Engineering Mathematics Iv Complex Variables And Fourier Analysis Jntu

This is the Second edition of the book "Engineering Mathematics Volume-IV (Complex Variables and Fourier Analysis)". This text book has been written strictly according to the revised syllabus (R-16) 2016-17 of B. Tech. II Year, First Semester students of Jawaharlal Nehru Technological University, Hyderabad. The treatment of all topics has been made as simple as possible and in some instances with detailed explanation as the book is meant to be understood with a minimum effort on the part of the reader. However, as Mathematics is a subject to be understood and practiced, the students are advised to practice the exercises.

Engineering Mathematic

This thoroughly revised book, now in its third edition, continues to discuss two important topics—special functions and complex variables. Chapters have been rearranged keeping in view the current syllabi of the universities. The book analyzes special functions, Legendre’s equation and function, and Bessel’s function. It explains how to solve Cauchy equations, differential equation with variable coefficients and Frobenius of solving differential equation at a regular singular point. Besides, the text also explains the notions of limit, continuity and differentiability by giving a thorough grounding on analytic functions and their relations with harmonic functions. In addition, the book introduces the exponential function of a complex variable, and with the help of this function, defines trigonometric and hyperbolic functions and explains their properties. While discussing different mathematical concepts, the book discusses a number of theorems such as Cauchy’s integral theorem for the integration of a complex variable, Taylor’s theorem for the analysis of complex power series, the residue theorem for evaluation of residues, the argument principle and Rouche’s theorem for the determination of the number of zeroes of complex polynomials. Finally, the book gives a thorough exposition of conformal mappings and develops the theory of bilinear transformation.

Unit I 1. Real And Complex Matrices And Linear System Of Equations 2. Eigen Values And Eigen Vectors 3. Quadratic Forms Unit Ii 4. Solution Of Algebraic And Transcendental Equations 5. Interpolation 6. Curve Fitting Unit Iii 7. Numerical Differentiation And Integration 8. Numerical Solution Of Ordinary Differential Equations Unit Iv 9. Fourier Series 10. Fourier Transforms Unit V 11. Partial Differential Equations

Engineering Mathematics Vol.-III

This Jntu, Hyderabad Edition Is Designed For The Core Course On The Subject And Presents A Detailed Yet Simple Treatment Of The Fundamental Principles Given In The Syllabus. All Basic Concepts Have Been Comprehensively Explained And Illustrated Through A Variety Of Solved Examples. Instead Of Too Much Mathematically Involved Illustrations, A Step-By-Step Approach Has Been Followed Throughout The Book.Unsolved Problems, Objective And Review Questions Along With Short-Answer Questions Have Been Also Included For A Thorough Grasp Of The Subject. Graded Problems Have Been Included. The Book Would Serve As An Excellent Text For The Subjects Mathematics-I (Common To All Branches), Mathematics-Ii/Mathematical Methods, Probability And Statistics And Partly For Numerical Methods. The Students Are Advised To Refer The Syllabus For The Respective Branches As This Has Been Framed Branch-Wise And For The Need In A Particular Semester.

This text on complex variables is geared toward graduate students and undergraduates who have taken an introductory course in real analysis. It is a substantially revised and updated edition of the popular text by Robert B. Ash, offering a concise treatment that provides careful and complete explanations as well as numerous problems and solutions. An introduction presents basic definitions, covering topology of the plane, analytic functions, real-differentiability and the Cauchy-Riemann equations, and exponential and harmonic functions. Succeeding chapters examine the elementary theory and the general Cauchy theorem and its applications, including singularities, residue theory, the open mapping theorem for analytic functions, linear fractional transformations, conformal mapping, and analytic mappings of one disk to another. The Riemann mapping theorem receives a thorough treatment, along with factorization of analytic functions. As an application of many of the ideas and results appearing in earlier chapters, the text ends with a proof of the prime number theorem.