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.