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Mathematical Modeling: Models, Analysis and Applications, by Sandip Banerjee
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Almost every year, a new book on mathematical modeling is published, so, why another? The answer springs directly from the fact that it is very rare to find a book that covers modeling with all types of differential equations in one volume. Until now. Mathematical Modeling: Models, Analysis and Applications covers modeling with all kinds of differential equations, namely ordinary, partial, delay, and stochastic. The book also contains a chapter on discrete modeling, consisting of differential equations, making it a complete textbook on this important skill needed for the study of science, engineering, and social sciences.
More than just a textbook, this how-to guide presents tools for mathematical modeling and analysis. It offers a wide-ranging overview of mathematical ideas and techniques that provide a number of effective approaches to problem solving. Topics covered include spatial, delayed, and stochastic modeling. The text provides real-life examples of discrete and continuous mathematical modeling scenarios. MATLAB® and Mathematica® are incorporated throughout the text. The examples and exercises in each chapter can be used as problems in a project.
Since mathematical modeling involves a diverse range of skills and tools, the author focuses on techniques that will be of particular interest to engineers, scientists, and others who use models of discrete and continuous systems. He gives students a foundation for understanding and using the mathematics that is the basis of computers, and therefore a foundation for success in engineering and science streams.
- Sales Rank: #1341035 in Books
- Published on: 2014-02-07
- Original language: English
- Number of items: 1
- Dimensions: 9.30" h x .80" w x 6.10" l, 1.35 pounds
- Binding: Hardcover
- 276 pages
Review
"…the book is rich with examples. There are examples from ecology, physics, chemistry, economy, medicine, sociology, epidemiology, and more, including specific examples that could be of interest in computer simulation … there are many solved problems and exercises … Both features makes the book a good selection for drawing out examples, problems, and exercises to show what differential equations have to offer to the aspiring modeler …"
―Computing Reviews, October 2014
"…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses."
―Svitlana P. Rogovchenko, Zentralblatt MATH 1298
Most helpful customer reviews
1 of 1 people found the following review helpful.
Lots of worked examples make this a good introductory text
By Physics Student
Overall,I think this is a really good text for an introduction to math modeling. The best attribute is the abundance of examples. And while most math textbooks claim to have a lot of examples, they typically just do 3-5 problems like the different types you would see at the end of the chapter. This book doesn't.
Each chapter is broken into sections, with theory and an example for each type of problem. But the very last section in the chapter is just example after example problem (all worked out, too). This last section has about 10-15 problems for each chapter.
The problem sets are also very good. The problems are similar to examples (so you have something to base your work on) and vary from "build your own model" to "interpret this pre-built model" both of which are valuable skills.
The book is not without it's blemishes, however. Sometimes the notation gets a little inconsistent. When solving for a steady state problem, it is shown to let L(n) = L(n+1) = L*. Then solve for L* algebraically. Sometimes L* is used exclusively in this process - that is, everything is rewritten as L* instead of L(n) and L(n+1). Sometimes L*(n) and L*(n+1) are used and then changed at the end to be L*. It's a pretty minor annoyance (and if it is intentional for certain models, I must've missed that part in the beginning).
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