ma215-080-f09 outline 2009-11-23

Last time we defined two operations on vector fields: curl F and div F
Note: curl F = 0 <=> F is conservative
Today we look at Parametrically Defined Surfaces
Recall how r(t) defines a curve.
We define surfaces parametrically the same way: Let
Game:
1. Find a parametric representation of this surfaces as r(r,theta). What is the (r,theta) domain?
2. If r = <2 cos(theta), 2 sin(theta), t>, pi/2 <= theta <= 2pi, 0 <= t <= 4, sketch the surface.
3. For this r, what curve does r(theta,1) trace out?
Next, we want to be able to integrate over a surface, e.g., to find surface area.
Key Point dS = |r_theta x r_t|dtheta dt
Game: Find dS for r(theta,t) = <2 cos(theta), 2 sin(theta), t>

2009-11-23: Parametrically Defined Surfaces