Final+and+solutions

Final+and+solutions - MAE 140 Final Examination Thursday,...

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MAE 140 Final Examination Thursday, December 13, 2007, 8:00am – 10:00am, SSPA 1100 Total Possible Score: 40 Points. No Books/Notes/Calculators/Computers/Phones. Problem 1 (20 Points): Diffusion Partial Differential Equation by Separation of Variables Consider this partial differential equation (PDE) for u x ,t with t 0 and 0 x L : u t = 2 u x 2 with boundary condition u /∂ x = 0 at x = 0 for t 0 , boundary condition u = 0 at x = L for t 0 , and initial condition u = 1 at t = 0 for 0 x L . Using separation of variables and superposition, find the solution u x ,t that satisfies the PDE as well as the boundary/initial conditions. Show all your steps. Express your final answer as a sum, or as the first three nonzero terms, without any integrals. Problem 2 (20 Points): Wave Partial Differential Equation by Separation of Variables Consider this partial differential equation (PDE) for u x ,t with t 0 and 0 x L : 2 u t 2 = 2 u x 2
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Final+and+solutions - MAE 140 Final Examination Thursday,...

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