Project Title: The Case of the Parabolic Pool Table

Difficulty Level: Easy

Mathematical Requirements: Students must know how to introduce Cartesian co-ordinate axes into a geometric situation in a well-chosen way. They must know the form of the equation of a parabola. They must know about normal lines, how to find the slope of a line through two given points, and how to differentiate polynomials.

They must realize the necessity of verifying that the X-co-ordinate of their “solution point” lies within an appropriate set of values, and that negative numbers do not have real square roots.

Project Title: Calculus for Climatologists

Difficulty Level: Easy

Mathematical Requirements: This is the easiest of the projects; once one sees how to do it, a detailed exposition of the solution can be very brief. Its attraction is that the result is both mildly counterintuitive (at first sight) and quickly achieved.

The only mathematical requirement is the Intermediate Value Theorem for continuous functions on closed intervals. It requires ingenuity, and one hopes that it will cause students to think carefully about what the Intermediate Value Theorem actually says.

This project has not been assigned to a class.

Project Title: The Case of the Swiveling Spotlight

Difficulty Level: Difficult

Mathematical Requirements: I've classified this as difficult because it would probably be assigned at an early point in the course, and it draws from several different knowledge areas.