Introduction to the Theory of Complex Functions

by Lu, Jian-Ke; Zhong, Shou-Guo; Liu, Shi-Qiang

• ISBN13: 9789812380470
• ISBN10: 9812380477
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

This book is based on the teaching experience of the authors, and therefore some of the topics are presented in a new form. The multi-valued properties of the argument function are discussed in detail so that the beginner may readily grasp the elementary multi-valued analytic functions. The residue theorem is extended to the case where the poles of analytic functions considered may occur on the boundary of a region - which is very useful in applications but not seen in textbooks written in English.

Table of Contents

Preface
Complex Numbers and Complex Functions
Complex Numbers	p. 1
Functions of a Complex Variable	p. 10
Complex Sequences and Complex Series	p. 24
Fundamentals of Analytic Functions
Analytic Functions	p. 28
Some Elementary Analytic Functions	p. 36
Complex Integrals
The Concept of Complex Integrals	p. 63
Fundamental Theorems	p. 70
Basic Formulas	p. 81
Improper Complex Integrals	p. 88
Theory of Series for Analytic Functions
General Theory	p. 100
Taylor Expansion and Uniqueness Theorem	p. 105
Laurent Expansion and Isolated Singularities	p. 118
Theory of Residue
Residue and its Evaluation	p. 138
Residue Theorem and its Generalization	p. 148
Applications of Evaluation of Integrals	p. 155
Argument Principle and Rouche Theorem	p. 170
Analytic Extension
Concept and Method of Analytic Extension	p. 178
Complete Analytic Functions and Monodrome Theorem	p. 191
Conformal Mapping
Fractional Linear Mapping	p. 200
General Theory of Conformal Mapping	p. 215
Some Elementary Function Mappings	p. 225
Miscellaneous Examples	p. 235
Harmonic Functions
Concept of Harmonic Functions and their Properties	p. 252
Dirichlet Problems	p. 260
Schwarz-Christoffel Formula	p. 267
Analytic Functions Applied to Planar Flow
Meaning of Analytic Functions in Fluid Mechanics	p. 280
Flow Around a Cylinder	p. 287
References	p. 295
Index	p. 297
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