The Nature of Mathematical Modeling |  | Author: Neil Gershenfeld
Publisher: Cambridge University Press
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Rating:  8 reviews
Sales Rank: 498674
Media: Hardcover
Pages: 356
Number Of Items: 1
Shipping Weight (lbs): 1.9
Dimensions (in): 9.8 x 7.2 x 1
ISBN: 0521570956
Dewey Decimal Number: 511.8
EAN: 9780521570954
ASIN: 0521570956
Publication Date: November 28, 1998
Availability: Usually ships in 1-2 business days
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Product Description
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.
Book Description
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.
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| Customer Reviews:
Showing reviews 1-5 of 8
 Looking forward to new edition January 6, 2008
William Addington
1 out of 1 found this review helpful
This is an excellent overview of various mathematical techniques used in creating models.
There are many code snippets in C, Java and Matlab but this is mainly a mathematics book, and only incidentally a programming book. The code is presented to show "simple efficient implementations on computers."
Great as a refresher when you know a technique will be useful in a model but you've forgotten the details.
The first two sections of the book (Analytical Models and Numerical Models) assume you know what model you are going to use. The last, Observational Models, is concerned with "inferring a model from measured data."
The is a new version of this book being released in Jan 08. I look forward to it.
 offers many problems and solutions January 19, 2006
W Boudville (Terra, Sol 3)
4 out of 5 found this review helpful
The book offers you a multidisciplinary survey of how to do modelling on a computer. Gershenfeld tries to give an appreciation of a wide variety of methods. Both in the diversity of these methods and in the fields to which they can be applied.
You might already be familiar with the classic "Numerical Recipes" text, which also offers a survey of the field. Gershenfeld takes the analysis to a slightly more advanced level. But not so much so as to be impenetrable to many readers.
The book also gives a nice summary of various maths packages that could be useful to you. Plus, as a further aid, the text has numerous problems and solutions. In fact, the solutions take up a considerable and worthy portion of the book.
Modeling: "All" in a single book October 18, 2005
Zelimir Kurtanjek (Zagreb, CROATIA)
4 out of 4 found this review helpful
Neil Gershenfeld "The Nature of Mathematical Modeling" is a unique and a successful attempt to enclose in a single book the main ideas of mathematical view on nature, numerical methods, modeling techniques and computer software. The unifying concept of mathematics and philosophy of extraction of the main modeling concepts from nature observations enabled the success with the apparently impossible task. The book lacks rigor in mathematical derivations, but excels in unification of ideas. It can be recommended to students of mathematics and computer science to learn about complexity of natural phenomena, and vice versa, to students of engineering fields to gain a broader view on richness of mathematical theories.
Great summary of applied mathematics July 26, 2002
Thy Yem (Madison, AL United States)
12 out of 12 found this review helpful
This book concisely describes critical ideas, techniques, and results of a wide range of applied mathematics which are useful in physical modelings. It has well chosen exercises, though not many, with detail answers. It provides good references for further study. This is important because the explanations given in this book are terse.I think the book is more valuable for those looking for concise reviews than those wanting to learn the materials the first time. Also, Author states (at MIT website) that he is working on the second edition for this book. He wants to add "control theory" and correct some typos.
A great overview of Mathematical Modeling April 4, 2000
Nicholas E. Athanas (Ratrace, IL)
15 out of 16 found this review helpful
Very readable and enjoyable book if you like Applied Mathematics. In addition to very broad but not shallow coverage of the various techniques used to model physical phenomena, the author provides *excellent* references for those who want to dig further. The Matlab code and computer techniques are an excellent addition.I agree with the previous reviewer, the book will become a classic.
Showing reviews 1-5 of 8
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