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Differential Equations and Linear Algebra

Stephen W. Goode and Scott A. Annin
Publication Date: 
Number of Pages: 
[Reviewed by
William J. Satzer
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This is the fourth edition of an introduction to ordinary differential equations and linear algebra intended for a sophomore-level course. The text appears to have been designed to be as flexible as possible. It could accommodate quite a variety of courses of different lengths that focus on various combinations of linear algebra and differential equations. The stated prerequisites are completion of three semesters of calculus and “the maturity of that success”.

The book’s topics are very similar to the many other textbooks that address this subject. Where there are differences, they are largely in the extent of the treatment and selection of optional topics. The most significant variation is with linear algebra; it gets a good deal more attention than in comparable books. Indeed, more than half the book is devoted to linear algebra.

The authors begin with a chapter on first order differential equations. This serves partly as a review for students who have seen at least some of the material before in calculus but also it also provides motivational examples with applications to biology and to physics. Then differential equations don’t appear again for almost four hundred pages.

Those intervening pages include six long chapters on linear algebra. As the authors note, it would be possible to omit several parts of this to get back to differential equations more quickly. At the same time, there is almost enough material in these six chapters to build a course that focuses almost entirely on linear algebra. Beginning with matrices and systems of linear equations, the authors proceed to determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors. In each chapter there are topics that could be included or not as the instructor chooses. These include things like the Gram-Schmidt process, quadratic forms and Jordan canonical forms.

Once we’re back to differential equations, the first two chapters treat linear differential equations of order n and systems of differential equations in more or less the usual way. Here as in the rest of the book the authors create a nice mix of exposition, examples and applications. The last two chapters address the Laplace transform and series solutions to linear differential equations. The treatment here is a cut above that of similar books in clarity and relative completeness.

In many respects this is an attractive book. It is clearly and carefully written with good examples, interesting applications, and many good exercises. Its layout on the page is particularly appealing. Its design offers instructors the opportunity to use it very flexibly for a variety of courses. However, the flexibility comes at a price — it is an expensive book — so it might fit best in courses where all of its content can be used.

Bill Satzer ( was a senior intellectual property scientist at 3M Company. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

The table of contents is not available.