Theory of functions

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Theory of functions / by Konrad Knopp ; translated by Frederick Bagemihl

資料種別:

図書

出版情報:

New York : Dover publications, c1945-47

形態:

2 v. ; 21 cm

著者名:

ISBN:

9780486601564 [0486601560] (Pt. 1)
9780486601571 [0486601579] (Pt. 2)

書誌ID:

BA21953881

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

その他の標題:

Funktionentheorie

注記:

Part 1 is translated, with minor changes in text, from the 5th German edition; pt. 2 is translated from the 4th German edition
Translation of Funktionentheorie
"First American edition."
Bibliography: v. 1, p. 141-142; v. 2, p. 147
Includes index

主題:

Functions of complex variables

言語:

英語

目次情報:

Fundamental Concepts / Section I：

Numbers and Points / Chapter 1：

Prerequisites / 1：

The Plane and Sphere of Complex Numbers / 2：

Point Sets and Sets of Numbers / 3：

Paths, Regions, Continua / 4：

Functions of a Complex Variable / Chapter 2：

The Concept of a Most General (Single-valued) Function of a Complex Variable / 5：

Continuity and Differentiability / 6：

The Cauchy-Riemann Differential Equations / 7：

Integral Theorems / Section II：

The Integral of a Continuous Function / Chapter 3：

Definition of the Definite Integral / 8：

Existence Theorem for the Definite Integral / 9：

Evaluation of Definite Integrals / 10：

Elementary Integral Theorems / 11：

Cauchy's Integral Theorem / Chapter 4：

Formulation of the Theorem / 12：

Proof of the Fundamental Theorem / 13：

Simple Consequences and Extensions / 14：

Cauchy's Integral Formulas / Chapter 5：

The Fundamental Formula / 15：

Integral Formulas for the Derivatives / 16：

Series and the Expansion of Analytic Functions in Series / Section III：

Series with Variable Terms / Chapter 6：

Domain of Convergence / 17：

Uniform Convergence / 18：

Uniformly Convergent Series of Analytic Functions / 19：

The Expansion of Analytic Functions in Power Series / Chapter 7：

Expansion and Identity Theorems for Power Series / 20：

The Identity Theorem for Analytic Functions / 21：

Analytic Continuation and Complete Definition of Analytic Functions / Chapter 8：

The Principle of Analytic Continuation / 22：

The Elementary Functions / 23：

Continuation by Means of Power Series and Complete Definition of Analytic Functions / 24：

The Monodromy Theorem / 25：

Examples of Multiple-valued Functions / 26：

Entire Transcendental Functions / Chapter 9：

Definitions / 27：

Behavior for Large z / 28：

Singularities / Section IV：

The Laurent Expansion / Chapter 10：

The Expansion / 29：

Remarks and Examples / 30：

The Various types of Singularities / Chapter 11：

Essential and Non-essential Singularities or Poles / 31：

Behavior of Analytic Functions at Infinity / 32：

The Residue Theorem / 33：

Inverses of Analytic Functions / 34：

Rational Functions Bibliography / 35：

Index

Fundamental Concepts / Section I：

Numbers and Points / Chapter 1：

Prerequisites / 1：

The Plane and Sphere of Complex Numbers / 2：

Point Sets and Sets of Numbers / 3：

Paths, Regions, Continua / 4：

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