Complex Function Theory

Contents: Preface to the second edition. Preface to the first edition. 1. Complex numbers. 2. Complex differentiation. 3. Linear-fractional transformations. 4. Elementary functions. 5. Power series. 6. Complex integration. 7. Core versions of Cauchy's Theorem, and consequences. 8. Laurent series and isolated singularities. 9. Cauchy's Theorem. 10. Further development of basic Complex Function Theory. Appendixes: i. Sufficient condition for differentiability. ii. Two instances of the chain rule. iii. Groups, and linear-fractional transformation. iv. Differentiation under the integral sign. References. Index.

"Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's Theorem and applications, plus the Riemann Mapping Theorem. It is suitable for either an introductory for students with adequate preparation." (jacket)