This is a standard course for students in science and engineering, dealing with differentiation and integration of multivariable real-valued functions, emphasizing basic concepts and applications. The topics are : vector space, inner products, cross products, matrixes, determinants, cylindrical coordinates, spherical coordinates, quadratic surfaces, limits and continuity of multivariable vector-valued functions, differentiability of multivariable functions, partial derivatives, directional derivatives, tangent planes, multiple integrals, vector fields and their divergence and curl, line integrals, surface integrals, Green's theorem, Stokes' theorem, divergence theorem, and conservative vector fields.