Calculus problems for a new century, edited by Robert Fraga. Pp427. $25. 1993. ISBN 0-88385-084-2 (Mathematical Association of America).

Abstract

Calculus problems for a new century, edited by Robert Fraga. Pp427. $25. 1993. ISBN 0-88385-084-2 (Mathematical Association of America). This is Volume 2 of the Resources for calculus series. It is divided more or less equally between the problems in the first half and commentaries on their solutions in the second. The problems cover the usual topics in calculus: functions and their graphs; derivatives and integrals in one, two and three dimensions; maxima and minima; and sequences and series. They range in difficulty from fairly straightforward to quite challenging, and many apply calculus to interesting and topical situations (for example, weather maps, the Kuwait oil slick, inflation, and Stock Exchange prices), though there are also non-trivial pure mathematical problems, too. All the problems are carefully worded to lead the student through, though not so copiously supplied with hints that they become trivial. Students learning calculus still need a few routine calculations to help them assimilate new ideas, and for such exercises instructors will need to look elsewhere. However, students should, as soon as possible, be introduced to problems of the kind posed in this book, and indeed in this Collection. (Instructors are invited to copy and distribute these problems freely for teaching purposes, though not for profit.) Whereas some students see the power and beauty of calculus at once, all will benefit from the life and inspiration injected into the subject by problems such as these. S. M. NUGENT 11 Ravensdale Drive, Wollaton, Nottingham NG8 2SL Applications of calculus, edited by P. Straffin. Pp 262. $24. 1993. ISBN 0-88385-085-0 (Mathematical Association of America) This is the third of five volumes in a series entitled Resources for calculus. The material reflects the (reviewer's perception of the) ethos of the American Liberal Arts College. The motivations for development of these texts will be familiar to teachers of applications-driven methods courses in the UK: "Classes too large-senior faculty deserted the course-teaching assistants whose time and interest were focused on their own graduate work." " well intentioned efforts to pack into the course all the topics demanded by the increasing number of disciplines requiring calculus " " if the course had indeed become a blur for students, it might be because those choosing the topics...the methods for presenting them had not kept their goals in focus." In many respects these teachers are further down the same road as British academics and, in consequence, we have the opportunity to benefit from their experience. The text contains some eighteen case studies typically ten to fifteen pages each. A wide range of problems is considered ranging over management (utility theory, actuarial estimation, portfolio theory), physics (raindrops, rainbows), production engineering (Bezier curves, robot kinematics), electronics (disk drives, radio transmission), epidemiology (I suppose modelling the AIDS epidemic was inevitable) as well as generic topics such as regressio...