u(x,0) = sum(n,1,Infinity, (a_n cos(n pi alpha 0/L) + b_n sin(n pi alpha 0/L))sin(n pi x/L)
u(x,0) = sum(n,1,Infinity, a_n sin(n pi x/L)) = f(x)
so it looks to me like your a_n are a sort of Fourier coefficients of f(x)
It's been forever since I've done a course in PDE's, so I'd really appreciate a step by step process for solving this
leads to a solution of the form
If , , and .
I want to say the due to the boundary condition, but I'm not sure.
I'm also not sure what the integral's should look like when I'm trying to find the fourier coefficents of u,f and g.
Thanks in advance.
u(x,0) = sum(n,1,Infinity, (a_n cos(n pi alpha 0/L) + b_n sin(n pi alpha 0/L))sin(n pi x/L)
u(x,0) = sum(n,1,Infinity, a_n sin(n pi x/L)) = f(x)
so it looks to me like your a_n are a sort of Fourier coefficients of f(x)