Introduction to Complex Analysis

By: Kodaira, KunihikoMaterial type: TextTextPublication details: Cambridge New York : Cambridge University Press, 1984Description: ix, 256 pages : illustrationsISBN: 9780521243919 ; 0521243912 ; 9780521286596; 052128659X Subject(s): Holomorphic functionsDDC classification: 515.98
Contents:
Holomorphic function -- Cauchy's theorem -- Conformal mappings -- Analytic continuation -- Riemann's mapping theorem.
Summary: This textbook is an introduction to the classical theory of functions of a complex variable. The author's aim is to explain the basic theory in an easy-to-understand and careful way. He emphasizes geometrical considerations and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions. The general versions of Cauchy's Theorem and integral formula are proved in Chapter 2. The remainder of the book deals with conformal mappings, analytic continuation, and Riemann's Mapping Theorem. The presentation here is very full and detailed. The book is profusely illustrated and includes many examples. Problems are collected together at the end of the book. It should be an ideal text for first courses in complex analysis.
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Item type Current library Collection Call number Status Date due Barcode Item holds
Reference Books Reference Books Main Library
Reference 		Reference 515.98 KOD (Browse shelf(Opens below)) Available 005612
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Includes Index

Holomorphic function --
Cauchy's theorem --
Conformal mappings --
Analytic continuation --
Riemann's mapping theorem.

This textbook is an introduction to the classical theory of functions of a complex variable. The author's aim is to explain the basic theory in an easy-to-understand and careful way. He emphasizes geometrical considerations and, to avoid topological difficulties associated with complex analysis, begins by deriving Cauchy's integral formula in a topologically simple case and then deduces the basic properties of continuous and differentiable functions. The general versions of Cauchy's Theorem and integral formula are proved in Chapter 2. The remainder of the book deals with conformal mappings, analytic continuation, and Riemann's Mapping Theorem. The presentation here is very full and detailed. The book is profusely illustrated and includes many examples. Problems are collected together at the end of the book. It should be an ideal text for first courses in complex analysis.

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