ma215-080-f09 outline 2009-11-20

Recall the definition of gradf: we can think of grad as a vector operator
Key Point This motivates writing curl F and div F as grad cross F and grad dot F.
Game: If F = <y² sin(z), 2xy sin(z), xy² cos(z)>,
1. Find curl F.
2. Find div F.
3. Find the line integral of F.dr on the line segment from (3,5,0) to (1,2,pi/2).
Key Point If curl F = 0, then F is conservative.
What's the meaning of curl F? Think about 2D: F = P i + Q j + 0 k.
Key Point curl F gives a measure of the propensity of the field F to rotate objects.
Game:
1. For F given by a graph, is curl F = 0?
2. If F = <y, y>, find the integral of F.dr on the unit circle.
Note: Green's Theorem
Note²: The second vector form of Green's Theorem on p.1103.
Finally, what's the meaning of div F?

2009-11-20: Curl and Divergence