Consider the numerical solution of the heat equation ut = cuxx. Peform a Fourier stability analysis (and plot the amplification factor of the numerical scheme vs the exact amplification factor) for the following numerical schemes for c = 1, t = 0.025 and c = 1, t = 0.0025, over the interval [0, 4] with 100 sampled points (i.e., as discussed in class, this will result in x = (4 0)/(100 1) = 4/99 as your spatial discretization step size): a) FTCS, b) BTCS