Description

About the Book:

This book is intended to be a simple and easy introduction to the subject. It is meant as a textbook for a course of Complex Analysis at graduate level of Indian universities.

Some of the welcome features of the book are proofs and motivation for the theory; examples are provided to illustrate the concepts; exercises are given at the end of every chapter; keeping in view the applied nature of the subject, ordinary linear homogeneous differential equations of the second order, conformal mapping and its applications are given more attention than most of the other books. Uniform approximation and elliptic functions are treated in great detail; there is also a detailed treatment of harmonic functions, Weierstrass approximation theorem, analytic continuation, Riemann mapping theorem, homological version of Cauchy’s theorem and its applications. Diagrams are also provided wherever feasible that will help the readers to develop skills by imagination to visualize abstract ideas. Solutions to some selected exercises which involve lots of new ideas and theoretical considerations have also been provided at the end.

Contents:

Sets, Functions and Complex Numbers

Metric Spaces

Elementary Properties of Analytic Functions

Line Integral and Cauchy’s Theorem

Applications of Cauchy’s Theorem

Power Series

Laurent Series, Singularities

Residue Theorem and its Applications

Conformal Mapping

Harmonic Functions

Weierstrass Factorization Theorem

Extension of the Maximum Modulus Principle

Elliptic Functions

Analytic Continuation, Differential Equation

Approximation by Rational Functions and Polynomials