Book Review of Landau & Paez by H. Gould and J. Tobochnik

American Journal of Physics,  67  (1), January 1999
Reviewed by Harvey Gould and Jan Tobochnik.

  Computational Physics.  Rubin H. Landau and Manuel Paez. 520 pp.
Wiley, New York, 1997. Price:  $69.95 ISBN 0-471-11590-8.

Landau and Paez's book begins with an excellent introduction to the nature of computational science and how it differs from computer science. Part I introduces various general ideas and methods, such as
fixed and floating point numbers, roundoff errors, and methods of integration. We found the discussion of the first two topics particularly useful. Part II of the text emphasizes applications, which include data fitting, random number generators, the numerical solution of differential equations, nonlinear systems, matrix computations, high performance computing, object-oriented programming, simulations of the Ising model, and fractals. Parts III and IV treat linear and nonlinear partial differential equations, respectively.

The discussion of such a wide range of applications illustrates the interdisciplinary nature of computational physics and ensures that readers will find at least several topics which interest them. However, such broad coverage carries with it the danger that some of the discussion will be too brief, and in a few cases might even be misleading. In the discussion of the Ising model (a topic close to our own research interests) we found many statements that could be misinterpreted by students and professors who are not expert in statistical mechanics or simulations. An example is the statement that the measured heat capacity in a simulation of the two-dimensional Ising model ``..should diverge at the transition (you may get only a peak).'' In fact, the heat capacity is divergent only in the limit of an infinite system, and simulations of a finite system can only exhibit a peak.

The authors make frequent reference to materials available on their Web site and to other sites as well. Although the text can be used independently of the Web, we found that the information referenced by the authors enhances the text. We believe that the complementary use of the Web is a harbinger of the way texts will be written and used in the future.

Many program listings are given in FORTRAN and C. Unfortunately, the former are in FORTRAN 77 rather than Fortran 90 or F. Fortran 90 compilers are readily available (though expensive), while F is freely available on Linux and is reasonably priced on other platforms. The programs do not incorporate the use of graphics; the authors acknowledge the importance of graphics, but expect readers to plot their results using separate programs.

The strength of the text is the discussion of numerical and programming methods, rather than simulations. We particularly enjoyed reading the chapters on computing hardware, high-performance
computing, parallel computing and parallel virtual machine (PVM), object-oriented programming, solitons and the Korteweg-de Vries and Sine-Gordon equations. An excellent course could easily be based on these topics. Landau and Paez's book would be an excellent choice for a course on computational physics which emphasizes computational methods and programming.