**Learning objectives**

- Define line integrals
- vector notation:
- differential notation:
- relationship: ;

- Understand 1-variable integrals as line integrals
- Develop geometric intuition for line integrals
- Compute line integrals geometrically
- when vector field is orthogonal to the path
- when vector field is tangent to the path and of constant magnitude on the path

- Compute line integrals analytically using parameterizations
- Compute line integrals of gradient vector fields

**Before class**

- Read Hughes-Hallett sections 18.1, 18.2, 18.3.
- Ponder Hughes-Hallett problems: 18.1: 1-13 odd,36; 18.2: 1, 9, 10, 25; 18-3:1, 13.

**In class**