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Unformatted text preview: f ( x ) = x,L < x < L ; , x =L or x = L ; f ( x2 L ) , otherwise . Its Fourier series is 2 L X n =1 (1) n +1 n sin( nx L ) . Use this information to nd a formula for of the form = a i where the a i do not include . 4. Use separation of variables to replace the PDE tu xx + xu t = 0 by a pair of ODE. 5. Consider the heat conduction problem u xx = u t , < x < , t > , u (0 ,t ) = , u ( ,t ) = 0 , t > , u ( x, 0) = sin( x ) + + sin(3 x )x, < x < . Do all necessary steps. 1...
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This note was uploaded on 01/17/2010 for the course MATH 108 taught by Professor Trangenstein during the Fall '07 term at Duke.
 Fall '07
 Trangenstein
 Math

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