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Unformatted text preview: April 9, 2010 Math 53 Worksheet GSI: Kelty Allen Work in groups of about 3. It is not important that you finish all problems or work through them quickly, it is important that everyone in the group understands the solutions. Greens Theorem 1. Suppose C is a closed curve in the plane oriented clockwise . Does Greens theorem give us any information about R C F d r ? 2. Let C be a closed curve in the plane. (a) Use the fundamental theorem of line integrals to compute R C F d r . (b) Use Greens Theorem to compute R C F d r . 3. It appears as if Greens theorem tells us that Z C xdx = Z Z D dxdy = 0 . But we know from single variable calculus that Z xdx = x 2 2 + c. Whats going on here? 4. Let C be a closed curve. What geometric quantity is computed by 1 / 2 R C- y dx + xdy ? 5. Compute R C y 2 dx + xdy where C is the ellipse x 2 a 2 + y 2 b 2 = 1 oriented counter- clockwise....
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- Spring '11