Complex Analysis
In the Spirit of Lipman Bers
Published on 1. December 2007
Book
Hardback
XIV, 220 pages
978-0-387-74714-9 (ISBN)
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.
Reviews / Votes
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 fur Mathematik, Vol. 156 (4), April, 2009)More details
Series
Edition
2007
Language
English
Place of publication
NY
United States
Target group
College/higher education
Graduate
Product notice
Laminated cover
Illustrations
20 s/w Abbildungen
1, black & white illustrations
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 14 mm
Weight
526 gr
ISBN-13
978-0-387-74714-9 (9780387747149)
DOI
10.1007/978-0-387-74715-6
Schweitzer Classification
Other editions
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11/2012
2nd Edition
Springer
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Book
11/2010
Springer
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E-Book
11/2007
1st Edition
Springer
€56.99
Available for download
Content
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.