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Unformatted text preview: just have to plug the solution into the equation and the initial and boundary con-ditions and see that the equations are veried. The details are sketched in Section 3.4, following Example 1 of that section. (b) In Example 1, we derived the solution as an inverse Fourier transform: u ( x, t ) = 1 2 - f ( w ) cos cwt + 1 cw g ( w ) sin cwt e iwx dx. Using properties of the Fourier transform, we will show that 1 2 - f ( w ) cos cwte iwx dw = 1 2 [ f ( x-ct ) + f ( x + ct )]; (1) 1 2 - 1 w g ( w ) sin cwte iwx dw = 1 2 x + ct x-ct g ( s ) ds. (2)...
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- Fall '11