Complex Analysis Through Examples and Exercises

by Pap, Endre

• ISBN13: 9780792357872
• ISBN10: 0792357876
• Format: Hardcover
• Copyright: 1999-09-01
• Publisher: Kluwer Academic Pub

Summary

This volume on complex analysis offers an exposition of the theory of complex analysis via a comprehensive set of examples and exercises. The book is self-contained and the exposition of new notions and methods is introduced step by step. A minimal amount of expository theory is included at the beginning of each section in the Preliminaries, with maximum effort placed on well-selected examples and exercises capturing the essence of the material. The examples contain complete solutions and serve as a model for solving similar problems given in the exercises. The readers are left to find the solution in the exercises; the answers, and occasionally, some hints, are given. Special sections contain so-called Composite Examples which consist of combinations of different types of examples explaining some problems completely and giving the reader an opportunity to check all his previously accepted knowledge. Audience: This volume is intended for undergraduate and graduate students in mathematics, physics, technology and economics interested in complex analysis.

Table of Contents

Contents	v
Preface	ix
The Complex Numbers	1	(36)
Algebraic Properties	1	(31)
Preliminaries	1	(1)
Examples and Exercises	2	(30)
The Topology of the Complex Plane	32	(5)
Preliminaries	32	(1)
Examples and Exercises	33	(4)
Sequences and series	37	(16)
Sequences	37	(7)
Preliminaries	37	(1)
Examples and Exercises	38	(6)
Series	44	(9)
Preliminaries	44	(1)
Examples and Exercises	45	(8)
Complex functions	53	(20)
General Properties	53	(11)
Preliminaries	53	(1)
Examples and Exercises	54	(10)
Special Functions	64	(4)
Preliminaries	64	(1)
Examples and Exercises	65	(3)
Multi-valued functions	68	(5)
Preliminaries	68	(1)
Examples and Exercises	68	(5)
Conformal mappings	73	(30)
Basics	73	(1)
Preliminaries	73	(1)
Examples and Exercises	73	(1)
Special mappings	74	(29)
Preliminaries	74	(1)
Examples and Exercises	75	(28)
The Integral	103	(26)
Basics	103	(26)
Preliminaries	103	(1)
Examples and Exercises	104	(25)
The Analytic functions	129	(42)
The Power Series Representation	129	(33)
Preliminaries	129	(2)
Examples and Exercises	131	(31)
Composite Examples	162	(9)
Isolated Singularities	171	(20)
Singularities	171	(6)
Preliminaries	171	(1)
Examples and Exercises	172	(5)
Laurent series	177	(14)
Preliminaries	177	(2)
Examples and Exercises	179	(12)
Residues	191	(36)
Residue Theorem	191	(15)
Preliminaries	191	(2)
Examples and Exercises	193	(13)
Composite Examples	206	(21)
Analytic continuation	227	(28)
Continuation	227	(6)
Preliminaries	227	(1)
Examples and Exercises	228	(5)
Composite Examples	233	(22)
Integral transforms	255	(58)
Analytic Functions Defined by Integrals	255	(13)
Preliminaries	255	(1)
Examples and Exercises	256	(12)
Composite Examples	268	(45)
Miscellaneous Examples	313	(20)
Bibliography	333	(2)
List of Symbols	335	(1)
Index	336