This is an advanced 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 spaces, inner product, cross product, matrix, determinant, 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. Except in extenuating circumstances, this course may not be repeated. Instead MA102 Calculus II must be substituted.