Unformatted text preview: A = x x ^ + 2 y y ^ + 3 z z ^ and B = 3y x ^2x y ^ . 6. Calculate the Laplacian of (a) T = x 2 + 2 xy + 3 z +4 and (b) v = x 2 x ^ + 3 xz 2 y ^ 2 xz z ^ . 7. Calculate the line integral of the function v = x 2 x ^ + 2 yz y ^ + y 2 z ^ along the paths (a) (0,0,0) → (1,0,0) → (1,1,0) → (1,1,1) and (b) the direct straight line. 8. If v = 4 xz x ^ y 2 y ^ + yz z ^ , calculate its surface integral over the surface bounded by the cube x = 0, x = 1, y = 0, y = 1, z = 0, z = 1. Notice that you will have to set up an integral over each of the six surfaces....
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 Fall '10
 LOWELLWOOD
 Vector Calculus, Work, Line integral, Vector field, Gradient, Direct straight line, Check product rule

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