Foundations of Complex Analysis

Foundations of Complex Analysis is aimed at giving students a good foundation of complex analysis and provides a basis for solving problems in mathematics, physics, engineering and many other sciences. Each chapter is supplemented with well-structured examples, and exercises with hints and outlines for solutions. This book can be used as a textbook for a two semester course in complex analysis, or as a supplementary text for an advanced course in function theory.

This second edition has gone through a major revision of the 1995 edition. As far as possible many sections are made less dependent on other sections in order to ensure flexibility in designing a course content.

Table of Contents

• Preface to the Second Edition
• Complex Numbers
• Functions, Limit and Continuity
• Analytic Functions and Power Series
• Complex Integration
• Conformal Mappings and Möbius Transformations
• Maximum Principle, Schwarz' Lemma, and Liouville's Theorem
• Classification of Singularities
• Calculus of Residues
• Evaluation of certain Integrals
• Analytic Continuation
• Representations for Meromorphic and Entire Functions
• Mapping Theorems
• Bibliography
• Index of Special Notations
• Hints and Solutions for Selected Exercises
• Index.