-spacing:-0.1pt\">Course Name<\/strong>:<\/p>\r\n<\/td>\r\n<td style=\"height: 25px; width: 531px;\" colspan=\"6\">\r\n<p style=\"margin-top:0pt; margin-left:5.5pt; margin-bottom:0pt; line-height:14.5pt\">\r\n <span style=\"font-family:Verdana; font-size:12pt; letter-spacing:-0.5pt\">Calculus I<\/span>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height:18.9pt\">\r\n<td style=\"width:203.05pt; border-style:solid; border-width:0.75pt; vertical-align:top\">\r\n\t\t\t\t\t\t<p style=\"margin-top:2.05pt; margin-left:5.5pt; margin-bottom:0pt; font-size:12pt\">\r\n\t\t\t\t\t\t\t<strong><span style=\"font-family:Verdana; letter-spacing:-0.1pt\">Credit Value:<\/span><\/strong>\r\n\t\t\t\t\t\t<\/p>\r\n\t\t\t\t\t<\/td>\r\n<td style=\"height: 25px; width: 531px;\" colspan=\"6\">\r\n<p style=\"margin-top:0pt; margin-left:5.5pt; margin-bottom:0pt; line-height:14.5pt\">\r\n <span style=\"font-family:Verdana; font-size:12pt; letter-spacing:-0.5pt\"> 4 (Notional hours: 200)<\/span>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height:18.9pt\">\r\n<td style=\"width:203.05pt; border-style:solid; border-width:0.75pt; vertical-align:top\">\r\n\t\t\t\t\t\t<p style=\"margin-top:2.05pt; margin-left:5.5pt; margin-bottom:0pt; font-size:12pt\">\r\n\t\t\t\t\t\t\t<strong><span style=\"font-family:Verdana; letter-spacing:-0.1pt\">Prerequisites:<\/span><\/strong>\r\n\t\t\t\t\t\t<\/p>\r\n\t\t\t\t\t<\/td>\r\n<td style=\"height: 25px; width: 531px;\" colspan=\"6\">\r\n<p style=\"margin-top:0pt; margin-left:5.5pt; margin-bottom:0pt; line-height:14.5pt\">\r\n <span style=\"font-family:Verdana; font-size:12pt; letter-spacing:-0.5pt\">None<\/span>\r\n<\/td>\r\n<\/tr>\r\n<tr style=\"height:18.9pt\">\r\n<td style=\"width:203.05pt; border-style:solid; border-width:0.75pt; vertical-align:top\">\r\n\t\t\t\t\t\t<p style=\"margin-top:2.05pt; margin-left:5.5pt; margin-bottom:0pt; font-size:12pt\">\r\n\t\t\t\t\t\t\t<strong><span style=\"font-family:Verdana; letter-spacing:-0.1pt\">Core\/Optional<\/span><\/strong>\r\n\t\t\t\t\t\t<\/p>\r\n\t\t\t\t\t<\/td>\r\n<td style=\"height: 25px; width: 531px;\" colspan=\"6\">\r\n<p style=\"margin-top:0pt; margin-left:5.5pt; margin-bottom:0pt; line-height:14.5pt\">\r\n <span style=\"font-family:Verdana; font-size:12pt; letter-spacing:-0.5pt\">Core<\/span>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td rowspan=\"2\" width=\"272\">\r\n<p><strong>Hourly Breakdown<\/strong><\/p>\r\n<\/td>\r\n<td colspan=\"2\" width=\"112\">\r\n<p>Lecture hrs.<\/p>\r\n<\/td>\r\n<td width=\"124\">\r\n<p>Tutorial hrs.<\/p>\r\n<\/td>\r\n<td width=\"142\">\r\n<p>Assignment hrs.<\/p>\r\n<\/td>\r\n<td colspan=\"2\" width=\"213\">\r\n<p>Independent Learning &amp; Assessment hrs.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\" width=\"112\">\r\n<p>48<\/p>\r\n<\/td>\r\n<td width=\"124\">\r\n<p>6<\/p>\r\n<\/td>\r\n<td width=\"142\">\r\n<p>12<\/p>\r\n<\/td>\r\n<td colspan=\"2\" width=\"213\">\r\n<p>134<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"7\" width=\"864\">\r\n<p><strong>Course Aim : <\/strong>To introduce mathematical concepts arising in the areas of calculus and functions of complex variables so as to build confidence in students in solving related problems.<\/p>\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\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>analyze <\/strong>concepts in limits, continuity, differentiability of real-valued functions of single and multiple variables and integration of single variable function.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>determine <\/strong>the convergence of sequences and infinite series, the power series expansion of real analytic functions.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>analyze <\/strong>lines, planes, curves and surfaces in 2D and 3D spaces<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>derive <\/strong>the mathematical models of physical problems as differential equations<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>solve <\/strong>first order separable, linear and exact differential equations and reducible forms.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>analyze <\/strong>limits, continuity, and differentiability of complex-valued functions, and determine holomorphic and harmonic functions.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"7\" width=\"864\">\r\n<p><strong>Course Content:<\/strong><\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Functions of a Single Variable<\/strong>: Functions and Limits, Continuity and Differentiability of real valued functions, Intermediate value theorem, Rolle&rsquo;s theorem, Mean value theorem, Leibnitz theorem, and tangent line approximation, extreme values, integration of single variable function.