# Functional Equations in Applied Sciences

Elsevier, Nov 4, 2004 - Mathematics - 408 pages
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.

ˇ A general methodology for solving functional equations is provided in Chapter 2.
ˇ It deals with functional networks, a powerful generalization of neural networks.
ˇ Many examples, coming from different fields, as geometry, science, engineering, economics, probability, statistics, etc, illustrate the concept of functional equation.
ˇ Functional equations are presented as a powerful alternative to differential equations.
ˇ The book contains end of chapter exercises.

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### Contents

 Introduction and Motivation 3 Some Methods for Solving Functional Equations 19 Equations for One Function of One Variable 35 Equations with Several Functions in One Variable 57 Equation for One Function of Several Variables 73 Equations with Functions of Several Variables 91 Functional Equations and Differential Equations 111 Vector and Matrix Equations 159
 Functional Networks 169 Applications to Science and Engineering 233 Applications to Geometry and CAGD 265 Applications to Economics 321 Applications to Probability and Statistics 351 Bibliography 377 Index 387 Mathematics in Science and Engineering 393

 Applications of Functional Equations 167

### Popular passages

Page 10 - R,R+ and R++ are the sets of real numbers, the set of non-negative real numbers and the set of positive real numbers, respectively. • Definition 1.2 (System of functional equations). A system of functional equations is a set of n > 2 functional equations. • Example 1.3 (Systems of functional equations). Examples of systems of functional equations are...