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.
Undergraduate honors students in mathematics, and engineering as well as graduate students in artificial Intelligence, engineering and statistics. In addition, students in Economics programs will also be interested in this book as many of the applications illustrated are from economics fields.
I. Functional Equations.
- Introduction and motivation
- Some methods for solving functional equations.
- Equations for one function of one variable.
- Equations with several functions in one variable.
- Equation for one function of several variables.
- Equations with functions of several variables.
- Functional equations and differential equations.
- Vector and matrix equations.
II. Applications of Functional Equations.
- Functional Networks.
- Applications to Science and Engineering.
- Applications to Geometry and CAGD.
- Applications to Economics.
- Applications to Probability and Statistics.
- No. of pages:
- © Elsevier Science 2005
- 4th November 2004
- Elsevier Science
- eBook ISBN:
- Hardcover ISBN:
Universidad de Santander, Spain
Universidad de Cantabrian, Santander, Spain
Universidad de Cantabria, Santander, Spain
"...the main strengths of this book are (a)its collection of solution methods for standard FE and (b)a substantial number of examples and applications that help make FE more accessible to people who are comfortable with standard methods of analysis (real, complex, differential equations, difference equations) but with little or no background in FE." -MATHEMATICAL REVIEWS