Infinite Series; Three Dimensional Vector Spaces; Vector valued Functions; Partial Derivatives: Functions of two variables, limits and continuity, partial derivatives,  differentiability and chain rule, directional derivatives and gradients, tangent planes and normal vectors, maxima and minima of functions of two variables. Multiple Integrals: Double integrals, double integrals over non-rectangular regions, double integrals in polar coordinates, triple integrals, centroid, center of  gravity, triple integrals in cylindrical and spherical coordinates, change of variables in multiple. Topics in vector calculus: Vector fields, line integrals, Green’s theorem, surface integrals, the divergence theorem, stokes theorem.