{"id":8,"date":"2016-08-27T19:23:17","date_gmt":"2016-08-27T19:23:17","guid":{"rendered":"http:\/\/www.inspirenignite.com\/vtu\/?p=8"},"modified":"2019-08-29T13:36:53","modified_gmt":"2019-08-29T13:36:53","slug":"vtu-b-e-b-tech-syllabus-for-mathematics-i-engineering","status":"publish","type":"post","link":"https:\/\/www.inspirenignite.com\/vtu\/vtu-b-e-b-tech-syllabus-for-mathematics-i-engineering\/","title":{"rendered":"VTU B.E \/ B.Tech Syllabus for Mathematics-I Engineering CBCS 2015-16"},"content":{"rendered":"<p>VTU B.E\/B.Tech \u00a0Syllabus for Mathematics-I Engineering gives you detail information of Mathematics-I syllabus It will be help full to understand you complete curriculum of the year.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Subject Code<\/th>\n<th>15MAT11<\/th>\n<th>IA Marks<\/th>\n<th>20<\/th>\n<\/tr>\n<tr>\n<td>Number of Lecture Hours\/Week<\/td>\n<td>4<\/td>\n<td>Exam Marks<\/td>\n<td>80<\/td>\n<\/tr>\n<tr>\n<td>Total Number of Lecture Hours<\/td>\n<td>50<\/td>\n<td>Exam Hours<\/td>\n<td>3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Course Objectives:<\/strong><br \/>\nTo enable the students to apply the knowledge of Mathematics in various engineering fields by making them to learn the following:<\/p>\n<ul>\n<li>nth derivatives of product of two functions and polar curves.<\/li>\n<li>Partial derivatives<\/li>\n<li>Vector calculus<\/li>\n<li>Reduction formulae of integration; To solve First order differential equations.<\/li>\n<li>Solution of system of linear equations , quadratic forms.<\/li>\n<\/ul>\n<table>\n<tbody>\n<tr>\n<th>Module &#8211; 1<\/th>\n<th><\/th>\n<\/tr>\n<tr>\n<td><strong>Differential Calculus -1:<\/strong> determination of nth order derivatives of Standard functions &#8211; Problems. Leibnitz\u2019s theorem (without proof) &#8211; problems.<\/p>\n<p><strong>Polar Curves<\/strong> &#8211; angle between the radius vector and tangent, angle between two curves, Pedal equation of polar curves. Derivative of arc length &#8211; Cartesian, Parametric and Polar forms (without proof) &#8211; problems. Curvature and Radius of Curvature \u2013 Cartesian, Parametric, Polar and Pedal forms (without proof) -problems<\/td>\n<td>Hours \u2013 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Module -2<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Differential Calculus -2<\/strong> Taylor\u2019s and Maclaurin\u2019s theorems for function of one variable(statement only)- problems. Evaluation of Indeterminate forms.<\/p>\n<p style=\"text-align: center\"><strong><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy\" target=\"_blank\" rel=\"noopener\">Download iStudy App (No Ads, No PDFs) for complete VTU syllabus, results, timetables and all other updates.<\/a><\/strong><\/p>\n<\/td>\n<td>Hours \u2013 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Module -3<\/strong><\/td>\n<td><strong>\u00a0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Vector Calculus:<\/strong> Derivative of vector valued functions, Velocity, Acceleration and related problems, Scalar and Vector point functions. Definition of Gradient, Divergence and Curl-problems. Solenoidal and Irrotational vector fields. Vector identities &#8211; div(\u0278A), curl (\u0278A ), curl( grad \u0278), div(curl A).<\/td>\n<td>Hours \u2013 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Module -4<\/strong><\/td>\n<td><strong>\u00a0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>Integral Calculus:<\/strong> Reduction formulae &#8211; and n are positive integers), evaluation of these integrals with standard limits (0 to \u03c0\/2) and problems.<\/p>\n<p><strong>Differential Equations<\/strong> <strong>; Solution of first order and first degree differential equations<\/strong> \u2013 Exact, reducible to exact and Bernoulli\u2019s differential equations .Orthogonal trajectories in Cartesian and polar form. Simple problems on Newton&#8217;s law of cooling.