How Milt got his sound so silky

An area of mathematics teaching that has benefited from the availability of personal computers is that of differential equations and their applications. These two texts take full advantage of the opportunities available, particularly through the additional associated material. The book by Kent Nagle et al comes with a CD-Rom, and both are supported by websites that contain additional projects. The site for the second book (which is rather less friendly) contains, among other material, hints on some of the exercises. Solutions and other manuals accompany both texts.

For their second edition, Henry Edwards and David Penney have removed seldom-used topics and placed a greater emphasis on core techniques, qualitative aspects and linear systems. Half the computing projects are new or substantially revised, and new in-text examples have been added.

For their third edition, Nagle et al have also raised the profile of qualitative methods for deducing information about intract-able equations. Vibrations are used to motivate the study of linear constant coefficient equations, and an expanded review of linear algebra has been added. The valuable technical writing exercises have been retained, and additional group projects, including one on Apollo re-entry, are provided.

Both books include chapters on models and numerical methods, linear constant coefficient equations of the first and higher orders and on systems of first-order equations. Laplace and power series methods are discussed, as well as Fourier methods for partial differential equations. Applications of the material abound. Among the less standard examples, Edwards and Penney explain the silkiness of the sound produced by Milt Jackson, formerly of the Modern Jazz Quartet. According to Nagle et al , some popular mattresses incorporate Duffing-like increasing stiffness for "therapeutic reasons". (A full discussion was banned by the editors.)

Nagle et al go a little further into fundamentals, with a fuller treatment of the Green's function and of existence theorems. The method of incorporation of the PC differs also. Edwards and Penney provide useful Matlab, Maple or Mathematica code at various points in the text, and the projects manual has parallel subsections devoted to each package. Nagle et al suggest use of the software provided on the CD for visualisation and experimentation, but also offer a Maple-based instructor's guide.

Both texts give excellent accounts of the material and are suitable for mathematics, science and engineering undergraduate students. They are also suitable for self-study, provided that the necessary PC is available.

Nigel Steele is professor of mathematics, University of Coventry.