The Nature of Mathematical Modeling

by Neil Gershenfeld

• ISBN13: 9780521210508
• ISBN10: 052121050X
• Edition: Revised
• Format: Paperback
• Copyright: 2011-06-23
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface

Introduction

Analytical Models

Ordinary differential and difference equations

Partial differential equations

Variational principles

Random systems

Numerical Models

Finite differences: ordinary difference equations

Finite differences: partial differential equations

Finite elements

Cellular automata and lattice gases

Observational Models

Function fitting

Transforms

Architectures

Optimization and search

Clustering and density estimation

Filtering and state estimation

Linear and nonlinear time series

Graphical and mathematical software

Network programming

Benchmarking

Problem solutions

Bibliography

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