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ISBN 0521570956

by Neil Gershenfeld at the Massachusetts Institute of Technology

This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications.

Contents

Preface

1. Introduction

Part I. Analytical Models

2. Ordinary differential and difference equations

3. Partial differential equations

4. Variational principles

5. Random systems

Part II. Numerical Models

6. Finite differences: ordinary difference equations

7. Finite differences: partial differential equations

8. Finite elements

9. Cellular automata and lattice gases

Part III. Observational Models

10. Function fitting

11. Transforms

12. Architectures

13. Optimization and search

14. Clustering and density estimation

15. Filtering and state estimation

16. Linear and nonlinear time series

Appendix 1. Graphical and mathematical software

Appendix 2. Network programming

Appendix 3. Benchmarking

Appendix 4. Problem solutions

Bibliography