Mathematica Projects to Accompany Calculus, Fifth Edition
By James Stewart
Objectives

The primary goal of these projects is to create new opportunities for students to learn Calculus. If, through these opportunities, students learn something about Mathematica or programming in general, then all the better; but the primary emphasis is to learn Calculus.

With this in mind, the objectives of these projects are:

1. To:

• address topics that are handled better by computer than by pencil and paper (topics such as Newton's Method),
• re-emphasize important topics (topics such as the Fundamental Theorem of Calculus),
• address topics that students have difficulty with and which bear review or repeating (possibly from a different point of view),
• clarify the steps in important algorithms and computations, and
• cover topics outside class that there's not time to cover during class.

2. To require little or no programming experience. If one or more students do have programming experience then all the better: they can help other students. But it's better to assume that students have little or no programming experience than it is to leave a student without any programming experience behind.

3. To require students to be active participants in each project, to the extent possible. Minimally this might involve having students do something by hand to a graphic they produce (something such as labeling the coordinate axes, or labeling a curve or surface with its equation); at the other extreme, students might be allowed to write their own code. The assumption in making students active participants is that students don't learn by just typing some code and then hitting the ENTER key.

4. To give the instructor (or course coordinator) some options in making assignments.

• There are (hopefully) enough projects that the instructor can pick and choose what works best. There are, for example, three options for a First Derivative Test project: one involves polynomials, another involves rational functions, and the third involves algebraic functions. (The Mathematica code used in each is a little different than the others.) The intention is to allow each instructor (or department course coordinator) to make choices depending on the strength of their class' (or university's) students.
• In most projects, points, intervals, functions, etc, can be replaced so as to allow for as much flexibility as possible with a given project.

5. To produce material that is text independent (so that a change from one edition to the next of a text, for example, is as seamless as possible), and, at the same time, short and to the point. The goal was for projects that are, on the average, do-able in 20-30 minutes (so as not to overburden the student or intrude on the rest of the course) and no longer than 2 pages (so as to minimize duplication, stapling and paper usage, etc.).