{"id":32273,"date":"2023-05-04T06:39:16","date_gmt":"2023-05-04T06:39:16","guid":{"rendered":"https:\/\/www.inspirenignite.com\/vtu\/21mat11-calculus-differential-equations-syllabus-physics-group-2021-scheme\/"},"modified":"2023-05-04T06:39:16","modified_gmt":"2023-05-04T06:39:16","slug":"21mat11-calculus-differential-equations-syllabus-physics-group-2021-scheme","status":"publish","type":"post","link":"https:\/\/www.inspirenignite.com\/vtu\/21mat11-calculus-differential-equations-syllabus-physics-group-2021-scheme\/","title":{"rendered":"21MAT11: Calculus & Differential Equations syllabus Physics Group 2021 Scheme"},"content":{"rendered":"

Calculus & Differential Equations detailed syllabus for Physics Group 2021 Scheme curriculum has been taken from the VTUs<\/a> official website and presented for the Physics Group students. For course code, course name, duration, number of credits for a course and other scheme related information, do visit full semester subjects post given below. <\/p>\n

For Physics Group 1st Sem scheme and its subjects, do visit Physics Group 1st Sem 2021 Scheme scheme<\/a>. The detailed syllabus of calculus & differential equations is as follows. <\/p>\n

Calculus & Differential Equations<\/title><\/p>\n<h4>Course Objectives:<\/h4>\n<h4 id=\"istudy\" style=\"text-align:center\"><a class=\"rank-math-link\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy\" style=\"color: inherit\" target=\"_blank\" rel=\"noopener\">Download the iStudy App for all Syllabus, QPs and other updates.<\/a><br \/><a class=\"rank-math-link\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy&pcampaignid=pcampaignidMKT-Other-global-all-co-prtnr-py-PartBadge-Mar2515-1\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/play.google.com\/intl\/en_us\/badges\/static\/images\/badges\/en_badge_web_generic.png\" alt=\"Get it on Google Play\" style=\"height:65px;text-align:center\"><\/a><\/h4>\n<h4>Teaching Learning Process (General Instructions):<\/h4>\n<p> These are sample Strategies, which teachers can use to accelerate the attainment of the various course outcomes.<\/p>\n<ol>\n<li>In addition to the traditional lecture method, different types of innovative teaching methods may be adopted so that the delivered lessons shall develop student\u2019s theoretical and applied mathematical skills.<\/li>\n<li>State the need for Mathematics with Engineering Studies and Provide real-life examples.<\/li>\n<li>Support and guide the students for self-study.<\/li>\n<li>You will also be responsible for assigning homework, grading assignments and quizzes, and documenting students’ progress.<\/li>\n<li>Encourage the students for group learning to improve their creative and analytical skills.<\/li>\n<li>Show short related video lectures in the following ways:\n<ul>\n<li>As an introduction to new topics (pre-lecture activity).<\/li>\n<li>As a revision of topics (post-lecture activity).<\/li>\n<li>As additional examples (post-lecture activity).<\/li>\n<li>As an additional material of challenging topics (pre-and post-lecture activity).<\/li>\n<li>As a model solution of some exercises (post-lecture activity).<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h4>Module 1:<\/h4>\n<p> Differential Calculus – 1 Polar curves, angle between the radius vector and the tangent, angle between two curves. Pedal equations. Curvature and Radius of curvature – Cartesian, Parametric, Polar and Pedal forms. Problems.<br \/>\n <i>Self-Study: Center and Circle of Curvature, Evolutes and Involutes.<\/i> (RBT Levels: L1, L2 and L3 )<\/p>\n<p><i>Teaching-Learning Process 1 Chalk and Talk Method \/ Power Point Presentation<\/i>\n <\/p>\n<h4>Module 2:<\/h4>\n<p> Differential Calculus – 2 Taylor\u2019s and Maclaurin\u2019s series expansion for one variable (Statement only) – problems. Indeterminate forms-L\u2019Hospital\u2019s rule. Partial differentiation, total derivative-differentiation of composite functions. Jacobian and problems. Maxima and minima for a function of two variables. Problems.<br \/>\n <i>Self-Study: Euler\u2019S Theorem and Problems. Method of Lagrange Undetermined Multipliers With Single Constraint.<\/i> (RBT Levels: L1, L2 and L3)<\/p>\n<p><i>Teaching-Learning Process Chalk and Talk Method \/ Power Point Presentation<\/i>\n <\/p>\n<h4>Module 3:<\/h4>\n<h4 id=\"istudy\" style=\"text-align:center\"><a class=\"rank-math-link\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy\" style=\"color: inherit\" target=\"_blank\" rel=\"noopener\">Download the iStudy App for all Syllabus, QPs and other updates.<\/a><br \/><a class=\"rank-math-link\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy&pcampaignid=pcampaignidMKT-Other-global-all-co-prtnr-py-PartBadge-Mar2515-1\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/play.google.com\/intl\/en_us\/badges\/static\/images\/badges\/en_badge_web_generic.png\" alt=\"Get it on Google Play\" style=\"height:65px;text-align:center\"><\/a><\/h4>\n<h4>Module 4:<\/h4>\n<p> Ordinary Differential Equations of higher order Higher-order linear ODE\u2019s with constant coefficients – Inverse differential operator, method of variation of parameters, Cauchy\u2019s and Legendre homogeneous differential equations. Problems.<br \/>\n <i>Self-Study: Applications to Oscillations of a Spring and L-C-R Circuits.