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Sequences and Series<\/strong>: Monotonic and bounded sequences, Convergence, divergence and oscillation of a sequence, Series and their convergence, Real power series and their convergence, Maclaurin and Taylor series approximation.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>First order Ordinary Differential Equations: <\/strong>Differential Equations as a mathematical model and Classification, Separable, Linear, Exact, Reducible forms.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Vector approach to geometry in space<\/strong>: Vectors, Determinant, Vector equations of lines and planes and their geometry, Parametric representation of curves in planes, Curvature, radius and center of curvature, Derivatives of vector valued function in parametric form.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Functions of Several Variables<\/strong>:&nbsp;&nbsp;&nbsp; Limit and continuity of functions of two and three variables, Partial derivatives and total differential, Chain rule and higher order partial derivatives.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; <strong>Functions of Complex Variables: <\/strong>Roots of unity and functions of complex variables, Mapping of complex variables, Derivatives of complex functions, Cauchy Riemann equation, Holomorphic functions, Harmonic functions.<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"7\" width=\"864\">\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 colspan=\"7\" width=\"864\">\r\n<p><strong>Assessment Strategy:<\/strong><\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\" width=\"355\">\r\n<p>Continuous Assessment <br>50%<\/p>\r\n<\/td>\r\n<td colspan=\"5\" width=\"509\">\r\n<p>Final Assessment <br>50%<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"2\" width=\"355\">\r\n<p>Details: Assignments\/Quizzes 10%<\/p>\r\n<p>Tutorials 10%<\/p>\r\n<p>Mid semester examination 30%<\/p>\r\n<\/td>\r\n<td colspan=\"2\" width=\"153\">\r\n<p>Theory (%)<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>50%<\/p>\r\n<\/td>\r\n<td colspan=\"2\" width=\"185\">\r\n<p>Practical (%)<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>-<\/p>\r\n<\/td>\r\n<td width=\"170\">\r\n<p>Other (%)<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>-<\/p>\r\n<\/td>\r\n<\/tr>\r\n<tr>\r\n<td colspan=\"7\" width=\"864\">\r\n<p><strong>Recommended Reading<\/strong>:<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Stewart, J. (2006). <em>Calculus <\/em>(5th edition), Thomson Brooks\/Cole<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Fulks, W. (1978). <em>Advanced Calculus an Introduction to Analysis <\/em>(3rd edition), John Wiley &amp; Sons, Inc.<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Dass, H.K. (2008). <em>Advanced Engineering Mathematics<\/em>. S. Chand Publishing<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Nagle, R.K., Saff, E,W. and Snider A.D. (2012). <em>Fundamentals of Differential Equations <\/em>(8th edition), Pearson Education<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; E. Kreyszig, E.(2011). <em>Advanced Engineering Mathematics <\/em>(10th Edition), Wiley<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Franklin, P. (1960). <em>Differential Equations for Engineers<\/em>, Dover Publications<\/p>\r\n<p>\u27a2&nbsp;&nbsp;&nbsp; Staff, E.B. and Snider A.D. (2013), <em>Fundamentals of Complex Analysis with applications to Engineering and Science <\/em>(3rd edition), Pearson Education<\/p>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>   \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: 1 Course Code EM1010 Course Name: Calculus I Credit Value: 4 (Notional hours: 200) Prerequisites: None Core\/Optional Core Hourly Breakdown Lecture hrs. Tutorial hrs. Assignment hrs. Independent Learning &amp; Assessment hrs. 48 6 12 134 Course Aim : To &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-17044","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages\/17044","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=17044"}],"version-history":[{"count":0,"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/pages\/17044\/revisions"}],"wp:attachment":[{"href":"https:\/\/eng.pdn.ac.lk\/civileng\/wp-json\/wp\/v2\/media?parent=17044"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}