A Second Course in Complex Analysis (Hardcover)

Peter V. Dovbush

ISBN 10: 1041197144 / ISBN 13: 9781041197140

Published by Taylor & Francis Ltd, London, 2026

About this Item

Hardcover. Few other books purport to be a second course in complex analysis. This book differs in that it covers more modern topics and is more geometric in focus. Most texts on complex variable theory contain the same material. However, complex analysis is a vast and diverse subject with a long history and many aspects. A second course will benefit students and introduce these new topics that they might not otherwise experience. Lars Ahlfors alone invented many new parts of the subject; Lipman Bers made decisive contributions, and there are many others. It is easy to justify a second course in complex analysis. That is what this book purports to be.Some of the topics presented here are:harmonic measureextremal lengthRiemann surfacesuniformizationautomorphism groupsthe Schwarz lemma and its generalizationsanalytic capacitythe Bergman theoryinvariant metricsPicards theoremthe boundary Schwarz lemmaThe goal is to expose the reader to unfamiliar parts of the subject of complex variables and perhaps to pique interest in further reading. As with the authors other books, not only theorems and proofs are included, but also many examples and some exercises. Numerous graphics illustrate the key ideas. This book covers more modern topics on complex analysis and is more geometric in focus. Topics covered include: harmonic measure, extremal length, Riemann surfaces, and uniformization, among others. It will benefit students and introduce new topics that they might not otherwise experience. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9781041197140

Bibliographic Details

• Title: A Second Course in Complex Analysis (Hardcover)
• Publisher: Taylor & Francis Ltd, London
• Publication Date: 2026
• Language: English
• ISBN 10: 1041197144
• ISBN 13: 9781041197140
• Binding: Hardcover
• Condition: new

About this title

Synopsis

Few other books purport to be a second course in complex analysis. This book differs in that it covers more modern topics and is more geometric in focus. Most texts on complex variable theory contain the same material. However, complex analysis is a vast and diverse subject with a long history and many aspects. A second course will benefit students and introduce these new topics that they might not otherwise experience.

Lars Ahlfors alone invented many new parts of the subject; Lipman Bers made decisive contributions, and there are many others. It is easy to justify a “second course” in complex analysis. That is what this book purports to be.

Some of the topics presented here are:

• harmonic measure
• extremal length
• Riemann surfaces
• uniformization
• automorphism groups
• the Schwarz lemma and its generalizations
• analytic capacity
• the Bergman theory
• invariant metrics
• Picard’s theorem
• the boundary Schwarz lemma

The goal is to expose the reader to unfamiliar parts of the subject of complex variables and perhaps to pique interest in further reading. As with the authors’ other books, not only theorems and proofs are included, but also many examples and some exercises. Numerous graphics illustrate the key ideas.

About the Author

Peter V. Dovbush, Dr. habil., is an Associate Professor at Moldova State University, in the Institute of Mathematics and Computer Science. He received his Ph.D. in Lomonosov Moscow State University in 1983 and Doctor of Sciences in 2003. He has published over 50 scholarly articles.

Steven G. Krantz is a Professor of Mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Penn State University. He received his Ph.D. from Princeton University in 1974. Krantz has directed 20 Ph.D. students and 8 Masters students. He has published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize and the Beckenbach Book Award and the Kemper Prize. He is a Fellow of the American Mathematical Society.