<\/i> (RBT Levels: L1, L2 and L3)<\/p>\n<p><i>Teaching Learning Process Chalk and Talk Method \/ Power Point Presentation<\/i>\n <\/p>\n<h4>Module 5:<\/h4>\n<p> Linear Algebra Elementary row transformation of a matrix, Rank of a matrix. Consistency and Solution of system of linear equations; Gauss-elimination method, Gauss-Jordan method and Approximate solution by Gauss-Seidel method. Eigenvalues and Eigenvectors-Rayleigh\u2019s power method to find the dominant Eigenvalue and Eigenvector.<br \/>\n <i>Self-Study: Solution of System of Equations By Gauss-Jacobi Iterative Method. Inverse of a Square Matrix By Cayley- Hamilton Theorem.<\/i> (RBT Levels: L1, L2 and L3).<\/p>\n<p><i>Teaching Learning Process Chalk and Talk Method \/ Power Point Presentation<\/i>\n <\/p>\n<h4>Course Outcomes:<\/h4>\n<p> (Course Skills Set) After successfully completing the course, the student will be able to understand the topics.<\/p>\n<ul>\n<li>Apply the knowledge of calculus to solve problems related to polar curves and its applications in determining the bentness of a curve.<\/li>\n<li>Learn the notion of partial differentiation to calculate rate of change of multivariate functions and solve problems related to composite functions and Jacobian.<\/li>\n<li>Solve first-order linear\/nonlinear ordinary differential equations analytically using standard methods.<\/li>\n<li>Demonstrate various models through higher order differential equations and solve such linear ordinary differential equations.<\/li>\n<li>Test the consistency of a system of linear equations and to solve them by direct and iterative methods.<\/li>\n<\/ul>\n<h4>Suggested Learning Resources:<\/h4>\n<h4 id=\"istudy\" style=\"text-align:center\"><a class=\"rank-math-link\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy\" style=\"color: inherit\" target=\"_blank\" rel=\"noopener\">Download the iStudy App for all Syllabus, QPs and other updates.<\/a><br \/><a class=\"rank-math-link\" href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy&pcampaignid=pcampaignidMKT-Other-global-all-co-prtnr-py-PartBadge-Mar2515-1\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"https:\/\/play.google.com\/intl\/en_us\/badges\/static\/images\/badges\/en_badge_web_generic.png\" alt=\"Get it on Google Play\" style=\"height:65px;text-align:center\"><\/a><\/h4>\n<h4>Reference Books:<\/h4>\n<ol>\n<li>V. Ramana: \u201cHigher Engineering Mathematics\u201d McGraw-Hill Education, 11th Ed.<\/li>\n<li>Srimanta Pal & Subodh C. Bhunia: \u201cEngineering Mathematics\u201d Oxford University Press, 3rd Reprint, 2016.<\/li>\n<li>N.P Bali and Manish Goyal: \u201cA textbook of Engineering Mathematics\u201d Laxmi Publications, Latest edition.<\/li>\n<li>C. Ray Wylie, Louis C. Barrett: \u201cAdvanced Engineering Mathematics\u201d McGraw – Hill Book Co.Newyork, Latest ed.<\/li>\n<li>Gupta C.B, Sing S.R and Mukesh Kumar: \u201cEngineering Mathematic for Semester I and II\u201d, Mc-Graw Hill Education(India) Pvt. Ltd 2015.<\/li>\n<li>H.K.Dass and Er. Rajnish Verma: \u201cHigher Engineering Mathematics\u201d S.Chand Publication (2014).<\/li>\n<li>James Stewart: \u201cCalculus\u201d Cengage publications, 7th edition, 4th Reprint 2019.<\/li>\n<\/ol>\n<h4>Web links and Video Lectures (e-Resources):<\/h4>\n<ul>\n<li>http:\/\/.ac.in\/courses.php?disciplineID=111<\/li>\n<li>http:\/\/www.class-central.com\/subject\/math(MOOCs)<\/li>\n<li>http:\/\/academicearth.org\/<\/li>\n<li>VTU e-Shikshana Program<\/li>\n<li>VTU EDUSAT Program<\/li>\n<\/ul>\n<h4>Activity Based Learning (Suggested Activities in Class)\/ Practical Based learning<\/h4>\n<ul>\n<li>Quizzes<\/li>\n<li>Assignments<\/li>\n<li>Seminars<\/li>\n<\/ul>\n<p align=\"justify\">For detailed syllabus of all other subjects of Physics Group, 2021 Scheme curriculum do visit <a class=\"rank-math-link\" href=\"..\/category\/physics-group+1st-sem\">Physics Group 1st Sem subject syllabuses for 2021 Scheme<\/a>. <\/p>\n<p align=\"justify\">For all Physics Group results, visit <a class=\"rank-math-link\" href=\"https:\/\/www.inspirenignite.com\/vtu\/vtu-be-btech-results\/\">VTU Physics Group all semester results<\/a> direct link. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculus & Differential Equations detailed syllabus for Physics Group 2021 Scheme curriculum has been taken from the VTUs official website and presented for the Physics Group students. For course code, […]<\/p>\n","protected":false},"author":2298,"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":[2,105],"tags":[],"class_list":["post-32273","post","type-post","status-publish","format-standard","hentry","category-1st-sem","category-physics-group"],"_links":{"self":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts\/32273","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\/2298"}],"replies":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/comments?post=32273"}],"version-history":[{"count":0,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts\/32273\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/media?parent=32273"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/categories?post=32273"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/tags?post=32273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}