Complex Function Theory (2/E)

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 graduate course or an undergraduate course for students with adequate preparation.

The first edition was published with the title Notes on Complex Function Theory.

Contents

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
Appendix
References
Index