Topics in Complex Analysis

Joel L. Schiff

Published by De Gruyter 2022

Topics in Complex Analysis

Joel L. Schiff

Volume 88 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110757828

Overview
Contents

About this book

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.

Provides a general overview complex analysis in a straightforward and accessible format.

Illustrates common methods, practices and applications that will be beneficial to STEM readers and researchers.

Author information

Joel L. Schiff, University of Auckland, New Zealand.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	VII
Acknowledgments Publicly Available Download PDF	XI
Contents Publicly Available Download PDF	XIII
1 Analytic functions Requires Authentication Unlicensed Licensed Download PDF	1
2 Entire functions Requires Authentication Unlicensed Licensed Download PDF	28
3 Meromorphic functions Requires Authentication Unlicensed Licensed Download PDF	43
4 Normal families Requires Authentication Unlicensed Licensed Download PDF	83
5 Hyperbolic geometry Requires Authentication Unlicensed Licensed Download PDF	109
6 Univalent functions Requires Authentication Unlicensed Licensed Download PDF	129
7 Harmonic functions Requires Authentication Unlicensed Licensed Download PDF	148
8 Subharmonic/superharmonic functions Requires Authentication Unlicensed Licensed Download PDF	186
9 Iteration of rational mappings Requires Authentication Unlicensed Licensed Download PDF	204
10 Analytic number theory Requires Authentication Unlicensed Licensed Download PDF	223
Bibliography Requires Authentication Unlicensed Licensed Download PDF	269
Index Requires Authentication Unlicensed Licensed Download PDF	271

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers in mathematics and graduate students.
Pages
- Front matter: 16
- Main content: 276
Illustrations
- Illustrations: 30
- Coloured Illustrations: 10
Keywords: Komplexe Analyse; Zahlentheorie; komplexe Variable

eBook

Published: October 24, 2022
ISBN: 9783110757828

Hardcover

Published: October 24, 2022
ISBN: 9783110757699