Theory of Functions

ISBN-10: 0486692191
ISBN-13: 9780486692197
Edition: 1996 (Unabridged)
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Description: Two volumes of a classic 5-volume work in 1 handy edition. Part I considers general foundations of the theory of functions; Part II stresses special functions and characteristic, important types of functions, selected from single-valued and  More...

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Book details

List price: $16.95
Copyright year: 1996
Publisher: Dover Publications, Incorporated
Publication date: 8/12/1996
Binding: Paperback
Pages: 320
Size: 5.50" wide x 8.00" long x 0.75" tall
Weight: 0.682
Language: English

Two volumes of a classic 5-volume work in 1 handy edition. Part I considers general foundations of the theory of functions; Part II stresses special functions and characteristic, important types of functions, selected from single-valued and multiple-valued classes. Demonstrations are full and proofs given in detail. Introduction. Bibliographies.

Fundamental Concepts
Numbers and Points
Prerequisites
The Plane and Sphere of Complex Numbers
Point Sets and Sets of Numbers
Paths, Regions, Continua
Functions of a Complex Variable
The Concept of a Most General (Single-valued) Function of a Complex Variable
Continuity and Differentiability
The Cauchy-Riemann Differential Equations
Integral Theorems
The Integral of a Continuous Function
Definition of the Definite Integral
Existence Theorem for the Definite Integral
Evaluation of Definite Integrals
Elementary Integral Theorems
Cauchy's Integral Theorem
Formulation of the Theorem
Proof of the Fundamental Theorem
Simple Consequences and Extensions
Cauchy's Integral Formulas
The Fundamental Formula
Integral Formulas for the Derivatives
Series and the Expansion of Analytic Functions in Series
Series with Variable Terms
Domain of Convergence
Uniform Convergence
Uniformly Convergent Series of Analytic Functions
The Expansion of Analytic Functions in Power Series
Expansion and Identity Theorems for Power Series
The Identity Theorem for Analytic Functions
Analytic Continuation and Complete Definition of Analytic Functions
The Principle of Analytic Continuation
The Elementary Functions
Continuation by Means of Power Series and Complete Definition of Analytic Functions
The Monodromy Theorem
Examples of Multiple-valued Functions
Entire Transcendental Functions
Definitions
Behavior for Large z
Singularities
The Laurent Expansion
The Expansion
Remarks and Examples
The Various types of Singularities
Essential and Non-essential Singularities or Poles
Behavior of Analytic Functions at Infinity
The Residue Theorem
Inverses of Analytic Functions
Rational Functions Bibliography
Index

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