Discussion 2: Functions of Several Variables

The goal of this discussion is to introduce students to the idea of working in groups, and to introduce students to functions of two variables by asking them to focus on examples of functions of more than one variable which they may have seen in other mathematics or science courses. This discussion is designed to be used as an introduction to the course and it should be used on the first day of class. Students should be able to complete this discussion in a single class period. Either Discussion 1 or Discussion 2 should be used, but not both.

The first exercise asks the students to describe their mathematical experiences to each other. The second asks them to give examples of functions of more than one variable which they may have encountered in other classes. The third exercise is designed to have students use their familiarity with one variable calculus to speculate on the types of mathematical questions which might be asked about functions of more than one variable. Throughout the course we will be asking students to use their knowledge of the calculus of functions of one variable to suggest appropriate techniques for dealing with functions of several variables.