Functional Equations in Applied Sciences

Enrique Castillo, Andrés Iglesias and Reyes Ruíz-Cobo (Eds.)044451788X, 9780444517883, 9781423742074

The book provides the reader with the different types of functional equations that s/he can find in practice, showing, step by step, how they can be solved. A general methodology for solving functional equations is provided in Chapter 2. The different types of functional equations are described and solved in Chapters 3 to 8. Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, help the reader to change his/her mind in order to state problems as functional equations as an alternative to differential equations, and to state new problems in terms of functional equations or systems. An interesting feature of the book is that it deals with functional networks, a powerful generalization of neural networks that allows solving many practical problems. The second part of the book, Chapters 9 to 13, is devoted to the applications of this important paradigm. The book contains many examples and end of chapter exercises, that facilitates the understanding of the concepts and applications. · A general methodology for solving functional equations is provided in Chapter 2. · It deals with functional networks, a powerful generalization of neural networks. · Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, illustrate the concept of functional equation. · Functional equations are presented as a powerful alternative to differential equations. · The book contains end of chapter exercises.

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Table of contents :
Content:
Note from the editor
Page vi
Charles Chui

Note from the publisher
Page vii
Keith Jones

Preface
Pages xi-xiii
Enrique Castillo, Andrés Iglesias, Reyes Ruíz-Cobo

Chapter 1 Introduction and motivation Original Research Article
Pages 3-18

Chapter 2 Some methods for solving functional equations Original Research Article
Pages 19-33

Chapter 3 Equations for one function of one variable Original Research Article
Pages 35-55

Chapter 4 Equations with several functions in one variable Original Research Article
Pages 57-71

Chapter 5 Equation for one function of several variables Original Research Article
Pages 73-90

Chapter 6 Equations with functions of several variables Original Research Article
Pages 91-110

Chapter 7 Functional equations and differential equations Original Research Article
Pages 111-158

Chapter 8 Vector and matrix equations Original Research Article
Pages 159-166

Chapter 9 Functional networks Original Research Article
Pages 169-232

Chapter 10 Applications to science and engineering Original Research Article
Pages 233-264

Chapter 11 Applications to Geometry and CAGD Original Research Article
Pages 265-319

Chapter 12 Applications to Economics Original Research Article
Pages 321-350

Chapter 13 Applications to Probability and Statistics Original Research Article
Pages 351-376

Bibliography
Pages 377-386

Index
Pages 387-391