{"id":32307,"date":"2023-05-04T06:39:59","date_gmt":"2023-05-04T06:39:59","guid":{"rendered":"https:\/\/www.inspirenignite.com\/vtu\/21mat21-advanced-calculus-and-numerical-methods-syllabus-chemistry-group-2021-scheme\/"},"modified":"2023-05-04T06:39:59","modified_gmt":"2023-05-04T06:39:59","slug":"21mat21-advanced-calculus-and-numerical-methods-syllabus-chemistry-group-2021-scheme","status":"publish","type":"post","link":"https:\/\/www.inspirenignite.com\/vtu\/21mat21-advanced-calculus-and-numerical-methods-syllabus-chemistry-group-2021-scheme\/","title":{"rendered":"21MAT21: Advanced Calculus and Numerical Methods syllabus Chemistry Group 2021 Scheme"},"content":{"rendered":"

Advanced Calculus and Numerical Methods detailed syllabus for Chemistry Group 2021 Scheme curriculum has been taken from the VTUs<\/a> official website and presented for the Chemistry 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 Chemistry Group 2nd Sem scheme and its subjects, do visit Chemistry Group 2nd Sem 2021 Scheme scheme<\/a>. The detailed syllabus of advanced calculus and numerical methods is as follows. <\/p>\n

Advanced Calculus and Numerical Methods<\/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 teacher can use to accelerate the attainment of the various course outcomes.<\/p>\n<ol>\n<li>In addition to the traditional lecture method, different type 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 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> Integral Calculus Multiple Integrals: Evaluation of double and triple integrals, evaluation of double integrals by change of order of integration, changing into polar coordinates. Applications to find: Area and Volume by double integral. Problems. Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions. Problems.<br \/>\n <i>Self-Study:<\/i> Center of gravity. (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 2:<\/h4>\n<p> Vector Calculus Vector Differentiation: Scalar and vector fields. Gradient, directional derivative, curl and divergence – physical interpretation, solenoidal and irrotational vector fields. Problems. Vector Integration: Line integrals, Surface integrals. Applications to work done by a force and flux. Statement of Green\u2019s theorem and Stoke\u2019s theorem. Problems.<br \/>\n <i>Self-Study:<\/i> Volume integral and Gauss divergence theorem. (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> Numerical methods -1 Solution of polynomial and transcendental equations: Regula-Falsi and Newton-Raphson methods (only formulae). Problems. Finite differences, Interpolation using Newton\u2019s forward and backward difference formulae, Newton\u2019s divided difference formula and Lagrange\u2019s interpolation formula (All formulae without proof). Problems. Numerical integration: Simpson’s (1\/3)rd and (3\/8)th rules(without proof). Problems. Self-Study: Bisection method, Lagrange\u2019s inverse Interpolation, Weddle’s rule. (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> Numerical methods -2 Numerical Solution of Ordinary Differential Equations (ODE\u2019s): Numerical solution of ordinary differential equations of first order and first degree: Taylor\u2019s series method, Modified Euler\u2019s method, Runge-Kutta method of fourth order, Milne\u2019s predictor-corrector formula (No derivations of formulae). Problems. Self-Study: Adam-Bashforth method. (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 concept of change of order of integration and change of variables to evaluate multiple integrals and their usage in computing the area and volume.<\/li>\n<li>Illustrate the applications of multivariate calculus to understand the solenoidal and irrotational vectors and also exhibit the inter dependence of line, surface and volume integrals.<\/li>\n<li>Formulate physical problems to partial differential equations and to obtain solution for standard practical PDE\u2019s.<\/li>\n<li>Apply the knowledge of numerical methods in modelling of various physical and engineering phenomena.<\/li>\n<li>Solve first order ordinary differential equations arising in engineering problems.<\/li>\n<\/ul>\n<h4>Text Books:<\/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 text book 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 Mathematics 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 Chemistry Group, 2021 Scheme curriculum do visit <a class=\"rank-math-link\" href=\"..\/category\/chemistry-group+2nd-sem\">Chemistry Group 2nd Sem subject syllabuses for 2021 Scheme<\/a>. <\/p>\n<p align=\"justify\">For all Chemistry Group results, visit <a class=\"rank-math-link\" href=\"https:\/\/www.inspirenignite.com\/vtu\/vtu-be-btech-results\/\">VTU Chemistry Group all semester results<\/a> direct link. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Advanced Calculus and Numerical Methods detailed syllabus for Chemistry Group 2021 Scheme curriculum has been taken from the VTUs official website and presented for the Chemistry Group students. For course […]<\/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":[3,106],"tags":[],"class_list":["post-32307","post","type-post","status-publish","format-standard","hentry","category-2nd-sem","category-chemistry-group"],"_links":{"self":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts\/32307","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=32307"}],"version-history":[{"count":0,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/posts\/32307\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/media?parent=32307"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/categories?post=32307"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/vtu\/wp-json\/wp\/v2\/tags?post=32307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}