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Softcover ISBN:  9781470463236 
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Softcover ISBN:  9781470463236 
Product Code:  MBK/49.S 
List Price:  $49.00 
MAA Member Price:  $44.10 
AMS Member Price:  $39.20 
eBook ISBN:  9781470411992 
Product Code:  MBK/49.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9781470463236 
eBook ISBN:  9781470411992 
Product Code:  MBK/49.S.B 
List Price:  $94.00 $71.50 
MAA Member Price:  $84.60 $64.35 
AMS Member Price:  $75.20 $57.20 

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 onesemester 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.

Table of Contents

Chapters

1. Complex numbers

2. Complex differentiation

3. Linearfractional 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 linearfractional transformations

Appendix 4. Differentiation under the integral sign


Additional Material

Reviews

From a review of the previous edition ...
The exposition is clear, rigorous, and friendly.
Zentralblatt MATH


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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 onesemester 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. Linearfractional 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 linearfractional transformations

Appendix 4. Differentiation under the integral sign

From a review of the previous edition ...
The exposition is clear, rigorous, and friendly.
Zentralblatt MATH