Function Theory of One Complex Variable

ISBN-10: 0821839624
ISBN-13: 9780821839621
Edition: 3rd 2006 (Revised)
List price: $86.00
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Description: 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  More...

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Book details

List price: $86.00
Edition: 3rd
Copyright year: 2006
Publisher: American Mathematical Society
Publication date: 3/29/2006
Binding: Hardcover
Pages: 504
Size: 7.25" wide x 10.50" long x 1.50" tall
Weight: 2.640
Language: English

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 andexercises 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 treatHp$ 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.

Fundamental concepts
Complex line integrals Applications of the Cauchy integral
Meromorphic functions and residues
The zeros of a holomorphic function
Holomorphic functions as geometric mappings
Harmonic functions Infinite series and products
Applications of infinite sums and products
Analytic continuation Topology
Rational approximation theory
Special classes of holomorphic functions
Hilbert spaces of holomorphic functions, the Bergman kernel, and biholomorphic mappings
Special functions The prime number theorem
Real analysis
The statement and proof of Goursat's theorem
References
Index

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