Rubí E. Rodríguez, Irwin Kra, Jane P. Gilman

Complex Analysis (eBook, PDF)

In the Spirit of Lipman Bers

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 306
• Erscheinungstermin: 28. November 2012
• Englisch
• ISBN-13: 9781441973238
• Artikelnr.: 37758484

Autorenporträt

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.

Inhaltsangabe

Preface to Second Edition.- Preface to First Edition.- Standard Notation and Commonly Used Symbols.- 1 The Fundamental Theorem in Complex Function Theory.- 2 Foundations.- 3 Power Series.- 4 The Cauchy Theory - A Fundamental Theorem.- 5 The Cauchy Theory - Key Consequences.- 6 Cauchy Theory: Local Behavior and Singularities of Holomorphic Functions.- 7 Sequences and Series of Holomorphic Functions.- 8 Conformal Equivalence and Hyperbolic Geometry.- 9 Harmonic Functions.- 10 Zeros of Holomorphic Functions.- Bibliographical Notes.- Bibliography.- Index.

Rezensionen

From the reviews of the second edition:

"The book under review is a second edition of a book by the same authors and with the same title, also published by Springer in 2007. It contains some amount of new information. ... The book is carefully written and each chapter has an interesting list of exercises. I found it very useful as am Undergraduate and Graduate Text in Mathematics." (José M. Ansemil, The European Mathematical Society, euro-math-soc.eu, January, 2014)

From the reviews:

"The book is written in a clear and easily readable manner, completed with a well cared selection of exercises. The book, which is certainly useful for all specialists and lecturers in complex analysis, I also recommend to beginners in this area." (Fernando Perez-Gonzalez, Zentralblatt MATH, Vol. 1262, 2013)

"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)