| SECTION |
CONCEPTS |
METHODS |
| 18.1 The Idea of a Line Integral |
- Integral = summing a vector field along an oriented curve
- Used to compute Work
- Circulation
|
- Deciding from a graph whether the line integral is positive, negative, or zero.
- Basic properties (page 931)
|
| 18.2 Computing Line Integrals over Parameterized Curves |
- Independence of parametrization
|
- Setting up the integral by substituting
|
| 18.3 Gradient Fields and Path-Independent Fields |
- Fundamental Theorem of Line Integrals
- Path-independence
- Theorem: gradient field = path-independent
|
- Creating a potential function from a gradient field
- Evaluating the Fundamental Theorem
|
| 18.4 Path-Dependent Fields and Green’s Theorem |
- What Green’s Theorem says
|
- Testing for path-independence by calculating circulation
- Testing for path-independence by computing the curl
- Setting up integrals for Green’s Theorem
|