Complex Analysis

An Invitation

Murali Rao, Henrik Stetkaer;;;

• Verlag: WSPC
• Jahr: 1991
• ISBN:
  9789813103610
• Thema: Matematica
• Thema: Equazioni differenziali

This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises.

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Inhaltsverzeichnis

• Contents
• Preface
• Chapter 1 Power Series
• Chapter 2 Holomorphic and Analytic Functions
• Chapter 3 The Exponential Function, the Logarithm and the Winding Number
• Chapter 4 Basic Theory of Holomorphic Functions
• Chapter 5 Global Theory
• Chapter 6 Isolated Singularities
• Chapter 7 The Picard Theorems
• Chapter 8 Geometric Aspects and the Riemann Mapping Theorem
• Chapter 9 Meromorphic Functions and Runge's Theorems
• Chapter 10 Representations of Meromorphic Functions
• Chapter 11 The Prime Number Theorem
• Chapter 12 Harmonic Functions
• Chapter 13 Subharmonic Functions
• Chapter 14 Various Applications
• References
• Index