pdsolve({diff(u(x, t), t) = diff(u(x, t), x, x), u(0, t) = f(t), u(L, t) = f(t), u(x, 0) = g(x)}, u(x, t));

pdsolve({diff(u(x, t), t) = diff(u(x, t), x, x), u(0, t) = 0, u(1, t) = 0, u(x, 0) = (x - 1/2)^2 - 1/4}, u(x, t));

plot3d(Sum(4*sin(n*Pi*x)*exp(-Pi^2*n^2*t)*((-1)^n - 1)/(n^3*Pi^3), n = 1 .. infinity), x = 0 .. 1, t = 0 .. 2, grid = [60, 60]);