This book caught my attention immediately, right from the preface. The author took the unusual step of polling students to find what they wanted in a textbook, and then writing an introduction to differential equations that met all those requirements. The students said they wanted a book that:
Was easy to follow and not excessively verbose;
Did not talk down to readers;
Kept theory to a minimum;
Did not embed computational devices in the instructional process;
Of these I only found the one about computation a little surprising. The students agreed that they did not learn much using any of the standard software. (I also note in passing that being verbose is apparently OK, but not excessively so.)
The last time I taught an introductory differential equations course — several years ago — I used an early edition of Simmons’ Differential Equations with Applications and Historical Notes. (There is now a thoroughly revised edition called Differential Equations: Theory, Technique, and Practice.) I am still very fond of the book, but the students hated it. I think they had expected a book much like the current one.
One could debate the question of the value of “give them what they want” versus “give them what you think they need”, but I expect the answer is not clear-cut and probably very much situation-dependent. Having chosen one path, the author of this book does a does a very creditable job of providing the basic material of ordinary differential equations. He assumes only basic courses in differential and integral calculus with reasonable skill in algebraic manipulation.
The book is largely aimed at average students in mathematics, science or engineering. The author suggests that stronger students can use the text as a bridge to more specialized books or more advanced courses. The topics are quite standard: first order equations, linear second order equations, higher order linear equations, and systems of differential equations. There are two separate chapters on mathematical models — one with first order equations, and another with second order equations. The final two chapters discuss the Laplace transform and series solutions of differential equations. Only the treatment of series solutions near singular points is a departure from the basics.
There are many exercises. The majority are computational and routine. Solutions to odd-numbered exercises are provided. The author uses Mathematica in some of his examples to verify solutions. A few exercises ask the students to do the same.
Bill Satzer (firstname.lastname@example.org) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.