Mathematics 317T2 Assignment10 - Mathematics 317...

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Mathematics 317 Assignment #10: due Wednesday, April 7, 2010 1. Verify Green’s theorem when j i F x y + = 2 and C is the circle . 1 2 2 = + y x 2. Verify Green’s theorem when j i F ) ( ) ( 3 3 2 2 y x y x + + - = and R is the rectangular region given by . 3 1 , 2 1 y x 3. Let C be a simple closed curve interior to a simple closed curve C and let R be the region between these two curves. Let . ) , ( ) , ( j i F y x N y x M = Show that . ∫∫ - =
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Unformatted text preview: ∂ ∂-∂ ∂ C C R d d dxdy y M x N r F r F 4. Calculate the area of the ellipse 1 2 2 2 2 = + b y a x by means of the formula ∫-= C ydx xdy A ). ( 2 1 5. BONUS QUESTION: Suppose ) , , ( = × ∫ C d z y x r F for all closed curves C in three dimensions. Prove or disprove that F ( x , y , z ) must be a constant vector....
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  • Spring '10
  • BLUMAN
  • Vector Calculus, Manifold, Conic section, General topology

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