Separated variables, applied b'dry condition at x=0 and x=l giving sin solutions, and found eigenvalues for separation constant, k
(Boundary condition at large time was what fixed the sign of the separation constant already)
Boundary condition at time =0: we must first solve for the steady state temperature function that it begins with (in this case u= 100 x/l) and then put this in at t=0. Gives us a Fourier sin series which will fix all the coefficients.
Extended to the case that right side goes to Tf (rather than 0). Solved this by adding in the final steady state solution by hand.
Considered the case of Dirichlet boundary conditions, and Neuman (where the derivative is specified, not the function)
Considered the b.c. of some y0(x), with derivative dy0/dt=0. Also considered the b.c. of dy0(x)/dt given, with yo(x)=0. Talked about normal modes, and the tones produced.
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