Complex Analysis

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Author(s): Elias M. Stein, Rami Shakarchi
Publisher: Princeton univ press
Year: 2003

Language: English
Pages: 398

Cover......Page 1
Princeton Lectures in Analysis......Page 3
COMPLEX ANALYSIS......Page 4
Foreword......Page 8
Contents......Page 12
Introduction......Page 16
1 Preliminaries to Complex Analysis......Page 20
2 Cauchy’s Theorem and Its Applications......Page 51
3 Meromorphic Functions and the Logarithm......Page 90
4 The Fourier Transform......Page 130
5 Entire Functions......Page 153
6 The Gamma and Zeta Functions......Page 178
8 Conformal Mappings......Page 224
9 An Introduction to Elliptic Functions......Page 280
10 Applications of Theta Functions......Page 302
Appendix A: Asymptotics......Page 337
Appendix B: Simple Connectivity and Jordan Curve Theorem......Page 363
Notes and References......Page 384
Bibliography......Page 388
Symbol Glossary......Page 392
Index......Page 394