Reference no: EM131103892
Math 054 Partial Differential Equations - HW Assignment 7
1. The following is a general Fourier series for u(x, y)
u(x, y) = ½ u0(t) + n=1∑∞un(t) cos nπx
Explain why we multiply u0(t) by ½. A thorough explanation will involve eigenfunctions and orthogonality.
2. Using results from class, solve for u(x, t).
ut(x, t) = Duxx(x, t), 0 < x < 1, t > 0,
u(0, t) = u(1, t) = 0, t > 0.
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