Nine introductions in complex analysis, revised edition

Sanford L. Segal (Eds.)0444862269, 0444518312, 9780444862266, 9780444518316, 9780080871646, 9780080550763

The book addresses many topics not usually in “second course in complex analysis” texts. It also contains multiple proofs of several central results, and it has a minor historical perspective. – Proof of Bieberbach conjecture (after DeBranges) – Material on asymptotic values – Material on Natural Boundaries – First four chapters are comprehensive introduction to entire and metomorphic functions – First chapter (Riemann Mapping Theorem) takes up where “first courses” usually leave off

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Table of contents :
Content:
Foreword
Pages v-ix

Conformal mapping and the riemann mapping theorem
Pages 1-34

Picard’s theorems
Pages 35-65

An introduction to entire functions
Pages 67-106

Introduction to meromorphic functions
Pages 107-154

Asymptotic values
Pages 155-187

Natural boundaries
Pages 189-256

The bieberbach conjecture
Pages 257-295

Elliptic functions
Pages 297-396

Introduction to the riemann zeta-function
Pages 397-450

Appendix
Pages 451-471

Bibliography
Pages 473-484

Index
Pages 485-487