Complex Analysis with Applications

This basic book on functions of a complex variable represents the irreducible minimum of what every scientist and engineer should know about this important subject. From a preliminary discussion of complex numbers and functions to key topics such as the Cauchy theory, power series, and residues, distinguished mathematical writer Richard Silverman presents the fundamentals of complex analysis in a concise manner designed not to overwhelm the beginner. The author's lively style and simplicity of approach enable the reader to grasp essential topics without being distracted by secondary issues.
Contents include: Complex Numbers
Some Special Mapping
Limits in the Complex Plane
Multiple-Valued Functions' Complex Functions
Taylor Series
Differentiation in the Complex Plane
Laurent Series
Integration in the Complex Plane
Applications of Residues
Complex Series
Mapping of Polygonal Domains
Power Series
and Some Physical Applications.
Abundant exercise material and examples, as well as section-by-section comments at the end of each chapter make this book especially valuable to students and anyone encountering complex analysis for the first time.