Complex Analysis: In the Spirit of Lipman Bers

Inhaltsverzeichnis

From the 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

Pressestimmen

From the reviews:"This is a fairly conventional text for a first course in complex analysis. It is an interesting mix of the concrete and the abstract, and of the formulaic and the geometric. It has good exercises ... . It is nominally a graduate text (it is in Springer's series of Graduate Texts in Mathematics) ... . The book covers all the usual topics for a first course and includes a lot of advanced topics ... ." (Allen Stenger, MathDL, February, 2008)"This book is based on the original courses of Complex Analysis that was delivered by the well-known American specialist and lecturer in Analysis, Professor Lipman Bers. ... the book is written in a clear and easily readable manner. ... this book is useful for all specialists and lecturers in Complex Analysis ... and also all specialists who deal with applications of Complex Analysis. I also recommend this book to beginners who want to study Complex Analysis ... ." (Peter Zabreiko, Zentralblatt MATH, Vol. 1139 (17), 2008)"An introduction to complex analysis based on original lectures by Lipman Bers ... . the whole text is clearly suitable as a first course in complex analysis. ... In addition, it contains many exercises and a brief guide to the literature." (G. Teschl, Monatshefte für Mathematik, Vol. 156 (4), April, 2009)