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An Introduction to Complex Function Theory (Lecture Notes in Statistics)

An Introduction to Complex Function Theory (Lecture Notes in Statistics) Cover

 

Synopses & Reviews

Publisher Comments:

This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.

Book News Annotation:

A rigorous yet elementary introduction to the theory of analytic functions of a single complex variable, aimed primarily at advanced undergraduate and beginning graduate students in mathematics. Requires no formal prerequisites beyond a sound knowledge of calculus.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

A rigorous yet elementary introduction to the theory of analytic functions of a single complex variable, aimed primarily at advanced undergraduate and beginning graduate students in mathematics. Requires no formal prerequisites beyond a sound knowledge of calculus. Annotation copyright Book News, In

Table of Contents

Contents: The Complex Number System.- The Rudiments of Plane Topology.- Analytic Functions.- Complex Integration.- Cauchy's Theorem and its Consequences.- Harmonic Functions.- Sequences and Series of Analytic Functions.- Isolated Singularities of Analytic Functions.- Conformal Mapping.- Constructing Analytic Functions.- Appendix A: Background on Fields.- Appendix B: Winding Numbers Revisited.- Index.

Product Details

ISBN:
9780387974279
Publisher:
Springer
Subject:
Calculus
Author:
Palka, Bruce P.
Subject:
Mathematical Analysis
Subject:
Functions of complex variables
Subject:
Analysis
Subject:
Mathematics-Calculus
Copyright:
Edition Number:
1
Edition Description:
1991. Corr. 2nd
Series:
Undergraduate Texts in Mathematics
Publication Date:
August 1995
Binding:
HARDCOVER
Language:
English
Illustrations:
138 schw.-w. Abb.
Pages:
577
Dimensions:
235 x 155 mm 2180 gr

Related Subjects

Reference » Science Reference » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General

An Introduction to Complex Function Theory (Lecture Notes in Statistics)
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Product details 577 pages Springer-Verlag - English 9780387974279 Reviews:
"Synopsis" by , A rigorous yet elementary introduction to the theory of analytic functions of a single complex variable, aimed primarily at advanced undergraduate and beginning graduate students in mathematics. Requires no formal prerequisites beyond a sound knowledge of calculus. Annotation copyright Book News, In
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