Complex Analysis : Introduced in the Spirit of Lipman Bers (Graduate Texts in Mathematics) 〈Vol. 245〉

Gilman, Jane P./ Kra, I./ Rodriguez, R. E.

Springer（2008/01発売）

• 製本 Hardcover:ハードカバー版／ページ数 250 p.
• 商品コード 9780387747149

基本説明

Organizes the basic material of complex analysis in a unique manner. Features - Covers vast majority of the material needed for a beginning graduate level course on complex analysis.

Full Description

The authors' aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.

Contents

Preface.- Standard Notation and Commonly used Symbols.- The Fundamental Theorem in Complex Function Theory.- Foundations.- Power Series.- The Cauchy Theory-A Fundamental Theorem.- The Cauchy Theory-Key Consequences.- Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions.- Sequences and Series of Holomorphic Functions.- Conformal Equivalence.- Harmonic Functions.- Zeros of Holomorphic Functions.- Bibliographical Notes.- Bibliography.- Index.