Calculus III and Vector Calculus

In this course, the primary goal is to study the geometry of change in two and three dimensional space. In particular, we use vectors to describe curves and surfaces in space mathematically, and to study the derivatives (rates of change) and integrals (average properties) of functions and vector fields that are defined on curves and surfaces. The unity between geometry and algebra is most succinctly expressed in the four versions of the Fundamental Theorem of Calculus that we study: the fundamental theorem of calculus for vector fields on curves, Green's theorem, Stokes' theorem, the Divergence theorem and applications. The emphasis will be on understanding the geometry behind numerous algebraic manipulations, while providing a bit more focus on mathematical concepts. Not open to students who have completed MTH 3020, MTH 3030, or MTH 3035.