Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, Third Edition

This book is a reprint of the third edition of a classic book on complex analysis, intended for first-year graduate students and advanced undergraduate students. It covers standard topics in an introductory course, with a focus on the geometric approach and including material on conformal mappings, the Riemann mapping theorem, Dirichlet's problem, the monodromy theorem, and the Cauchy integral theorem. The coverage of special functions is concise but reasonably complete, and the presentation is concise, clear, and thorough.

Format: Paperback / softback
Length: 331 pages
Publication date: 01 December 2021
Publisher: American Mathematical Society

This remarkable book is a faithful reproduction of the third edition of the renowned classic on complex analysis. It serves as an exceptionally rigorous introduction to the theory of analytic functions of one complex variable, designed primarily for first-year graduate students and advanced undergraduate students. Spanning a wide range of standard topics within an introductory complex analysis course, the book adopts a geometric perspective, emphasizing conformal mappings, the Riemann mapping theorem, Dirichlet's problem (the existence of a harmonic function with prescribed boundary values), the monodromy theorem, and the study of regions where the Cauchy integral theorem holds true. Additionally, it delves into analytic concepts such as power series, contour integrals, and infinite products. While the coverage of special functions may be concise, it remains remarkably comprehensive. The presentation is concise, clear, and thorough, making it a timeless resource that has remained relevant and valuable even after more than thirty years since its last revision.

Weight: 612g
Dimension: 178 x 258 x 23 (mm)
ISBN-13: 9781470467678
Edition number: 3 Revised edition