2007;
163 pp;
Hardcover

MSC: Primary 30;

Print ISBN: 978-0-8218-4428-1

Product Code: MBK/49

List Price: $42.00

Individual Member Price: $33.60

**Electronic ISBN: 978-1-4704-1199-2
Product Code: MBK/49.E**

List Price: $42.00

Individual Member Price: $33.60

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#### Supplemental Materials

# Complex Function Theory: Second Edition

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*Donald Sarason*

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.

#### Readership

Undergraduate and graduate students interested in complex analysis.

#### Reviews & Endorsements

The exposition is clear, rigorous, and friendly.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Complex Function Theory: Second Edition

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Preface ix10 free
- Complex numbers 114 free
- Complex differentiation 1326
- Linear-fractional transformations 2740
- Elementary functions 3548
- Power series 4962
- Complex integration 6578
- Core versions of Cauchy’s theorem, and consequences 7588
- Laurent series and isolated singularities 97110
- Cauchy’s theorem 109122
- Further development of basic complex function theory 125138
- Appendix 1: Sufficient condition for differentiability 151164
- Appendix 2: Two instances of the chain rule 153166
- Appendix 3: Groups, and linear-fractional transformations 155168
- Appendix 4: Differentiation under the integral sign 157170
- References 159172
- Index 161174 free
- Back Cover Back Cover1178