Pub. Date:
World Scientific Publishing Company, Incorporated
Complex Analysis

Complex Analysis

by Man-wah Wong


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This book is ideal for a one-semester course for advanced undergraduate students and first-year graduate students in mathematics. It is a straightforward and coherent account of a body of knowledge in complex analysis, from complex numbers to Cauchy's integral theorems and formulas to more advanced topics such as automorphism groups, the Schwarz problem in partial differential equations, and boundary behavior of harmonic functions.The book covers a wide range of topics, from the most basic complex numbers to those that underpin current research on some aspects of analysis and partial differential equations. The novelty of this book lies in its choice of topics, genesis of presentation, and lucidity of exposition.

Product Details

ISBN-13: 9789812811073
Publisher: World Scientific Publishing Company, Incorporated
Publication date: 03/14/2008
Series: Series On Analysis, Applications And Computation Series
Pages: 160
Product dimensions: 6.00(w) x 9.00(h) x 0.70(d)

Table of Contents

Preface v

1 Complex Numbers 1

2 Arguments and Polar Forms of Complex Numbers 5

3 Exponentials, Powers and Roots 9

4 Functions of a Complex Variable 13

5 Holomorphic Functions and the Cauchy-Riemann Equations 17

6 The Exponential, Trigonometric and Hyperbolic Functions 25

7 Logarithms, Complex Powers, Branches and Cuts 29

8 Contour Integrals and Path Independence 37

9 Cauchy's Integral Theorems 45

10 Cauchy's Integral Formulas 53

11 Taylor Series and Power Series 63

12 Laurent Series and Isolated Singularities 73

13 Residues 83

14 Trigonometric Integrals 89

15 Cauchy Principal Values of Improper Integrals on (-[infinity], [infinity]) 93

16 Fourier Transforms of Rational Functions 99

17 Singular Integrals on (-[infinity], [infinity]) 105

18 Integrals on Branch Cuts 109

19 Biholomorphisms 115

20 Zeros, Maximum Modulus Principle and Schwarz's Lemma 119

21 Aut(D) and SU(1,1) 125

22 Aut(H), SL(2, R) and the Iwasawa Decomposition 131

23 Harmonic Functions and the Schwarz Problem on D 137

Bibliography 147

Index 149

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