Enhanced descriptions from Syndetics:

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.

Table of contents provided by Syndetics

• 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

Reviews provided by Syndetics

CHOICE Review

As a compact exposition of the nature and techniques of contemporary mathematical modeling and computational tools needed for efficient implementation, Mathematical Modeling is right on target. Although several essential topics covered in the book are themselves worthy of stand-alone works, Gershenfeld's style of giving brief overviews together with a concise summary of key results in the subject area makes it invaluable for mathematical and computational modelers. The author's writing style risks leaving out several salient topics; however, the alternative for not exposing readers to the most current, contemporary tools may lead to arid mathematical modeling aptitude. To compensate for the lack of depth, several pointers and references allow readers to explore, in depth, some topical material of their choice. Abstract concepts are carefully explained and supported with a wealth of examples and illustrations, and a wonderful collection of problems are provided, a few of which are elementary enough for any beginner. Highly recommended. Graduate students; faculty; professionals. D. E. Bentil University of Vermont