MATH 223-01, Calculus III, Fall 2012

Abstract

In Calculus I and II, you studied real-valued functions of a single real variable. In this class, we will build upon that knowledge as we study real-valued functions of several real variables and vector-valued functions of a single real variable. We will find that derivatives and integrals are still meaningful in these contexts, though they are, unsurprisingly, a bit different from what we encounter in the earlier context. Increasing the number of functional arguments or working with vector-valued functions forces us to move our thinking from the xy-plane, where we are accustomed to plotting graphs, to xyz-space or beyond. Doing this necessitates developing your ability to visualize and to think geometrically. It also leads naturally to the study of linear algebra. Thus, we will spend some time discussing some linear algebraic concepts like determinants and dot products. We will also explore polar, cylindrical, and spherical coordinate systems.