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7.38 U, §4 Solve

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

Initial condition:

where the sum over the

includes

,and

and

for

, and the generalized Fourier coefficients fⁱ_nm can be found from the integrals of the last section.

Unknown temperature:

Put into P.D.E. :

Because of the choice of the :

Because of the choice of the J_n:

At time zero, the series expansion for u must be the same as the one for the given initial condition f:

Dⁱ_nm(0) = fⁱ_nm

Next: 7.38 U, §5 Up: 7.38 Unsteady Previous: 7.38 U, §3