Cylindrical and spherical coordinates. Partial derivatives: Functions of several variables. Limits and continuity. Partial derivatives. Tangent planes and linear approximations. The chain rule. Directional derivatives and the gradient vector. Maximum and minimum values. Lagrange multiplies. Multiple integrals: Double integrals over rectangles. Iterated integrals. Double integrals over general regions. Double integrals in polar coordinates. Application of double integrals. Surface Area. Triple integrals. Triple integrals in cylindrical and spherical coordinates. Change of variables in multiple integrals