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Other titles in the International Series in Pure & Applied Mathematics series:

International Series in Pure & Applied Mathematics #0007: Complex Analysis

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International Series in Pure & Applied Mathematics #0007: Complex Analysis Cover

 

Synopses & Reviews

Publisher Comments:

A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.

Table of Contents

Chapter 1: Complex Numbers

1 The Algebra of Complex Numbers

1.1 Arithmetic Operations

1.2 Square Roots

1.3 Justification

1.4 Conjugation, Absolute Value

1.5 Inequalities

2 The Geometric Representation of Complex Numbers

2.1 Geometric Addition and Multiplication

2.2 The Binomial Equation

2.3 Analytic Geometry

2.4 The Spherical Representation

Chapter 2: Complex Functions

1 Introduction to the Concept of Analytic Function

1.1 Limits and Continuity

1.2 Analytic Functions

1.3 Polynomials

1.4 Rational Functions

2 Elementary Theory of Power Series

2.1 Sequences

2.2 Series

2.3 Uniform Coverages

2.4 Power Series

2.5 Abel's Limit Theorem

3 The Exponential and Trigonometric Functions

3.1 The Exponential

3.2 The Trigonometric Functions

3.3 The Periodicity

3.4 The Logarithm

Chapter 3: Analytic Functions as Mappings

1 Elementary Point Set Topology

1.1 Sets and Elements

1.2 Metric Spaces

1.3 Connectedness

1.4 Compactness

1.5 Continuous Functions

1.6 Topological Spaces

2 Conformality

(and more...)

Product Details

ISBN:
9780070006577
Author:
Ahlfors, Lars V.
Publisher:
McGraw-Hill Education
Author:
Ahlfors, Lars
Author:
Ahlfors Lars
Location:
New York :
Subject:
General
Subject:
Mathematical Analysis
Subject:
Advanced
Subject:
Analytic functions
Subject:
Mathematics - General
Copyright:
Edition Number:
3
Series:
International Series in Pure & Applied Mathematics
Series Volume:
10
Publication Date:
January 1979
Binding:
Hardcover
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
345
Dimensions:
9.30x5.98x.98 in. 1.31 lbs.

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Related Subjects

Reference » Science Reference » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Complex Analysis
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General

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