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

Bruce P. Palka

ISBN 10: 354097427X / ISBN 13: 9783540974277

Published by Springer Nature

About this Item

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Bibliographic Details

• Title: An Introduction to Complex Function Theory (Undergraduate Texts in Mathematics)
• Publisher: Springer Nature
• Language: English
• ISBN 10: 354097427X
• ISBN 13: 9783540974277
• Binding: Hardcover
• Condition: good

About this title

Synopsis

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.