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An Introduction to Complex Function Theory (Undergraduate Texts in Mathematics)

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An Introduction to Complex Function Theory (Undergraduate Texts in Mathematics) 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.

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:
9781461269670
Author:
Palka, Bruce P.
Publisher:
Springer
Location:
New York, NY
Subject:
Mathematical Analysis
Subject:
Analysis
Subject:
Mathematics-Calculus
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Copyright:
Edition Description:
Softcover reprint of the original 1st ed. 1991
Series:
Undergraduate Texts in Mathematics
Publication Date:
20121231
Binding:
TRADE PAPER
Language:
English
Pages:
577
Dimensions:
235 x 155 mm

Related Subjects

Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

An Introduction to Complex Function Theory (Undergraduate Texts in Mathematics) New Trade Paper
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Product details 577 pages Springer - English 9781461269670 Reviews:
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