Gilman / Kra / Rodríguez Complex Analysis

In the Spirit of Lipman Bers
1. Auflage 2007
ISBN: 978-0-387-74715-6
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 220 Seiten, Web PDF

Reihe: Mathematics and Statistics (R0)

Here is a work that breaks with tradition and organizes the basic material of complex analysis in a unique manner. The authors’ aim 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. The first part of the book is a study of the many equivalent ways of understanding the concept of analyticity, and move on to offer a leisurely exploration of interesting consequences and applications. The book covers most, if not all, of the material contained in Bers’s courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra.

Zielgruppe

Graduate

Autoren/Hrsg.

Gilman, Jane P.

Kra, Irwin

Rodríguez, Rubí E.

Inhaltsverzeichnis

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.