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Unformatted text preview: Physics 604 Homework #9 Fall 11 Dr. Drake 1. Arfken 15.3.16, 15.3.17, 15.4.3. For 15.4.3 also calculate the solution by inte- grating across x = 0 to obtain the jump in the first derivative and then match to the solutions in the outer region. 2. The temperature in a one-dimensional medium satisfies a diffusion equation with diffusion coefficient D . At t = 0 a very localized source of heat is turned on. The equation satisfied by T is T t- D 2 x 2 T = H ( t ) ( x ) where H = 0 for t < 0 and H = 1 for t > 0. Assume that T = 0 for t < 0. (a) Solve for the space/time dependence of T ( x,t ) by first completing a Laplace transform and then a Fourier transform of the equation and then complet- ing the subsequent inverse Laplace transform. The inversion of the Fourier transform can not be done exactly so you will have an integral representa- tion for the solution given by a k space integral....
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