**Learning objectives**

- Compute line integrals of gradient vector fields
- Distinguish between path dependent and path independent vector fields
- Vocabulary: potential function, conservative vector field, exact differential
- Apply Green’s theorem
- Gain familiarity with some applications of line integrals

**Before class**

- Read Hughes-Hallett sections 18.3, 18.4
- Ponder Hughes-Hallett problems: 18.4: 2, 4, 10, 17, 21, 22.

**In class**

- Work some problems
- Work some problems
- Pressure-volume loops for the cardiac cycle
- How does a planimeter work?
- Glance at differentials in chemistry

** **