1550251515-Classical_Complex_Analysis__Gonzalez_

CLASSICAL COMPLEX ANALYSIS Mario 0. Gonzalez Professor Emeritus of Mathematics University of Alabama Marcel Dekker, Inc. New Yor ...

/ Library olf Congress Cataloging-in-Publication Data Gonz~lez, Mario 0. Classical complex analysis/ Mario 0. Gondlez. p. cm. -- ...

To my wife Lola, to my daughters Vicky and Laura, and to my son-in-law Harold C. Raley, with deep affection. ...

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Preface This is a book on the theory of functions of one complex variable. It contains, with many elaborations, the subject of t ...

vi Preface I am especially grateful to my brother Luis R. Gonzalez for his expertise in computer programming which made possible ...

Contents ...

viii 2 2. 2. 2. 2. 2. 2. 2. 2. 2. Contents Geometric Representation of the Operations with Com ...

Contents ix ...

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Contents xi 6.5 The Cauchy-Riemann Equations 317 6.6 Laplace Equation. Harmonic and Subharmonic Functions 320 6.7 The Concept of ...

xii Contents ...

Singularities. The Calculus of Residues. Applications ...

Introduction Preface v 0.1 Sets 0.2 Mappings 0.3 Notations 1 Complex Numbers 1.1 The Complex Number System 1.2 Real and Imagi ...

CLASSICAL COMPLEX ANALYSIS ...

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Introduction In this treatise we assume the reader to be familiar with the real number system ~' as well as with the properties ...

2 Introduction There is a relation between the elements of a set and that set, which is expressed by such phrases as "a is an el ...

Introduction a property .that is vacuously satisfied. For example, 0 = { x : x E ~' x^2 = -1} 3 The empty set 0 is regarded as a ...

4 Introduction Fig. 0. A mapping with rule f, domain G, and range contained in P(Y) is denoted f: G ---t P(Y), which is read "th ...