Complex Analysis
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.
| Autor: | Gilman, Jane P. Kra, Irwin Rodríguez, Rubí E. |
|---|---|
| ISBN: | 9781441973221 |
| Auflage: | 2 |
| Sprache: | Englisch |
| Seitenzahl: | 306 |
| Produktart: | Gebunden |
| Verlag: | Springer US |
| Veröffentlicht: | 20.11.2012 |
| Untertitel: | In the Spirit of Lipman Bers |
| Schlagworte: | Cauchy theory Dirichlet problem Green's function Riemann Mapping Theorem analytic functions complex analysis complex power series conformal equivalence harmonic functions holomorphic functions |
Rubí E. Rodríguez is a professor of mathematics at Pontificia Universidad Católica de Chile. Irwin Kra is an emeritus distinguished service professor of mathematics at SUNY, Stony Brook. Jane P. Gilman is a professor II of mathematics at Rutgers University.