Midterm2

Midterm2 - MAE105 Mid-term 2 (open book, closed notes)...

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MAE105 Mid-term 2 (open book, closed notes) Name:_________________________ Time: 3:35 to 4:45pm Date: May 22, 2007 Problem 1 (a) (1 Point) Find a general expression x = x ( t ), for the characteristics of the following PDE: u t - x cos t u x =- u sin t . [Note that your expression must include a constant of integration, say, x (0) = x 0 .] (b) (1 Point) In the x , t -plane, t >0 ,sketch a typical characteristic curve. (c) (1 Point) Find the general solution of this PDE. (d) (1 Point) Specialize the solution in (b) such that at t = 0, we have u ( x 0 ,0) = u 0 = ( x 2 0 + 1). Problem 2 Consider the wav e equation 2 u t 2 - 2 u x 2 = 0( 1) in an infinite domain, - < x < , t >0 ,with the initial conditions u ( x ,0) = f ( x ) = x 1 - x for 0 < x <1 / 2 for 1/2 < x <1 , u t ( x ,0) = g ( x ) = sin( π x ), 0 < x <1 , with both f ( x )and g ( x )being zero for all other values of
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This note was uploaded on 05/21/2008 for the course MAE 105 taught by Professor Neiman-nassat during the Spring '07 term at UCSD.

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Midterm2 - MAE105 Mid-term 2 (open book, closed notes)...

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