{"id":970,"date":"2016-06-03T15:36:35","date_gmt":"2016-06-03T15:36:35","guid":{"rendered":"http:\/\/www.inspirenignite.com\/jntuh\/?p=970"},"modified":"2019-07-14T10:42:44","modified_gmt":"2019-07-14T10:42:44","slug":"jntuh-b-tech-2nd-year-1-sem-electronic-computer-engineering-2-1-mathematics-iii-engineering-r13","status":"publish","type":"post","link":"https:\/\/www.inspirenignite.com\/jntuh\/jntuh-b-tech-2nd-year-1-sem-electronic-computer-engineering-2-1-mathematics-iii-engineering-r13\/","title":{"rendered":"JNTUH B.Tech 2nd Year 1 sem Electronic Computer Engineering (2-1) Mathematics \u2013 III Engineering R13."},"content":{"rendered":"<p>JNTUH B.Tech 2nd year Mathematics \u2013 III gives you detail information about Mathematics \u2013 III Engineering R13 year subject. It will be help full you to understand you complete curriculum of the year.<\/p>\n<p><strong>Objectives<\/strong>: To learn<\/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>Differentiation 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<\/strong><\/p>\n<p>Linear ODE with variable coefficients and series solutions(second order only): 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<\/strong><\/p>\n<p>Special Functions : 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<\/strong><\/p>\n<p>Complex Functions \u2013Differentiation and Integration : Complex functions and its representation on Argand\u00a0plane, Concepts of limit Continuity, Differentiability, Analyticity, Cauchy-Riemann conditions, Harmonic functions\u00a0\u2013 Milne \u2013 Thompson method. Line integral \u2013 Evaluation along a path and by indefinite integration \u2013 Cauchy\u2019s\u00a0integral 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<ul>\n<li>Advanced Engineering Mathematics by Kreyszig, John Wiley &amp; Sons.<\/li>\n<li>Higher Engineering Mathematics by Dr. B.S. Grewal, Khanna Publishers.<\/li>\n<\/ul>\n<p><strong>REFERENCES<\/strong><\/p>\n<ul>\n<li>Complex Variables Principles And Problem Sessions By A.K.Kapoor, World Scientific Publishers<\/li>\n<li>Engineering Mathematics-3 By T.K.V.Iyengar andB.Krishna Gandhi Etc<\/li>\n<li>A Text Book Of Engineering Mathematics By N P Bali, Manesh Goyal<\/li>\n<li>Mathematics for Engineers and Scientists, Alan Jeffrey, 6th Edit. 2013, Chapman &amp; Hall\/CRC<\/li>\n<li>Advanced Engineering Mathematics, Michael Greenberg, Second Edition. Person Education.<\/li>\n<li>Mathematics For Engineers By K.B.Datta And M.A S.Srinivas,Cengage Publications.<\/li>\n<\/ul>\n<p><strong>Outcome<\/strong><\/p>\n<p>After going through this course the student will be able to:<\/p>\n<p>Apply the Frobenius method to obtain a series solution for the given linear 2nd ODE.\u00a0Identify Bessel equation and Legendre equation and solve them under special conditions with the help of series\u00a0solutions method. Also recurrence relations and orthogonality properties of Bessel and Legendre polynomials.\u00a0After going to through this course the student will be able to analyze the complex functions with reference to their\u00a0analyticity, Integration using Cauchy\u2019s integral theorem, Find the Taylor\u2019s and Laurent series expansion of\u00a0complex functions. 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.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>JNTUH B.Tech 2nd year Mathematics \u2013 III gives you detail information about Mathematics \u2013 III Engineering R13 year subject. It will be help full you to understand you complete curriculum [&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-970","post","type-post","status-publish","format-standard","hentry","category-syllabus"],"_links":{"self":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/970","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=970"}],"version-history":[{"count":4,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/970\/revisions"}],"predecessor-version":[{"id":17800,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/posts\/970\/revisions\/17800"}],"wp:attachment":[{"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/media?parent=970"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/categories?post=970"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inspirenignite.com\/jntuh\/wp-json\/wp\/v2\/tags?post=970"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}