\begin{problem}{MATH 294}{FALL 1982}{FINAL}{6}{}
\probb{Determine the solution to Laplace's equation} \probpartnn{$
\ndpd{u}{x} + \ndpd{u}{y} = 0 \mbox{ on } 0 < x < 1, \; 0 0, $ with boundary conditions $u(0,y) = 0, u(L,y) =
0, u(x,0) = f(x), $ and $u$ must not approach $\infty$ as $y$
approaches $\infty.$} \probpart{Find a general solution for these
conditions. } \probpart{Write out the solution for this problem
in the case that $f(x) = x.$ You are given the Fourier sine and
cosine series for $x, (0 < x