A Second Course in Complex Analysis (Textbooks in Mathematics) - Hardcover

Dovbush, Peter V.; Krantz, Steven G.

 
9781041197140: A Second Course in Complex Analysis (Textbooks in Mathematics)
Hardcover
ISBN 10: 1041197144 ISBN 13: 9781041197140
Publisher: Chapman and Hall/CRC, 2026

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.

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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.

"About this title" may belong to another edition of this title.

Publisher
Chapman and Hall/CRC
Publication date
2026
Language
English
ISBN 10 
1041197144
ISBN 13 
9781041197140
Binding
Hardcover
Edition number
1
Number of pages
462