Unformatted text preview: ze xy i and S is the ellipsoid x 2 + 2 y 2 + 3 z 2 = 1. 3. (20 points) The function F = 24 xz i − 12 z 2 k has zero divergence. (a) Find a vector potential for F ; that is, ±nd G whose curl is F . (b) Find a vector potential for F that has no k component. (This may or may not be the same as your answer to (a).) 4. (12 points) Let D be the region in the xyplane where  x  +  y  ≤ 1. In other words, it is the region given by − 1 ≤ x + y ≤ 1 and − 1 ≤ x − y ≤ 1 . Rewrite ii D ( x − y ) 2 e x 2y 2 dx dy as an integral over u and v by using the substitution u = x + y , v = x − y . Remember to describe the domain of integration. Remark: The ( u, v ) integral can be evaluated by integrating over u and then v ; however, you are NOT being asked to evaluate it. END OF EXAM...
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 Spring '07
 Enright
 Math, Vector Calculus, Vector field, 2 g, vector curl divergence, nice vector function, vector analysis states

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