
Lectures on Functional Equations and Their Applications
Description
Alles über E-Books | Antworten auf Fragen rund um E-Books, Kopierschutz und Dateiformate finden Sie in unserem Info- & Hilfebereich.
More details
Other editions
Additional editions
Content
- 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
System requirements
File format: PDF
Copy protection: Watermark-DRM (Digital Rights Management)
System requirements:
- Computer (Windows; MacOS X; Linux): Use the free software Adobe Reader, Adobe Digital Editions, or any other PDF viewer of your choice (see eBook Help).
- Tablet/Smartphone (Android; iOS): Install the free app Adobe Digital Editions or another reading app for eBooks, e.g., PocketBook (see eBook Help).
- E-reader: Bookeen, Kobo, Pocketbook, Sony, Tolino and many more (only limited: Kindle).
The file format PDF always displays a book page identically on any hardware. This makes PDF suitable for complex layouts such as those used in textbooks and reference books (images, tables, columns, footnotes). Unfortunately, on the small screens of e-readers or smartphones, PDFs are rather annoying, requiring too much scrolling.
This eBook uses Watermark-DRM, a „soft” copy protection. This means that there are no technical restrictions to prevent illegal distribution. However, there is a personalised watermark embedded in the eBook that can be used to identify the purchaser of the eBook in the event of misuse and to provide evidence for legal purposes.
For more information, see our eBook Help page.