Topics in Complex Analysis

✍ Scribed by Joel L. Schiff

• Publisher: De Gruyter
• Year: 2022
• Tongue: English
• Leaves: 292
• Series: De Gruyter Studies in Mathematics, 88
• Category: Library

✦ Synopsis

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green's function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.

✦ Table of Contents

Preface
Acknowledgments
Contents
1 Analytic functions
2 Entire functions
3 Meromorphic functions
4 Normal families
5 Hyperbolic geometry
6 Univalent functions
7 Harmonic functions
8 Subharmonic/superharmonic functions
9 Iteration of rational mappings
10 Analytic number theory
Bibliography
Index