November 24, 2009
The Calculus Collection: A Resource for AP and Beyond
Caren L. Diefenderfer and Roger B. Nelsen, Editors
527 pp., hardcover, 2010. Series: Classroom Resource Materials
To support high school teachers and undergraduate instructors of mathematics, the MAA has published this extensive collection of expository writing that deals with calculus. Especially noteworthy is the fact that its nearly 125 articles, which first appeared in MAA periodicals and journals, were selected by, and chosen for, those who teach Advanced Placement courses in calculus.
The material encompasses nine general and historical articles; six on functions, graphs, and limits; nearly 50 on derivatives; another 50 on integrals; and a dozen on polynomial approximations and series.
Excerpt (p. 133): "Do Dogs Know Bifurcations?" by Roland Minton and Timothy J. Pennings
Elvis burst upon the mathematical scene in May, 2003. The second author's article "Do Dogs Know Calculus?" (pdf) introduced his dog Elvis and Elvis's ability to solve a classic optimization problem. Peruchet and Gallego's article "Do Dogs Know Related Rates Rather than Optimization?" gave an alternative explanation of how dogs (including their own) might solve the problem. Elvis's surprising repudiation of that explanation . . . inspired this article. Here, we explore Elvis's problem-solving ability when he must choose between two qualitatively different options. Such a situation induces a bifurcation in his optimal strategy. As a bonus, our analysis reveals a neat geometric proof of the arithmetic mean-geometric mean inequality.
About the Editors:
Caren L. Diefenderfer (Hollins University), who received a Ph.D. from the University of California, Santa Barbara, has been involved with AP calculus programs for 20 years. She chairs the SIGMAA on High School Mathematics.
Roger B. Nelsen (Lewis & Clark College), who received his Ph.D. from Duke University, has written several books published by the MAA. Nelsen is an active AP calculus reader.
Order The Calculus Collection: A Resource for AP and Beyond from the MAA Bookstore or call 1.800.331.1622.
MAA Member Price: $59.95