SPECIAL FUNCTIONS AND COMPLEX VARIABLES (ENGINEERING MATHEMATICS III)

Download or read book SPECIAL FUNCTIONS AND COMPLEX VARIABLES (ENGINEERING MATHEMATICS III) written by BATHUL, SHAHNAZ and published by PHI Learning Pvt. Ltd.. This book was released on 2017-07-07 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Intended as a textbook for engineering students, this book will also be useful for undergraduate and postgraduate students of mathematics. NEW TO THE THIRD EDITION • Includes a new chapter on ‘Linear Ordinary Differential Equations with Variable Coefficients and Series Solutions’ • Incorporates ‘Short Questions and Answers’ to help students to prepare for examinations • Provides several worked-out problems and previous years’ questions and also includes more MCQs and exercises in each chapter