Handbook for Calculus Instructors

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1989. Mathematical Biology. Springer-Verlag. An excellent resource with a good bibliography and lots of projects you could get your students working on by the time they are in the second or third semester of calculus. 32 CHAPTER-BY-CHAPTER COMMENTARY Chapter 2. Successive Approximations The basic idea in this chapter—that when we can’t solve a problem, being able to approximate the answer to an arbitrary degree of accuracy may be just as good—requires a radical shift for many students in the way they think about what it means to solve a mathematics problem.

It is important, though, to be sure that students really understand what the slope of a straight line is and can visually estimate slopes of lines. 2 and the appendix are valuable, and some students might profitably revisit them now. Students who have had some calculus will try to guess formulas for the functions given graphically and then write down formulas for their derivatives. It is important to discourage this, since we are trying to develop students’ geometric understanding of what the derivative means.

Birkh¨auser. Part of the UMAP Expository Monograph Series. An interesting development, presented as an investigation for undergraduates. It even throws in a little catastrophe theory. Chapter 9.

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