The Nature Of Mathematical Modelling Neil Gershenfeld

Contents......Page 1
Preface......Page 6
1 Introduction......Page 8
Part One Analytical Models......Page 11
2 Ordinary Differential and Difference Equations......Page 13
3 Partial Differential Equations......Page 28
4 Variational Principles......Page 38
5 Random Systems......Page 48
Part Two Numerical Models......Page 66
6 Finite Differences: Ordinary Differential Equations......Page 69
7 Finite Differences: Partial Differential Equations......Page 80
8 Finite Elements......Page 95
9 Cellular Automata and Lattice Gases......Page 104
Part Three Observational Models......Page 113
10 Function Fitting......Page 115
11 Transforms......Page 128
12 Architectures......Page 139
13 Optimization and Search......Page 156
14 Clustering and Density Estimation......Page 169
15 Filtering and State Estimation......Page 186
16 Linear and Nonlinear Time Series......Page 204
Appendix 1 Graphical and Mathematical Software......Page 225
Appendix 2 Network Programming......Page 250
Appendix 3 Benchmarking......Page 257
Appendix 4 Problem Solutions......Page 259
Bibliography......Page 330
Index......Page 340