Vector-valued Functions of a Single Variable: derivatives, and integrals of vector valued functions; Differential Geometry of Vector-valued Function: tangent lines to vector-valued functions, arc length; curvature of plane and space curves; Partial Differentiation: functions of several variables, limits and continuity, partial derivatives; Directional Derivatives: gradient vectors and tangent planes; Extrema of Functions of Several Variables: Lagrange multipliers, Taylor’s formula; Vector Differential Calculus: vector fields, gradient, divergence, and curl; Line Integral: integral along a path; Multiple integrals: double and triple integrals, iterated integrals, areas and volumes, general multiple integrals; Change of Variables in Multiple Integrals: Jacobians, integrals in cylindrical and spherical coordinates; Green’s Theorem: proof and applications; Gauss’s Theorem: proof and applications; Stokes’ Theorem: proof and applications.