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Unformatted text preview: CAAM 336 · DIFFERENTIAL EQUATIONS Problem Set 11 Posted Thursday 18 November 2010. Due Tuesday 23 November 2010, 5pm. This problem set counts for 75 points. Late problem sets are due by 5pm on Wednesday 24 November 2010. 1. [30 points: 7 points each for (a), (b), (c); 9 points for (d)] This question concerns the homogeneous wave equation on an unbounded spatial domain: u tt ( x,t ) = u xx ( x,t ) ,∞ < x < ∞ , t > . Find the solution u ( x,t ) to this equation with the following initial conditions: (a) u ( x, 0) = 2sin( x ) e x 2 , u t ( x, 0) = 0; (b) u ( x, 0) = 0, u t ( x, 0) = 2 x (1 + x 2 ) 2 ; (c) u ( x, 0) = 2sin( x ) e x 2 , u t ( x, 0) = 2 x (1 + x 2 ) 2 . (d) Produce a plot (or plots) showing your solution to part (c) over 10 ≤ x ≤ 10 at times t = 0 , 1 , 2 , 3 , 4 , 5. 2. [10 points] Consider the wave equation on an infinite spatial domain, x ∈ (∞ , ∞ ), but now with a forcing term: u tt ( x,t ) = u xx ( x,t ) + f ( t ) , x ∈ (∞ , ∞ ) subject again to the initial data...
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This note was uploaded on 01/21/2012 for the course CAAM 330 taught by Professor Tompson during the Fall '09 term at UVA.
 Fall '09
 Tompson

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