Homework Statement
Consider
\frac{\partial u}{\partial t} = k\frac{\partial^2u}{\partial x^2} subject to
u(0,t) = A(t),\ u(L,t) = 0,\ u(x,0) = g(x). Assume that u(x,t) has a Fourier sine series. Determine a differential equation for the Fourier coefficients (assume appropriate continuity)...