Students should understand the concept of continuity and
differentiability in two and three variables. They should be 
able to calculate partial derivatives, directional derivatives 
and gradients. Students should be able to solve maximum and 
minimum problems using Lagrange multipliers. Students are 
introduced to multiple integrals and are expected to be able to 
calculate volumes and areas using multiple integrals. They are 
expected to understand and apply Green's theorem.

1. Review of vector algebra and geometry.
2. Parametric curves, velocity, acceleration.
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, and physical applications as time allows. Polar,
cylindrical, and spherical coordinates.
4. Line integrals, work, path-independence, and Green's Theorem.
5. Brief survey of surface integrals and flux, curl, divergence,
Stokes's and Divergence Theorems.