This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves.

Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool.

Readership

Advanced undergraduates, graduate students, and research mathematicians interested in functions of a complex variable.

Reviews

"[This book] covers all essential topics of a classical introductory part of complex analysis. Features: a rigorous treatment (accessible to students), detailed description of the homotopy of plane curves, neat proofs given in compact form, careful explanation of some more advanced themes. The material is organized very well and presented clearly in a modern setting, gradually increasing in complexity ... The book under review is a distinguished work in the field."

-- Mathematical Reviews

Table of Contents

• Complex numbers
• Complex functions
• Holomorphic functions
• Residue theorem
• Analytic continuation
• Holomorphic mappings
• Meromorphic functions
• Hints and answers
• References
• Index
• Symbols
• Errata