Description
Book SynopsisProvides a concise and rigorous introduction to the theory of functions of a complex variable. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. The book is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation.
Trade ReviewFrom a review of the previous edition: ""The exposition is clear, rigorous, and friendly."" —
Zentralblatt MATHTable of 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
