| Softcover ISBN: | 978-1-4704-6323-6 |
| Product Code: | MBK/49.S |
| List Price: | $45.00 |
| MAA Member Price: | $40.50 |
| AMS Member Price: | $36.00 |
| Electronic ISBN: | 978-1-4704-1199-2 |
| Product Code: | MBK/49.E |
| List Price: | $42.00 |
| MAA Member Price: | $37.80 |
| AMS Member Price: | $33.60 |
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Book Details2007; 163 ppMSC: Primary 30;
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.ReadershipUndergraduate and graduate students interested in complex analysis.
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Table of Contents
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Chapters
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1. Complex numbers
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2. Complex differentiation
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3. Linear-fractional transformations
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4. Elementary functions
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5. Power series
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6. Complex integration
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7. Core versions of Cauchy’s theorem, and consequences
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8. Laurent series and isolated singularities
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9. Cauchy’s theorem
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10. Further development of basic complex function theory
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Appendix 1. Sufficient condition for differentiability
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Appendix 2. Two instances of the chain rule
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Appendix 3. Groups, and linear-fractional transformations
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Appendix 4. Differentiation under the integral sign
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Additional Material
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Reviews
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From a review of the previous edition … The exposition is clear, rigorous, and friendly.
Zentralblatt MATH
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- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
Undergraduate and graduate students interested in complex analysis.
-
Chapters
-
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 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
-
From a review of the previous edition … The exposition is clear, rigorous, and friendly.
Zentralblatt MATH
