Solve the heat equation modeling the heat conduction inside of a metal rod of length L, which is perfectly insulated on all sides, including the ends, so that it satisfies the homogeneous Neumann boundary conditions u(x = 0, t) = 0 and u(x=L, t) = 0, if the initial temperature in the rod is u(x,t = 0) = x. Caution: it is easy to miss a term in the Fourier series. Please plot your solution as a function of a for a few values of time t, including t = 0, and a "relatively long time"