Math Refresher for Scientists and Engineers (Paperback)

This book is, as the title says, a refresher. It's intended for the reader who has already complete course work in the material, but wants to review it, or use it possibly as a reference. Fanchi's book covers most branches of mathematics that the typical undergraduate is likely to encounter, with a few notable exceptions. There is no discussion about tensors and nothing on things like topology. The book's chapters follow what is probably the traditional route many of us took in our introduction to mathematics. The first chapter is a review of algebra, followed by geometry, trigonometry, and hyperbolic functions. These are followed by analytic geometry, linear algebra, and calculus (broken into chapters dealing with differential calculus, partial derivatives, integrals, and ordinary differential equations).

Since this is a refresher book, the author assumes that the reader has already been exposed, either through experience or course work, to the subjects being covered. So, the material is not introduced the way it typically is found in traditional texts. There is, for example, relatively little developmental material leading up to key concepts. This is both expected and appropriate.

The book excels in several areas, including the use of examples, which are found liberally throughout the text. I highly recommend readers work through these exercises, especially since many of them have solutions that are, themselves, important and useful material. Each exercise comes complete with worked-out solutions in the back of the book, so if you want, you can use this as a very effective book for self-education, almost as if you were going back to school to take a refresher course.

As with any book, reliability and accuracy is critical. Especially for a reference-type book that you are likely to use when you don't have a lot of time to question, or check, the accuracy of the material. Fanchi does an excellent job in this regard; I found almost no errors (and none that were serious). Another thing I look for in a reference book is a good index. I know that the next time I pick it up, it'll be because I remember reading something in it, and I know the answer I'm looking for is in there somewhere, but I cannot remember the page. The first place I'll go is the index, and with a good one (like the one in Fanchi's book) I should be able to track down the solution without too much wasted time.

There were a couple of pleasant surprises in this book. One was the three chapters on probability and statistics. The other was the section (in the chapter on ordinary differential equations) dealing with nonlinear dynamics and chaos. Frankly, I was surprised to see the subject of chaos discussed in this book at all (especially since tensors are not). My only complaint is that there is not an entire chapter devoted to the subject.

The book is easy to read, and well organized. I found it very enjoyable. It's the sort of book that you can easily read for an hour, cover 20 or 30 pages, and not feel too exhausted - if, that is, you are reading it as a review. However, as I said, I'd not recommend this as an introductory text for any of these subjects (and I think the author, by reason of his choice of title, would agree).