Lectures on Functional Equations and Their Applications
Erschienen am 14. Mai 2014
533 Seiten
978-0-08-095525-4 (ISBN)
Beschreibung
Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.
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Buch
01/1966
Academic Press
100,00 €
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Inhalt
- Front Cover
- Lectures on Functional Equations and Their Applications
- Copyright Page
- Contents
- Foreword to the German Edition
- Foreword to the English Edition
- Introduction
- 0.1 Definition and Examples
- 0.2 History
- PART I: Equations for Functions of a Single Variable
- CHAPTER 1. Equations Which Can Be Solved by Simple Substitutions
- 1.1 Equations of the Form f[G(x, y)] = F[f(x), y]
- 1.2 Methods of Solving Similar Types of Equations
- 1.3 An Application: Scalar Product and Vector Product
- CHAPTER 2. Solution of Equations by Determining the Values of the Unknown Function on a Dense Set
- 2.1 Cauchy's Equations and Jensen's Equation
- 2.2 Equations of the Type f(x + y ) = F[f(x), f (y)], Related Equations, and Generalizations
- 2.3 Some Applications (Euclidean and Non-Euclidean Geometry, Mechanics, Business Mathematics, Probability Theory)
- 2.4 D'Alembert's Functional Equation and Its Application
- 2.5 Additional Functional Equations with One Function of One Variable
- CHAPTER 3. Equations with Several Unknown Functions
- 3.1 Pexider's and Related Equations
- 3.2 Functional Equations for the Trigonometric Functions and Related Equations
- CHAPTER 4. Reduction to Differential and Integral Equations, General Methods
- 4.1 Integral Transformations and Reduction to Integral Equations
- 4.2 Reduction to Differential Equations. Some General Methods
- PART II: Equations for Functions of Several Variables
- CHAPTER 5. Simple Equations
- 5.1 Generalizations of Cauchy's and Similar Equations and Their Applications
- 5.2 The Equations of Homogeneous Functions and Related Equations
- 5.3 The Equations of the Weighted Mean
- CHAPTER 6. Composite Equations
- 6.1 The Translation Equation
- 6.2 The Associativity Equation
- 6.3 The Transitivity Equation
- 6.4 The Bisymmetry Equation
- 6.5 The Autodistributivity Equations
- CHAPTER 7. Equations with Several Unknown Functions of Several Variables. Reduction to Partial Differential Equations
- 7.1 Equations with Several Unknown Functions That Are Solvable by Elementary Methods
- 7.2 Reduction to Partial Differential Equations and Functional Differential Equations
- CHAPTER 8. Vector and Matrix Equations
- 8.1 Cauchy-Pexider-Sincov Equations
- 8.2. Associativity, Transformation, and Distributivity Equations
- Concluding Remarks. Some Unsolved Problems
- Bibliography
- Author Index
- Subject Index
