Difference between revisions of "File:Gershenfeld.jpg"
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− | + | by [http://ng.cba.mit.edu/ Neil Gershenfeld] at the [http://www.mit.edu Massachusetts Institute of Technology] | |
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− | Preface | + | This [[book]] first covers exact and approximate [[analysis|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=== |
Latest revision as of 01:54, 4 January 2009
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
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