<\/td>\n<td>Hours \u2013 10<\/td>\n<\/tr>\n<tr>\n<td><strong>Module -5<\/strong><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><strong>Linear Algebra<\/strong>\u00a0:\u00a0Rank of a matrix by elementary transformations, solution of system of linear equations &#8211; Gauss-elimination method, Gauss \u2013Jordan method and Gauss-Seidel method Eigen values and Eigen vectors, Rayleigh\u2019s power method to find the largest Eigen value and the corresponding Eigen vector. Linear transformation, diagonalisation of a square matrix . Reduction of Quadratic form to Canonical form<\/td>\n<td>Hours \u2013 10<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Course outcomes:<\/strong><br \/>\nOn completion of this course, students are able to<\/p>\n<ul>\n<li>Use partial derivatives to calculate rates of change of multivariate functions.<\/li>\n<li>Analyze position, velocity, and acceleration in two or three dimensions using the calculus of vector valued functions.<\/li>\n<li>Recognize and solve first-order ordinary differential equations, Newton\u2019s law of cooling<\/li>\n<li>Use matrices techniques for solving systems of linear equations in the different areas of Linear Algebra.<\/li>\n<li>Question paper pattern:<\/li>\n<li>The question paper will have ten questions.<\/li>\n<li>Each full Question consisting of 16 marks<\/li>\n<li>There will be 2 full questions(with a maximum of four sub questions) from each module.<\/li>\n<li>Each full question will have sub questions covering all the topics under a module.<\/li>\n<li>The students will have to answer 5 full questions, selecting one full question from each module.<\/li>\n<\/ul>\n<p><strong>Text Books:<\/strong><\/p>\n<ul>\n<li>B.S. Grewal, &#8220;Higher Engineering Mathematics&#8221;, Khanna publishers, 42nd edition, 2013.<\/li>\n<li>Erwin Kreyszig, &#8220;Advanced Engineering MathematicsI, Wiley, 2013<\/li>\n<li>Reference Books:<\/li>\n<li>B.V. Ramana, &#8220;Higher Engineering M athematics&#8221;, Tata Mc Graw-Hill, 2006<\/li>\n<li>N.P.Bali and Manish Goyal, &#8220;A text book of Engineering mathematics\u201d, Laxmi publications, latest edition.<\/li>\n<li>H.K. Dass and Er. RajnishVerma, &#8220;Higher Engineerig Mathematics&#8221;, S.Chand publishing, 1st edition, 2011.<\/li>\n<\/ul>\n<div>For all other BE\/B.Tech 1st Sem Subject syllabus do follow\u00a0<a href=\"https:\/\/www.inspirenignite.com\/vtu\/vtu-be-frist-1st-sem-be-b-tech-cbcs-scheme-syllabus-for-chemistry-group\/\">VTU 1st Sem BE \/ B.Tech Syllabus CBCS (2015-16) Scheme for Chemistry Group.<\/a><\/div>\n<div><\/div>\n<div>For all other BE\/B.Tech 2nd\u00a0Sem Subject syllabus do follow\u00a0<a href=\"https:\/\/www.inspirenignite.com\/vtu\/vtu-be-second-2nd-sem-be-b-tech-cbcs-scheme-syllabus-for-chemistry-group\/\">VTU 2nd Sem BE \/ B.Tech Syllabus CBCS (2015-16) Scheme for Chemistry Group<\/a>.<\/div>\n<p>For more information about all VTU updates please stay connected to us on FB and don\u2019t hesitate to ask any questions in the comment.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>VTU B.E\/B.Tech \u00a0Syllabus for Mathematics-I Engineering gives you detail information of Mathematics-I syllabus It will be help full to understand you complete curriculum of the year. Subject Code 15MAT11 IA [&hellip;]<\/p>\n","protected":false},"author":2259,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[15,2,32],"tags":[],"class_list":["post-8","post","type-post","status-publish","format-standard","hentry","category-syllabus","category-1st-sem","category-b-e-b-tech"],"_links":{"self":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts\/8","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/users\/2259"}],"replies":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/comments?post=8"}],"version-history":[{"count":9,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts\/8\/revisions"}],"predecessor-version":[{"id":2754,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts\/8\/revisions\/2754"}],"wp:attachment":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/media?parent=8"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/categories?post=8"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/tags?post=8"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}