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Unformatted text preview: SSM 317—01 Engineering Mathematics Wednesday, March 12, 2003
Open Book Exam One Hour Examination ‘ Numbe; 2 Answer a_ll questions. Questions have equal weight. If you are taking the course for
2 units= answer only question 1: in 20 minutes. A 341
431 002 Find 'all eigenvalues and correSponding eigenvectors of A. 2. A bug is crawling on the curve C:
r = costz' + sintj + :51]: 2» (a) Show that C is on the cylinders?2 + y2 = 1. I
L (b) How far has the bug traveled from t = 0 to t = 211'?
1 (c) Find the unit tangent vector E to C at time t = 211.
There is a rainstorm whose velocity at each point is ﬁx, 3;, z) = $315+ ysj + 231: 1 ((1) Compute f(m,y,z) : v  o.
l (e) Compute '2'; in the direction of E at P(1,0, (270%).
i (f) What is the maximum rate of change of f at_P? C,U,14‘] ﬁ,(ljd,o“
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a. ezyi+(m+(2+c)z)j+2yk B. 53"” Let C be the closed triangle going from A1(1,0,0) to Bl(l,2,0) to Cl(l,2,1)
and then back to A1(1,0, 0). Compute W = fee. dr. For which values of c is W independent of path? Why? 9’ 3) I .... (3 “r\)[(3A)Cz,x)  a]
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 Fall '05
 Axelbaum

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