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Unformatted text preview: MAE 105 Quiz #5 (Closed book/notes/calculator) Name: ______________________________ Time: 3:35 to 3:55pm Date: May 17, 2007 Problem 1 (2.5 points) Consider: u t u 1 + + 1 x = tu t 2 x 2 u ( x0 , 0 ) = cos x0 . a. (1 point): Find the expression for the characteristic that renders (): du 1 = tu dt 2 () () b. (1 point): Integrate () to obtain u in terms of t. [Note: the solution must include a constant of integration.] c. (0.5 points): Use the initial condition to obtain the final complete solution. Problem 2 (2.5 points) Consider: d 2 j + l x = 0 , j dx 2 j ( 0 ) = j ( p ) = 0 . 0 < x < p a. (1.5 points): Multiply by , integrate from x=0 to x= and use the boundary conditions to obtain the Rayleigh quotient for . b. (1 point): Assume an approximate solution sin x and substitute into the Rayleigh quotient to estimate the first eigenvalue. Note: To receive full credit, all steps must be neatly shown. Writing down the final results will receive no credit. ...
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This note was uploaded on 05/21/2008 for the course MAE 105 taught by Professor Neimannassat during the Spring '07 term at UCSD.
 Spring '07
 NeimanNassat

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