Differential Equations for Dummies by Steven Holzner

Cover of DE for Dummies

The cover of Differential Equations for Dummies, by Steven Holzner, claims the book will allow the reader to increase equation-solving skills and tackle higher-dimension math concepts. Holzner is a good writer and he complies with the editorial requirement for a cute and friendly conversational style. One would hope that this would lead to a brilliant illumination of the fundamentals of differential equations leading to mastery of the subject. Not likely.

Differential Equations for Dummies?

Differential Equations (DE) is a class often taken by engineering and science students after a calculus sequence. Indeed DE makes no sense without a good background in calculus. Is there a way to make DE easier to understand and apply than the way the subject is usually presented in a formal class that uses a formal DE textbook? If there is, Holzner hasn't found it.

It's not the author's fault. He has been given a nearly impossible task. If the approach had been to offer analogies to illustrate what is really going on with DE, in order to provide some base-level insight into that derivative and integral world, that might have been useful. There would have been a lot more drawings, diagrams and illustrations, and a lot less "symbol pushing." As it is, the explanations and examples are little different from what are found in many introductory texts, only bracketed by friendly conversation intended to reassure the reader that it's really not all that hard.

So what's the point? There isn't one. Anyone with sufficient background to understand what Holzner is talking about doesn't need this book. Anyone who lacks sufficient background will find it incomprehensible.

From First Order Differential Equations to Numerical Methods

The book does discuss and provide worked examples of problems likely to be encountered in a course on differential equations. First and higher order DE, power series, Laplace transforms and Euler's method--they're all here. Some of the discussions are actually interesting and do provide insight into how certain forms of equations are generally approached and solved. But just barely.

The author is fond of presenting an equation and coolly stating something like "...and then with a little rearranging, the equation becomes..." while leaving out the intermediate steps. That doesn't seem like the right approach for a book aimed at dummies.

Minimal Differential Equations Help

A major weakness in the book is that there are no practice problems with worked solutions for the DE student to attempt. Reading about how to solve math problems is fine, but it has been said that mathematics is not a spectator sport. In other words, math is best "learned through the arm." Insufficient arm movement (as is required to drag a pencil across a piece of paper) is prompted in this book.

The best part of the book comes at the end, in a chapter called The Part of Tens. This section provides ten on-line DE tutorials and ten on-line DE solving tools. Odds are that readers will get more out of these resources than can be had by reading the preceding chapters of Differential Equations for Dummies.

References

Holzner, Steven; Differential Equations for Dummies; Hoboken, NJ; Wiley Publishing, 2008.