Basic Complex Analysis of One Variable

Anant R. Shastri began his mathematical career at School of Mathematics, TIFR Mumbai. After obtaining his doctorate from Mumbai University, he has visited universities and research institutes all over Europe, USA, Canada, Taiwan and Japan. He was an associate at International Centre for Theoretical Physics, Trieste, Italy during 1993-99. Since 1988, Dr. Shastri is serving in the Department of Mathematics, IIT Bombay, as a full professor.

He has been continually associated with the Advanced Training in Mathematics programme of National Board for Higher Mathematics. He takes keen interest in teaching mathematics at all levels. Professor Shastri plays Dhrupad style music on flute and is an ardent chess player.

Thorough, yet simple, Basic Complex Analysis is an ideal mathematics text and reference for students as well as teachers at graduate and postgraduate levels. Written in an informal and interactive style, the book does not confront burden the students with definitions and theorems. Rather, each result is approached logically and explained patiently, with special emphasis on common questions that bother learners. The topological background needed in the development has been woven into the main body with great restraint.

The book covers most of the standard topics. It begins with the basics of complex numbers with equal emphasis on algebraic and geometric aspects. Analytic functions are introduced immediately after complex differentiation. Cauchy''s theorem on line integrals is treated in two essentially different approaches with many immediate applications. The book later explains local properties of holomorphic functions, the concept of winding numbers, etc. There is an entire chapter on computing line integrals. The book then takes the student to the deeper aspects of Cauchy''s theory, meromorphic functions, Runge''s theorem, special functions such as the gamma-function and Riemann zeta-function, Riemann mapping theorem, Dirichlet''s problem for harmonic functions with an application to the classification of multiply connected domains, etc.
The book concludes with a discussion on periodic functions, modular functions, and Picard''s theorems as an application.

ISBN: 9780230330733
Author: Anant R. Shastri
Published by: Macmillan India Ltd
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