2009-11-16: Green's Theorem and Line Integral Review
Stewart section 17.4, review
- Key Point Last time we introduced Green's Theorem. Note:
- We're in two dimensions ((x,y), not (x,y,z));
- D is a simply connected region (no breaks or holes---but see also p.1095);
- C is a simple closed curve (doesn't cross itself, starts and ends at the same place);
- C is positively oriented (traversed counterclockwise);
- Use Green's Theorem to evaluate the double integral instead of the line integral, or, occasionally, the other way around.
- Game:
- Find int F.dr if F = 3xy i + 2y^{2} j, given C.
- Rewrite the double integral of y/(x^{2} + 2) over the quarter circle of radius one in the first quadrant, by letting P_{y} = y/(x^{2} + 2) and Q = 0.
- Line Integral Summary
ma215-080-f09 lecture outline 2009-11-16
Created: Mon Nov 16 13:01:39 EST 2009
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©2009 Gavin LaRose