Complex Analysis

by V. Karunakaran

As an introduction to Complex Analysis at the undergraduate and postgraduate levels, this new edition features an integrated approach to various areas; the concept of differentiation for complex valued functions of a complex variable, unified Cauchy Riemann equations, a detailed discussion on the construction of Riemann surfaces for elementary functions leading to its abstract concept, step-by-step development of the most general form of Cauchy's theorem, the complex version of the real intermediate value theorem, exhaustive treatment of contour integration and an introduction to the theory of univalent functions on the unit disc. Karunakaran's contributions also include a brief history of the Bieberbach's conjecture and its solution and a complete section on Analytic automorphisms on plane domains, exclusive to the Second Edition.

Table of Contents

• Preface to the Second Edition
•

• Preface to the First Edition
• A Bird's eye view of the complex plane
• Elementary Properties of Analytic Functions
• Conformal Mappings
• Complex Integral Calculus
• Riemann Mapping Theorem
• Solved Exercises
• Index.

438 pages, Hardcover

First published March 1, 2004