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Function Theory of One Complex Variable: (Graduate Studies in Mathematics)

Function Theory of One Complex Variable: (Graduate Studies in Mathematics)

          
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About the Book

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 Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year 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.

Table of Contents:
Preface to the Third Edition Preface to the Second Edition Preface to the First Edition Acknowledgments 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 References Index


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Product Details
  • ISBN-13: 9780821839621
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Depth: 38
  • Height: 255 mm
  • No of Pages: 504
  • Series Title: Graduate Studies in Mathematics
  • Weight: 1088 gr
  • ISBN-10: 0821839624
  • Publisher Date: 30 Mar 2006
  • Binding: Hardback
  • Edition: New edition
  • Language: English
  • Returnable: N
  • Spine Width: 32 mm
  • Width: 184 mm


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