ma215-080-f09 outline 2009-11-16

Key Point Last time we introduced Green's Theorem. Note:
1. We're in two dimensions ((x,y), not (x,y,z));
2. D is a simply connected region (no breaks or holes---but see also p.1095);
3. C is a simple closed curve (doesn't cross itself, starts and ends at the same place);
4. C is positively oriented (traversed counterclockwise);
5. Use Green's Theorem to evaluate the double integral instead of the line integral, or, occasionally, the other way around.
Game:
1. Find int F.dr if F = 3xy i + 2y² j, given C.
2. Rewrite the double integral of y/(x² + 2) over the quarter circle of radius one in the first quadrant, by letting P_y = y/(x² + 2) and Q = 0.
Line Integral Summary

2009-11-16: Green's Theorem and Line Integral Review