One of the most frustrating aspects of modern physics and related disciplines is the lack of analytic solutions, or even nontrivial approximations, for real-world problems. For the two-body problem, there are plenty of solutions that can be manipulated for a variety of applications. For three-body (or more) problems, one must head straight to numerical solutions. Semi-analytic solutions are possible, but keeping track of terms becomes laborious. This difficulty explains the attraction of symbolic manipulation systems such as Maple and Macsyma and interfaces such as MATLAB and MathCad, which facilitate attempts to craft semi-analytic solutions.
One problem for newcomers to such systems is learning how to map a problem onto an analytic representation that lends itself to symbolic manipulation. The authors have selected a variety of scientific and mathematical problems, and show how to use Maple and MATLAB to solve these problems and display the results. Familiarity with Maple and MATLAB is assumed; the book is not intended to introduce either system. Each of the book’s 27 chapters treats a scientific problem with Maple and/or MATLAB code:
The Tractix and Similar Curves
Trajectory of a Spinning Tennis Ball
The Illumination Problem
Orbits in the Planar Three-Body Problem
The Internal Field in Semiconductors
Some Least Squares Problems
The Generalized Billiard Problem
Mirror Curves
Smoothing Filters
The Radar Problem
Conformal Mapping of a Circle
The Spinning Top
The Calibration Problem
Heat Flow Problems
Modeling Penetration Phenomena
Heat Capacity of System of Bose Particles
Free Metal Compression
Gauss Quadrature
Symbolic Computation of Explicit Runge-Kutta Formulas
Transient Response of a Two-Phase Half-Wave Rectifier
Circuits in Power Electronics
Newton’s and Kepler’s Laws
Least Squares Fit of Point Circle
Modeling Social Processes
Contour Plots of Analytic Functions
Non Linear Least Squares: Finding the Most Accurate Location of an Aircraft
Computing Plane Sundials
In general, I like and can recommend the book. The authors move smoothly from analytical approximations for each problem to Maple and MATLAB code. The book is well written; each chapter introduces a scientific or mathematical problem from an analytic point of view, and then gives Maple and/or MATLAB code to solve the problem or to generate an approximate solution. Thus, anyone with a similar problem can manipulate the formulas to move to a symbolic environment. The examples lend themselves to use in the classroom, where symbolic manipulation traditionally take too much time.
The authors provide access to machine-readable versions of the programs listed in the book via anonymous ftp at ftp://ftp.inf.ethz.ch. This is the third edition of the book, with six new example chapters. While MATLAB and Maple are separate systems, there is a toolbox that allows MATLAB users to access Maple. A brief appendix listing Internet sites that maintain libraries of Maple and MATLAB code for scientific and engineering problems would improve the book.
