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7.28, §4 Solve

Expand all variables in the problem for u in a Fourier series:

Put into P.D.E. utt = a2 uxx:

Because of the choice of the Xn:

Put into I.C.s u(x,0) = f(x) and ut(x,0) = g(x):

Solve this O.D.E. and initial condition for Cn:

Characteristic polynomial:

Note: I would have gotten this same solution if I would have solved for C(t) in the previous section.

Initial conditions:


Next: 7.28, §5 Total Up: 7.28 Previous: 7.28, §3 Eigenfunctions
11/20/00 0:46:23