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

Bruce P. Palka

Hardcover

ISBN 10: 354097427X ISBN 13: 9783540974277

Publisher: Springer Nature

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.

Edition details

• Publisher: Springer Nature
• Language: English
• ISBN 10: 354097427X
• ISBN 13: 9783540974277
• Binding: Hardcover
• Number of pages: 559