Complex analysis in one variable.

Format:

Book

Author/Creator:

Narasimhan, Raghavan.

Contributor:

Nievergelt, Yves.

Language:

English

Subjects (All):

Functions of complex variables.

Mathematical analysis.

Physical Description:

xiv, 381 pages : illustrations ; 25 cm

Edition:

Second edition / Raghavan Narasimhan, Yves Nievergelt.

Place of Publication:

Boston : Birkhäuser Boston, [2001]

Summary:

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.

Notes:

Includes bibliographical references (pages 373-377) and index.

ISBN:

0817641645

3764341645

OCLC:

45223595