The nature of mathematical modeling
著者
書誌事項
The nature of mathematical modeling
Cambridge University Press, 1999
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注記
Includes bibliographical references (p. 330-339) and index
内容説明・目次
内容説明
This 1998 book, about the nature and techniques of mathematical modeling, is oriented towards simple efficient implementations on computers. The text is in three 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, 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. The text is complemented by extensive worked problems.
目次
- 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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