Cylinders and quadric surfaces. Functions of several variables: limits, continuity, partial derivatives, Chain Rule, directional derivatives, gradients, tangent planes, differentials, extreme values, and Lagrange multipliers. Multiple integrals: areas and volumes, triple integrals in rectangular, cylindrical and spherical coordinates. Integration in vector fields, Green’s Theorem in the plane, Stoke’s Theorem, the Divergence Theorem. Prerequisite: MAT 213.