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Full Description
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
Complex numbers
Complex differentiation
Linear-fractional transformations
Elementary functions
Power series
Complex integration
Core versions of Cauchy's theorem, and consequences
Laurent series and isolated singularities
Cauchy's theorem
Further development of basic complex function theory
Appendix 1: Sufficient condition for differentiability
Appendix 2: Two instances of the chain rule
Appendix 3: Groups, and linear-fractional transformations
Appendix 4: Differentiation under the integral sign
References
Index
