The Nature of Mathematical Modeling

The Nature of Mathematical Modeling

by Neil Gershenfeld
     
 

ISBN-10: 0521570956

ISBN-13: 9780521570954

Pub. Date: 11/28/1998

Publisher: Cambridge University Press

This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in…  See more details below

Overview

This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. 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. The text is complemented by extensive worked problems.

Product Details

ISBN-13:
9780521570954
Publisher:
Cambridge University Press
Publication date:
11/28/1998
Edition description:
New Edition
Pages:
344
Product dimensions:
6.85(w) x 9.72(h) x 1.18(d)

Table of Contents

Preface
1Introduction1
Pt. 1Analytical Models5
2Ordinary Differential and Difference Equations9
3Partial Differential Equations24
4Variational Principles34
5Random Systems44
Pt. 2Numerical Models63
6Finite Differences: Ordinary Differential Equations67
7Finite Differences: Partial Differential Equations78
8Finite Elements93
9Cellular Automata and Lattice Gases102
Pt. 3Observational Models111
10Function Fitting115
11Transforms128
12Architectures139
13Optimization and Search156
14Clustering and Density Estimation169
15Filtering and State Estimation186
16Linear and Nonlinear Time Series204
App. 1Graphical and Mathematical Software225
App. 2Network Programming250
App. 3Benchmarking257
App. 4Problem Solutions259
Bibliography330
Index340

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