Hardcover ISBN:  9780821839621 
Product Code:  GSM/40.R 
List Price:  $92.00 
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Book DetailsGraduate Studies in MathematicsVolume: 40; 2006; 504 ppMSC: Primary 30;
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point.
The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat \(H^p\) spaces and Painlevé's theorem on smoothness to the boundary for conformal maps.
This book is a text for a firstyear graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.ReadershipGraduate students interested in complex analysis.

Table of Contents

Chapters

Chapter 1. Fundamental concepts

Chapter 2. Complex line integrals

Chapter 3. Applications of the Cauchy integral

Chapter 4. Meromorphic functions and residues

Chapter 5. The zeros of a holomorphic function

Chapter 6. Holomorphic functions as geometric mappings

Chapter 7. Harmonic functions

Chapter 8. Infinite series and products

Chapter 9. Applications of infinite sums and products

Chapter 10. Analytic continuation

Chapter 11. Topology

Chapter 12. Rational approximation theory

Chapter 13. Special classes of holomorphic functions

Chapter 14. Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings

Chapter 15. Special functions

Chapter 16. The prime number theorem

Appendix A. Real analysis

Appendix B. The statement and proof of Goursat’s theorem


Additional Material

Reviews

I can say that I have read this book with great pleasure and I do recommend it for those who are interested in complex analysis.
Zentralblatt MATH


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Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point.
The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat \(H^p\) spaces and Painlevé's theorem on smoothness to the boundary for conformal maps.
This book is a text for a firstyear graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.
Graduate students interested in complex analysis.

Chapters

Chapter 1. Fundamental concepts

Chapter 2. Complex line integrals

Chapter 3. Applications of the Cauchy integral

Chapter 4. Meromorphic functions and residues

Chapter 5. The zeros of a holomorphic function

Chapter 6. Holomorphic functions as geometric mappings

Chapter 7. Harmonic functions

Chapter 8. Infinite series and products

Chapter 9. Applications of infinite sums and products

Chapter 10. Analytic continuation

Chapter 11. Topology

Chapter 12. Rational approximation theory

Chapter 13. Special classes of holomorphic functions

Chapter 14. Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings

Chapter 15. Special functions

Chapter 16. The prime number theorem

Appendix A. Real analysis

Appendix B. The statement and proof of Goursat’s theorem

I can say that I have read this book with great pleasure and I do recommend it for those who are interested in complex analysis.
Zentralblatt MATH