Unformatted text preview: f ( x ) = x,L < x < L ; , x =L or x = L ; f ( x2 L ) , otherwise . Its Fourier series is 2 L π ∞ X n =1 (1) n +1 n sin( nπx L ) . Use this information to ﬁnd a formula for π of the form π = ∑ a i where the a i do not include π . 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 < π, t > , u (0 ,t ) = π, u ( π,t ) = 0 , t > , u ( x, 0) = sin( x ) + π + π sin(3 x )x, < x < π. Do all necessary steps. 1...
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 Fall '07
 Trangenstein
 Math, Fourier Series, 75 minutes, 2L, PDE tuxx

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