Special Functions and Complex Variables (Engineering Mathematics III)  (English, Paperback, Bathul Shahnaz)

This well-received book, which is a new edition of Textbook of Engineering Mathematics: Special Functions and Complex Variables by the same author, continues to discuss two important topics—special functions and complex variables. It analyzes special functions such as gamma and beta functions, Legendre’s equation and function, and Bessel’s function. Besides, the text 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 the trigonometric and hyperbolic functions and explains their properties.

While discussing different mathematical concepts, the book analyzes 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, besides the argument principle and Rouche’s theorem for the determination of the number of zeros of complex polynomials. Finally, the book gives a thorough exposition of conformal mappings and develops the theory of bilinear transformation.

Intended as a text for engineering students, this book will also be useful for undergraduate and postgraduate students of Mathematics and students appearing in competitive examinations.

What is New to This Edition:

• Chapters have been reorganized keeping in mind changes in the syllabi.
• A new chapter is exclusively devoted to Graph Theory.

About The Author
Shahnaz Hathul, PhD, is Professor, Department of Mathematics, JNTUH College of Engineering, Kukatpally, Hyderabad. She has more than two decades of teaching experience. A member of the Indian Statistical Association and the Mathematical Association of America, Prof. Bathul has also authored four textbooks on engineering mathematics and statistics.

Table of Contents

Preface
1. Special Functions–I
2. Special Functions–II
3. Complex Differentiation And Elementary Functions
4. Complex Integration
5. Complex Power Series
6. Contour Integration
7. The Conformal Mappings
8. Elementary Graph Theory
9. Argument Principle And Rouche’S Theorem
Index