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Unformatted text preview: 5. (15 points) Solve the heat conduction equation, u t = 4 u xx , x 3 , u (0 , t ) = 0 u (3 , t ) = 0 u ( x, 0) = sin( 2 3 x )sin( x ) + 7 sin( 5 3 x ) 6. (10 points) Solve the eigenvalue problem, X = X, x , with boundary conditions, X (0) = 0 , X ( ) = 0 . Find all eigenvalues and eigenfunctions. 7. (15 points) Solve the wave equation, u tt = 9 u xx , x 4 , u (0 , t ) = 0 u (3 , t ) = 0 u ( x, 0) = 0 u t ( x, t ) = g ( x ) , where g ( x ) is given by, g ( x ) = b 1 , 2 x 3 , , otherwise ....
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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 Pennsylvania State University, University Park.
 Spring '08
 CHEZHONGYUAN
 Differential Equations, Equations, Critical Point, Partial Differential Equations

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