Complex analysis : in the spirit of Lipman Bers
著者
書誌事項
Complex analysis : in the spirit of Lipman Bers
（Graduate texts in mathematics, 245）
Springer, c2013
2nd ed
- : softcover
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注記
Includes bibliographical references (p. 299-300) and index
内容説明・目次
内容説明
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.
目次
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.
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