PHYS124 Midterm: PHYS 124 UofA syFall 2007 Exam
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PHYS124 Full Course Notes
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0 < x < 1, t > 0 (1, t) = 0, t > 0 u(x, 0) = cos x, X t = x t, T which leads to the two ordinary di erential equations. X (0, t) = x (0) t (t) and. X (1, t) = x (1) t (t) we can satisfy the boundary conditions by requiring that x (0) = x (1) = 0, so that x(x) must satisfy the boundary value problem. Now we must nd those values of for which this boundary value problem has a nontrivial solution. In this case, the di erential equation is x = 0, with general solution. X(x) = ax + b, where a and b are constants. Applying the boundary condition x (0) = 0, we get b = 0, so that x(x) = a, a constant. In this case, the second boundary condition is automatically ful lled, and the only nontrivial solution is the constant solution.
