This course will learn the basics of the calculus of functions of two and three variables. This course will cover vectors and Euclidean geometry in three-dimensional space, vector valued functions, partial derivatives, the gradient vector, Lagrange multipliers, double and triple integrals, and line integrals, culminating with Green's Theorem, Stokes' Theorem, and the Gauss Divergence Theorem. Also, students will apply these ideas to a wide range of problems that include motion in space, optimization, arc length, surface area, volumes, and mass.