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The original edition of this book has been out of print for some years. The appear ance of the present second edition owes much to the initiative of Yves Nievergelt at Eastern Washington University, and the support of Ann Kostant, Mathematics Editor at Birkhauser. Since the book was first published, several people have remarked on the absence of exercises and expressed the opinion that the book would have been more useful had exercises been included. In 1997, Yves Nievergelt informed me that, for a decade, he had regularly taught a course at Eastern Washington based on the book, and that he had systematically compiled exercises for his course. He kindly put his work at my disposal. Thus, the present edition appears in two parts. The first is essentially just a reprint of the original edition. I have corrected the misprints of which I have become aware (including those pointed out to me by others), and have made a small number of other minor changes.
- Sales Rank: #1556561 in Books
- Brand: Brand: Birkhäuser
- Published on: 2000-12-21
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.00" w x 6.14" l, 1.56 pounds
- Binding: Hardcover
- 381 pages
- Used Book in Good Condition
Review
"The first part of the book under review represents essentially the material of R. Narasimhan’s 'Complex analysis in one variable' (first edition, 1985). The second part of the book, authored by Y. Nievergelt, consists of exercises and relevant references…. There are notes at the end of each chapter which contain brief remarks on the history of the material presented as well as references to the literature. The exercises of part II give the reader the opportunity to consolidate his knowledge in complex analysis. At the end of this part there are notes for the exercises and references. The book can be highly recommended for a thorough study of complex analysis."
―ZENTRALBLATT MATH (Review of the second edition)
"The book introduces and makes use of concepts from many different areas of mathematics, especially ideas used in several complex variables and differential geometry. There is also a short…introductory chapter dealing with several complex variables…. The exercises in Part 2 vary from basic to advanced, and provide good practice for the concepts and techniques of the subject…. The choice of topics covered gives an excellent introduction to modern complex analysis. The exposition is well written. All in all, this book is a welcome addition to the list of books presenting a first course in complex analysis."
―MATHEMATICAL REVIEWS (Review of the second edition)
"Provides a smooth and unintimidating transition from classical complex analysis in the plane to modern abstract theory on manifolds... An excellent, carefully written and thematically rich book which does not overwhelm the reader... Well-suited as a textbook either for sophisticated beginners or as a sequel to a one-semester introductory course."
―JAHRESBERICHT DER DMV (Review of the first edition)
From the Back Cover
This book presents complex analysis in one variable in the context of modern mathematics, with clear connections to several complex variables, de Rham theory, real analysis, and other branches of mathematics. Thus, covering spaces are used explicitly in dealing with Cauchy's theorem, real variable methods are illustrated in the Loman-Menchoff theorem and in the corona theorem, and the algebraic structure of the ring of holomorphic functions is studied.
Using the unique position of complex analysis, a field drawing on many disciplines, the book also illustrates powerful mathematical ideas and tools, and requires minimal background material. Cohomological methods are introduced, both in connection with the existence of primitives and in the study of meromorphic functionas on a compact Riemann surface. The proof of Picard's theorem given here illustrates the strong restrictions on holomorphic mappings imposed by curvature conditions.
New to this second edition, a collection of over 100 pages worth of exercises, problems, and examples gives students an opportunity to consolidate their command of complex analysis and its relations to other branches of mathematics, including advanced calculus, topology, and real applications.
Most helpful customer reviews
20 of 20 people found the following review helpful.
A great way to begin learning Complex Analysis
By A Customer
This book, like each lecture by Narasimhan that I have had the pleasure to hear, exhibits masterful understanding and exposition of the material. His proofs are extremely elegant, and it is always clear where he is going with the material. His writing flows very smoothly, and the addition of exercises to this edition is very helpful in the process of learning to prove things in the various areas covered in the chapter. He also does a great job of allowing one to make the connections between complex analysis and other fields of mathematics, and the notes at the end of each chapter offer interesting insight into the material such as various mathematicians involved in developing the topics and other areas of interest relative to the particular chapter. It is rare that an elementary book on complex analysis goes into further topics like several complex variables and complex manifolds, so if you are interested in learning complex analysis and preparing to extend to further related topics, this is the book for you.
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