Week 12 -- Sections 7.5-7.6

Short-term objectives

1. Evaluate line and surface integrals by the integral theorems, when appropriate. (Sec. 7.5)
2. Evaluate line and surface integrals by projection or parametrization, within the "algebraic viewpoint", when appropriate. (Sec. 7.6)
3. Evaluate line and surface integrals within the "geometric viewpoint", when appropriate. (Sec. 7.6)
4. Recognize which method is appropriate in any particular case! (Sec. 7.5, 7.6)
5. Construct a potential for a given conservative (curl-free) vector field. (Sec. 7.5)
6. Recognize topological restrictions on the existence of scalar and vector potentials. (Sec. 7.5)

Long-term objectives

1. Appreciate the geometrical significance and integral definition of divergence and curl . (Sec. 7.5)
2. Appreciate the analogies between the various methods for evaluating line and surface integrals. (Sec. 7.6)