Complex Analysis In the Spirit of Lipman Bers /

• Main Authors: Rodrg̕uez, Rub ̕E. (Author), Kra, Irwin. (Author), Gilman, Jane P. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York : Imprint: Springer, 2013.
• Edition: 2nd ed. 2013.
• Series: Graduate Texts in Mathematics, 245
• Subjects: Mathematics.; Functions of complex variables.; Functions of a Complex Variable.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4419-7323-8

This book is intended for a graduate course in complex analysis, where the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many areas of mathematics, including the theory of several finitely and infinitely many complex...

Table of Contents:

• Preface to Second Edition
• Preface to First Edition
• Standard Notation and Commonly Used Symbols
• 1 The Fundamental Theorem in Complex Function Theory
• 2 Foundations
• 3 Power Series
• 4 The Cauchy Theory - A Fundamental Theorem
• 5 The Cauchy Theory - Key Consequences
• 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions
• 7 Sequences and Series of Holomorphic Functions
• 8 Conformal Equivalence and Hyperbolic Geometry
• 9 Harmonic Functions
• 10 Zeros of Holomorphic Functions
• Bibliographical Notes
• Bibliography
• Index.