Discussion 7: Parametric Curves

The goal of this discussion is for students to develop the concept of a parametrization as a way to represent the motion of an object in the plane or in space. This discussion is designed to be used before parametrizations are formally introduced. The discussion should be preceded by a comment on the problem of describing rectilinear motion and a brief set-up of the problem of describing motion in the plane and in space, which should not include any mention of parametric curves or parametrizations.

In the first exercise, students are asked to give a general mathematical description of motion in the plane. In the second exercise, they must use their general description to model a specific motion. They must pay attention to the different parts of the path and the domains of the parametrizations. Finally, in the third exercise, they are asked to extend their description to the motion of objects in space. Students should be able to complete this discussion in one class period with time at the end to summarize and introduce the correct notation and language. Students should then read Section 2.1: Parametric Representations of Curves.