{"id":650,"date":"2016-05-23T06:36:25","date_gmt":"2016-05-23T06:36:25","guid":{"rendered":"http:\/\/www.inspirenignite.com\/jntuh\/?p=650"},"modified":"2019-07-14T10:06:10","modified_gmt":"2019-07-14T10:06:10","slug":"jntuh-b-tech-2nd-year-1-sem-2-1-mathematics-iii-engineering-r13","status":"publish","type":"post","link":"https:\/\/www.inspirenignite.com\/jntuh\/jntuh-b-tech-2nd-year-1-sem-2-1-mathematics-iii-engineering-r13\/","title":{"rendered":"JNTUH B.Tech 2nd Year 1 sem (2-1) Mathematics \u2013 III Engineering R13"},"content":{"rendered":"<p>JNTUH B.Tech 2nd year\u00a0Mathematics \u2013 III\u00a0Engineering gives you detail information about\u00a0Mathematics \u2013 III\u00a0Engineering subject.<\/p>\n<p><strong>Objectives: To learn<\/strong><\/p>\n<ul>\n<li>Transforming the given variable coefficient equation (Cauchy\u2019s and Lagrange\u2019s) into the one with\u00a0constant coefficients.<\/li>\n<li>Identifying ordinary points, singular points and regular singular points for the given ODE.<\/li>\n<li>Finding the series solution around a regular singular point.<\/li>\n<li>Solve the given ODE with variable coefficients by Frobenius method and test the convergence of its\u00a0series solution.<\/li>\n<li>Series solutions for Legendre and Bessel differential equations, analyzing the properties of\u00a0Legendre and Bessel polynomials.<\/li>\n<li>\u00a0Differentiation and Integration of complex valued functions.<\/li>\n<li>Evaluation of integrals using Cahchy\u2019s integral formula.<\/li>\n<li>Taylor\u2019s series, Maclaurin\u2019s series and Laurent\u2019s series expansions of complex functions<\/li>\n<li>Evaluation of integrals using residue theorem.<\/li>\n<li>Transform a given function from z &#8211; plane to w \u2013 plane.<\/li>\n<li>Identify the transformations like translation, magnification, rotation and reflection and inversion.<\/li>\n<li>Properties of bilinear transformations.<\/li>\n<\/ul>\n<p><strong>UNIT \u2013 I:\u00a0 Linear ODE with variable coefficients and series solutions(second order only):<\/strong><\/p>\n<p>Equations reducible to\u00a0constant coefficients-Cauchy\u2019s and Lagrange\u2019s differential equations. Motivation for series solutions, Ordinary\u00a0point and Regular singular point of a differential equation , Transformation of non-zero singular point to zero\u00a0singular point. Series solutions to differential equations around zero, Frobenius Method about zero.<\/p>\n<p><strong>Unit-II:\u00a0Special Functions<\/strong> :<\/p>\n<p>Legendre\u2019s Differential equation, General solution of Legendre\u2019s equation, Legendre\u00a0polynomials Properties: Rodrigue\u2019s formula \u2013 Recurrence relations, Generating function of Legendre\u2019s\u00a0polynomials \u2013 Orthogonality. Bessel\u2019s Differential equation, Bessel functions properties: \u2013 Recurrence relations,\u00a0Orthogonality, Generating function , Trigonometric expansions involving Bessel functions.<\/p>\n<p><strong>UNIT-III:Complex Functions<\/strong><\/p>\n<p>Differentiation and Integration : Complex functions and its representation on Argand plane, Concepts of limit Continuity, Differentiability, Analyticity, Cauchy-Riemann conditions, Harmonic functions \u2013 Milne \u2013 Thompson method. Line integral \u2013 Evaluation along a path and by indefinite integration \u2013 Cauchy\u2019s integral theorem \u2013 Cauchy\u2019s integral formula \u2013 Generalized integral formula.<\/p>\n<p style=\"text-align: center\"><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=ini.istudy\" target=\"_blank\" rel=\"noopener\"><strong><em><span style=\"color: #ff0000\">Download iStudy Android App for complete JNTUH syllabus, results, timetables and all other updates. There are no ads and no pdfs and will make your life way easier<\/span>.<\/em><\/strong><\/a><\/p>\n<p><strong>TEXT BOOKS:<\/strong><\/p>\n<p>1. Advanced Engineering Mathematics by Kreyszig, John Wiley &amp; Sons.<br \/>\n2. Higher Engineering Mathematics by Dr. B.S. Grewal, Khanna Publishers.<\/p>\n<p><strong>REFERENCES:<\/strong><\/p>\n<p>1) Complex Variables Principles And Problem Sessions By A.K.Kapoor, World Scientific Publishers<br \/>\n2) Engineering Mathematics-3 By T.K.V.Iyengar andB.Krishna Gandhi Etc<br \/>\n3) A Text Book Of Engineering Mathematics By N P Bali, Manesh Goyal<br \/>\n4) Mathematics for Engineers and Scientists, Alan Jeffrey, 6th Edit. 2013, Chapman &amp; Hall\/CRC<br \/>\n5) Advanced Engineering Mathematics, Michael Greenberg, Second Edition. Person Education<br \/>\n6) Mathematics For Engineers By K.B.Datta And M.A S.Srinivas,Cengage Publications<\/p>\n<p><strong>Outcome<\/strong>: After going through this course the student will be able to:<\/p>\n<ul>\n<li>Apply the Frobenius method to obtain a series solution for the given linear 2nd ODE.<\/li>\n<li>Identify Bessel equation and Legendre equation and solve them under special conditions with\u00a0the help of series solutions method. Also recurrence relations and orthogonality properties of\u00a0Bessel and Legendre polynomials.<br \/>\nAfter going to through this course the student will be able to.<\/li>\n<\/ul>\n<p>a. analyze the complex functions with reference to their analyticity, Integration \u00a0using Cauchy\u2019s\u00a0integral theorem,<br \/>\nb. Find the Taylor\u2019s and Laurent series expansion of complex functions<br \/>\nc. The conformal transformations of complex functions can be dealt with ease.<\/p>\n<p><strong>For more information about all JNTU updates please stay connected to us on FB and don\u2019t hesitate to ask any questions in the comment. \ud83d\ude42\u00a0<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>JNTUH B.Tech 2nd year\u00a0Mathematics \u2013 III\u00a0Engineering gives you detail information about\u00a0Mathematics \u2013 III\u00a0Engineering subject. Objectives: To learn Transforming the given variable coefficient equation (Cauchy\u2019s and Lagrange\u2019s) into the one with\u00a0constant [&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":[62],"tags":[],"class_list":["post-650","post","type-post","status-publish","format-standard","hentry","category-syllabus"],"_links":{"self":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/650","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/users\/2259"}],"replies":[{"embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/comments?post=650"}],"version-history":[{"count":4,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/650\/revisions"}],"predecessor-version":[{"id":17714,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/650\/revisions\/17714"}],"wp:attachment":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/media?parent=650"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/categories?post=650"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/tags?post=650"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}