Students should be able to calculate partial derivatives,
directional derivatives and gradients. Students should be able 
to solve maximum and minimum problems using Lagrange 
multipliers. They should learn to calculate area, volume, 
center of mass, and moment of inertia using multiple integrals. 
They are expected to understand integrals along curves and 
surfaces, culminating in various generalizations of the 
Fundamental Theorem of Calculus. Students should be able to 
apply the tools learned in this course to areas such as 
planetary motion, gravitation,  data fitting, Gauss's Law, and 
fluid dynamics.

1. Review of vector algebra.
2. Parametric curves; Kepler's laws.
3. Partial differentiation: directional derivatives, gradients,
tangent planes, chain rule, maximum/minimum problems, and
Lagrange multipliers.
4. Multiple integration: double and triple integrals, change of
order of integration, applications to computations of areas,
volumes, center of mass and moments of inertia. Polar,
cylindrical, and spherical coordinates.
5. Line integrals, work, path-independence, and Green's Theorem.
6. Surface integrals and flux. Curl, divergence, Stokes's and
Divergence Theorems and their applications.