2009-11-20: Curl and Divergence
Stewart section 17.5
- 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 = <y^{2} sin(z), 2xy sin(z), xy^{2} cos(z)>,
- Find curl F.
- Find div F.
- 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:
- For F given by a graph, is curl F = 0?
- If F = <y, y>, find the integral of F.dr on the unit circle.
- Note: Green's Theorem
- Note^{2}: The second vector form of Green's Theorem on p.1103.
- Finally, what's the meaning of div F?
ma215-080-f09 lecture outline 2009-11-20
Created: Fri Nov 20 12:47:40 EST 2009
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©2009 Gavin LaRose