In the thermal context, one might expect steepness in the initial temperature prole to be smoothed out as time goes on. To check this out use Fourier methods to determine the solution of the (scaled) Heat Eqn

T_t = T_xx in 0 < x < 1, with T (0, t) = T_x(1, t) = 0, and T (x, 0) = sin(2.1x) + 0.1 sin(20.2x).

Plot out the solution at t = 0. Check to see how many terms are required here, and at subsequent time intervals and Physics: comment on the physics of the results obtained (smoothing etc.).