This course covers vector valued functions. It introduces students to the concept of change and motion and the manner in which quantities approach other quantities.  Topics include limits, continuity,  derivatives of vector functions, gradient, divergence, curl, formulae involving gradient, divergence, laplacian, orthogonal curvilinear coordinates,  line integrals, Green’s theorem in the plane, surface integrals. Other topics are the divergence theorem, improper integrals, Gamma functions, Beta functions, the Riemann Stieltjes Integral,  pointwise and uniform convergence of sequence and series, integration and differentiation term by term.

Limits, continuity and derivatives of vector functions; gradient, divergence and curl; formulae involving gradient, divergence, curl and laplacian and orthogonal curvilinear coordinates; line integrals; Green’s theorem in the plane; surface integrals; the divergence theorem; improper integrals; Gamma and Beta functions; The Riemann Stieltjes integral; pointwise and uniform convergence of sequence and series; integration and differentiation term by term.