An Introduction to Complex Analysis [Hardcover]

Recent decades have seen profound changes in the way we understand complex analysis. This new work presents a much-needed modern treatment of the subject, incorporating the latest developments and providing a rigorous yet accessible introduction to the concepts and proofs of this fundamental branch of mathematics. With its thorough review of the prerequisites and well-balanced mix of theory and practice, this book will appeal both to readers interested in pursuing advanced topics as well as those wishing to explore the many applications of complex analysis to engineering and the physical sciences.
* Reviews the necessary calculus, bringing readers quickly up to speed on the material
* Illustrates the theory, techniques, and reasoning through the use of short proofs and many examples
* Demystifies complex versus real differentiability for functions from the plane to the plane
* Develops Cauchy's Theorem, presenting the powerful and easy-to-use winding-number version
* Contains over 100 sophisticated graphics to provide helpful examples and reinforce important conceptsPreliminaries.

Basic Tools.

The Cauchy Theory.

The Residue Calculus.

Boundary Value Problems.

Lagniappe.

References.

Index. ...well written ,very readable...stylish, up-to-date text... (The Mathematical Gazette, July 2002)

McGehee discusses the basics of complex variables and a few applications to physics in a rigorous and understandable manner. He begins with motivation and the necessary background of the subject in chapter 1. Chapter 2 includes the fundamentals of the algebra, geometry, and calculus of complex numbers. The core topics (Cauchy's theorem and the residue calculus) of complex variable make up chapters 3 and 4. The author then applies the techniques of complex variables to val“+