1.

Use plane and space vectors to solve geometry and physics problems.
(I)

2.

Use space curves to analyze the motion of an object. (II)

3.

Use contour diagrams to analyze the behavior of a function of several
variables. (III)

4.

Use partial derivatives to solve optimization problems. (III)

5.

Set up and compute double and triple integrals in any order of
integration using rectangular coordinates. (IV)

6.

Set up and compute double and triple integrals using polar,
cylindrical, and spherical coordinates. (IV)

7.

Use line integrals to compute the work done by a vector field along a
curve. (V)

8.

Use surface integrals to compute the flux of a vector field through a
surface. (V)

9.

Use multiple integrals to calculate line and surface integrals. (V)

