Description
New Age International The Elements of Complex Analysis 3rd Edition by Choudhary B
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.
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About the Author:
B Choudhary an MSc and PhD from London University, retired as a Professor of Mathematics from Indian Institute of Technology, Delhi. He has done research work in Mathematical Analysis and Functional Analysis. Professor Choudhary has authored several research papers in reputed international journals of mathematics. He has taught Complex Analysis for more than two decades and applied theory of complex variables in some of his research papers.
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
Appendices