This is a concise, practical overview of vector calculus as used in engineering. For the purposes of this book, all vectors are directed line segments in the three-dimensional real space. All major topics of vector calculus are discussed and treated in a simple and reader-friendly fashion.

The book can probably be best used for self-study, by an individual who has a reasonably good two-semester background in elementary calculus, or by an instructor needing supplementary material for his third-semester Calculus course, or his Advanced Engineering Analysis course.

Adopting this book as a textbook could be somewhat problematic for the following reasons. First, there is the very high, 165-dollar price. Second, the fundamentals of the material here are discussed in third semester Calculus by most textbooks for that course, so it is unlikely that many professors would require their students to buy another expensive textbook just to get the extra material that can be found here. Third, most textbooks in Advanced Engineering Mathematics also have a chapter on the material covered here, and then the previous sentence applies.

Answers to some selected exercises are included. It would have probably been worth the effort to rearrange the exercises in the conventional way, so that the odd-numbered ones have their answered in the book.

Each chapter ends with a very well-done summary, and the book ends with a very welcome overview of the history of the subject. On the whole, given the unusual depth of the treatment of the subject, and the usefulness of the book for self-study, this reviewer believes that the book should be part of every college library that is used by engineering students.

Miklós Bóna is Associate Professor of Mathematics at the University of Florida.