Introduction to the Theory of Complex Functions
by Lu, Jian-Ke; Zhong, Shou-Guo; Liu, Shi-QiangFormat: Hardcover
Pub. Date: 2003-01-01
Publisher(s): WORLD SCIENTIFIC PUB CO INC
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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 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
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