Mathematica for Scientists and Engineers: Using Mathematica to Do Science

by Richard Gass

This text is aimed at junior/graduate-level courses in science or engineering that use Mathematica as a problem-solving tool and integrates symbolic, numerical and graphical techniques throughout.... This description may be from another edition of this product.

• Format: Paperback
• Language: English
• ISBN: 0132276127
• ISBN13: 9780132276122
• Release Date: August 1997
• Publisher: Prentice Hall
• Length: 498 Pages
• Weight: 1.65 lbs.
• Dimensions: 0.8" x 7.0" x 9.2"

Customer Reviews

Somewhat dated....but still useful

Since this book was published, Mathematica has come out with version 4.1, which makes the book somewhat dated, since it is written in 3.0. However, it could still be of benefit to someone who wants to use Mathematica for more specialized tasks in science and enginnering. Some of the Mathematica code in the book is given for problems that are not usually discussed in books on Mathematica. It could serve as a supplement to a course in Mathematica if one is willing to put up with its being out of date, since there are many interesting exercises assigned at the end of each chapter. It would not be too difficult to update the book to Mathematica 4.1. Practicing scientists interested in using Mathematica for visualization could use the book as a handy reference. Chapter 1 begins with a short review of how to use Mathematica and then the author jumps right into the Riemann zeta function. He gives a fairly lengthy discussion of this function, complete with graphics and Mathematica code. He uses both his own code for the function as well as the built-in function Zeta to illustrate the properties of the Riemann zeta function, particularly its zeros. He shows how the choice of grid spacing can hide the singularity structure of this function, if not chosen finely enough. Chapter 2 is an overview of numerical methods in Mathematica. He begins with the problem of numerical integration by calculating the specific heat of a crystalline lattice using Nintegrate. The ability of Mathematica to integrate numerically nasty integrands, such as sin(1/x), is then investigated, with the problems with the singularity and convergence discussed in some detail. He also discusses numerical contour integration, which is not usually done in Mathematica books. The Duffing oscillator is treated as an example of solving differential equations numerically using Mathematica. Most importantly though the author shows how to solve partial differential equations numerically using Mathematica. Although performance issues in solving PDEs will appear in using Mathematica to do this, the author uses the built-in function NDSolve to show how one might gain insight into the behavior of solutions. He treats the case of sound waves in a pipe and the elastic string with fixed ends subjected to a constant transverse force. Then after a brief look at numerical sums and products, he treats the quantum mechanical problem of a particle in a one-dimensional well. The chapter ends with a consideration of the 3-body problem, including the restricted 3-body problem. The author's treatment is pretty good but he fails to discuss in detail the numerical instability of the orbits at large times. Symbolic manipulation, the tour-de-force in Mathematica, is treated in detail in chapter 3. He gives as an example a very interesting simulation of a cyclotron, and shows how Mathematica can be used to efficiently do the algebra in this problem. He then illustrates how to use Mathematica to manipulate series, with se