Complex Analysis
Published on 23. August 2007
978-1-316-04460-5 (ISBN)
Description
Written by a master of the subject, this text will be appreciated by students and experts for the way it develops the classical theory of functions of a complex variable in a clear and straightforward manner. In general, the approach taken here emphasises geometrical aspects of the theory in order to avoid some of the topological pitfalls associated with this subject. Thus, Cauchy's integral formula is first proved in a topologically simple case from which the author deduces the basic properties of holomorphic functions. Starting from the basics, students are led on to the study of conformal mappings, Riemann's mapping theorem, analytic functions on a Riemann surface, and ultimately the Riemann-Roch and Abel theorems. Profusely illustrated, and with plenty of examples, and problems (solutions to many of which are included), this book should be a stimulating text for advanced courses in complex analysis.
Reviews / Votes
'While most of the material included in the first part could be used in a basic course on complex analysis, the whole book could serve as a text for an advanced course on Riemann surfaces. The book contains many pictures (helping to build geometric intuition) and problems (elementary and advanced). The book could be very helpful for students as well as for experts in the field.' European Mathematical Society NewsletterMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 160 Line drawings, unspecified
File size
18,31 MB
ISBN-13
978-1-316-04460-5 (9781316044605)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Kunihiko Kodaira
Complex Analysis
Book
08/2007
Cambridge University Press
€114.30
Shipment within 15-20 days
Person
Kunihiko Kodaira (1915-97) worked in many areas including harmonic integrals, algebraic geometry and the classification of compact complex analytic surfaces. He held faculty positions at many universities including the University of Tokyo, Harvard University, Massachusetts, Stanford University, California, and The Johns Hopkins University, and the Institute for Advanced Study in Princeton. He was awarded a Fields medal in 1954 and a Wolf Prize in 1984.
Content
1. Holomorphic functions; 2. Cauchy's theorem; 3. Conformal mappings; 4. Analytic continuation; 5. Riemann's mapping theorem; 6. Riemann surfaces; 7. The structure of Riemann surfaces; 8. Analytic functions on a closed Riemann surface.
