Functional Equations in Applied Sciences

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Elsevier, Nov 4, 2004 - Mathematics - 408 pages
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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

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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...

About the author (2004)

Enrique Castillo is Professor of Applied Mathematics at the University of Cantabria in Santander (Spain). He is a Mathematician and a Civil engineer and Member of the Spanish Royal Academy of Engineering. He has taught at several other universities in the Europe and America. The author/coauthor of eleven other books in English and fourteen in Spanish, and more than 300 papers in journals and Congresses. More information can be found at his Web site: http: //personales.unican.es/castie//.

Juan R. Ruiz-Tolosa is an Industrial and Civil Engineer and has been Professor of Algebra, Tensors, Topology, Differential Geometry and Calculus at the Civil Engineering School, University of Cantabria for 30 years. His field of research includes Number Theory, Euclidean Geometry, Elliptic Integrals, Algebraic Roots of Equations, etc.

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