Exam 3 Solutions and Grading.pdf - ESE 318-01 Exam 3 Apr 12...

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ESE 318-01 Exam 3, Apr. 12, 2018 NAME: ___59 papers received from 60 enrolled__ Problem 1. (20 points) Consider the scalar function z z e y xy e x z y x F 2 2 2 2 , , and the point P = (1, 1, 0). (a) Find the direction in which F is increasing fastest from P . (b) Find the rate of that maximum increase. (c) Find the rate of increase of F from P toward the point (-1,4,6). (d) Find F of Laplacian gradF div F at P .     34 16 9 9 0 , 1 , 1 4 , 3 , 3 2 2 , 2 1 , 1 2 0 , 1 , 1 2 2 , 2 , 2 2 2 2 2 2 2 F b F a e y e x ye x y xe F z z z z   7 27 7 24 9 6 36 9 4 6 , 3 , 2 4 , 3 , 3 6 , 3 , 2 0 , 1 , 1 6 , 4 , 1 F Dir b c b     12 3 4 1 4 4 4 2 2 2 2 2 2 2 2 2 2 2 y x e e y e x e e F d z z z z z Grading: 21 papers earned all 20 points and another 18 earned 19 points with the only error being to fail to evaluate the Laplacian at the point P . 5 points per part, in general. Only 7 papers earned fewer than 16 points, and only 1 below 12. Gradient or Laplacian not evaluated at P : -1 point. “Sloppy” error: -1 to -2 pts. Sign error on (c) due to backward direction: -2 pts. Method/approach seriously bad or botched: -3 to -5 pts per part.
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