Krantz S A Guide to Complex Variables 2008

Textbook in PDF format

This quick and easy-to-use guide provides a solid grounding in the fundamental area of complex variables. Copious figures and examples are used to illustrate the principal ideas, and the exposition is lively and inviting. In addition to important ideas from the Cauchy theory, the author also includes the Riemann mapping theorem, harmonic functions, the argument principle, general conformal mapping, and dozens of other central topics. An undergraduate taking a first look at the subject, or a graduate student preparing for their qualifying exams, will find this book to be both a valuable resource and a useful companion to more exhaustive texts in the field. For mathematicians and non-mathematicians alike.
The complex plane
Complex line integrals
Applications of the Cauchy theory
Isolated singularities and Laurent series
The argument principle
The geometric theory of holomorphic functions
Harmonic functions
Infinite series and products
Analytic continuation