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Unformatted text preview: u t = 9 u xx , ≤ x ≤ 2 , u x (0 , t ) = 0 u x (2 , t ) = 0 u ( x, 0) = cos( 3 π 2 x )cos( πx ) . 6. (20 points) Let f ( x ) = b 2x ≤ x ≤ 2 , 2 + x2 ≤ x ≤ . a. Compute the Fourier coefcients o± f ( x ) ±or2 ≤ x ≤ 2. b. Solve the initialboundary value problem, u tt = 4 u xx , ≤ x ≤ 2 , u (0 , t ) = 0 u (2 , t ) = 0 u ( x, 0) = f ( x ) u t ( x, 0) = 0 . Express the solution as a Fourier series....
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This note was uploaded on 07/16/2011 for the course MATH 251 taught by Professor Chezhongyuan during the Spring '08 term at Penn State.
 Spring '08
 CHEZHONGYUAN
 Differential Equations, Equations, Critical Point, Partial Differential Equations

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