Concise Complex Analysis

By: Sheng Gong

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Hardcover | 1 December 2000

At a Glance

Hardcover
196 Pages

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23.0 x 15.88 x 1.91

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This is a concise textbook of complex analysis for undergraduate and graduate students. It has been written from the viewpoint of modern mathematics -- the equation, differential geometry, Lie groups, etc. It contains all the traditional material on complex analysis, but many statements and proofs of classical theorems in complex analysis have been made simpler, shorter and more elegant due to modern mathematical ideas and methods. For example, the Mittag-Leffler theorem is proved by the equation, the Picard theorem is proved using the methods of differential geometry, and so on.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis Geometry Differential & Riemannian Geometry Differential Calculus & Equations Booktopia Publisher Services World Scientific Publishing

Preface	p. v
Foreward	p. vii
Calculus	p. 1
A glimpse of calculus	p. 1
Complex number field, extended complex plane and spherical representation	p. 8
Complex differentiation	p. 11
Complex integration	p. 16
Elementary functions	p. 19
Complex series	p. 26
Exercises I	p. 30
Cauchy integral theorem and Cauchy integral formula	p. 37
Cauchy-Green formula (Pompeiu formula)	p. 37
Cauchy-Goursat theorem	p. 41
Taylor series and Liouville theorem	p. 48
Some results on zero points	p. 55
Maximum modulus principle, Schwarz lemma, group of holomorphic automorphism	p. 60
Integral representation of holomorphic function	p. 65
Exercises II	p. 70
Partition of unity	p. 77
Theory of series of Weierstrass	p. 81
Laurent series	p. 81
Isolate singularity	p. 86
Entire functions and meromorphic functions	p. 89
Weierstrass factorization theorem, Mittag-Leffler theorem and interpolation theorem	p. 93
Residue theorem	p. 102
Analytic continuation	p. 107
Exercises III	p. 110
Riemann mapping theorem	p. 115
Conformal mapping	p. 115
Normal family	p. 120
Riemann mapping theorem	p. 123
Symmetric principle	p. 126
Examples of Riemann surface	p. 128
Schwarz-Christoffel formula	p. 130
Exercises IV	p. 133
Riemann surface	p. 135
Differential geometry and Picard theorem	p. 137
Metric and curvature	p. 137
Ahlfors-Schwarz lemma	p. 142
Extension of Liouville theorem and value distribution	p. 144
Picard little theorem	p. 146
Extension of normal family	p. 147
Picard great theorem	p. 151
Exercises V	p. 153
Curvature	p. 154
Elementary facts on several complex variables	p. 159
Introduction	p. 159
Cartan theorem	p. 162
Groups of holomorphic automorphisms of unit ball and unit bidisk	p. 164
Poincare theorem	p. 168
Hartogs theorem	p. 170
References	p. 175
Table of Contents provided by Syndetics. All Rights Reserved.

Concise Complex Analysis

At a Glance

Hardcover

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How to return your order

Defective items

You Can Find This Book In

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