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Complex Analysis 1st Edition by Kunihiko Kodaira ISBN 0521809371 9780521809375

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Complex Analysis 1, Fourth printing 2008 Edition Kunihiko Kodaira Digital Instant Download

Author(s): Kunihiko Kodaira; A. Sevenster (Translator); A.F. Beardon, T.K. Carne (Editors)
ISBN(s): 9780521809375, 0521809371
Edition: 1, Fourth printing 2008
File Details: PDF, 19.34 MB
Year: 2008
Language: english
SKU: EB-35152352 Category: Tags: , , ,

Complex Analysis 1st Edition by Kunihiko Kodaira – Ebook PDF Instant Download/Delivery: 0521809371, 9780521809375
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ISBN 10: 0521809371 
ISBN 13: 9780521809375
Author: Kunihiko Kodaira

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.

Complex Analysis 1st Table of contents:

Ch. I. The Complex Plane and Elementary Functions

Ch. II. Analytic Functions

Ch. III. Line Integrals and Harmonic Functions

Ch. IV. Complex Integration and Analyticity

Ch. V. Power Series

Ch. VI. Laurent Series and Isolated Singularities

Ch. VII. The Residue Calculus

Ch. VIII. The Logarithmic Integral

Ch. IX. The Schwarz Lemma and Hyperbolic Geometry

Ch. X. Harmonic Functions and the Reflection Principle

Ch. XI. Conformal Mapping

Ch. XII. Compact Families of Meromorphic Functions

Ch. XIII. Approximation Theorems

Ch. XIV. Some Special Functions

Ch. XV. The Dirichlet Problem

Ch. XVI. Riemann Surfaces

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Tags: Kunihiko Kodaira, Complex Analysis