Consider a thin rod of length [i]L [/i]with an initial temperature [i]f[/i]([i]x[/i]) throughout and whose ends are held at temperature zero for all time [i]t[/i]>0. The temperature u([i]x,t[/i]) in the rod is determined from the boundary-value problem:[br]u[sub]t[/sub]([i]x,t[/i])=au[sub]xx[/sub]([i]x,t[/i]), 0<[i]x[/i]<[i]L[/i], [i]t[/i]>0;[br]u(0,[i]t[/i])=0, u([i]L[/i],t)=0, [i]t[/i]>0;[br]u([i]x[/i],0)=f([i]x[/i]), 0<[i]x[/i]<[i]L[/i].[br][br]In the following simulation, the temperature u(x,t) is graphed as a function of [i]x[/i] for various times.[br][br][b]Things to try: [/b][br][list][*]Change the initial condition u(x,0)=f(x).[/*][*]Increase [b]n[/b], the number of terms in the solution.[br][/*][*]Change the length [b]L[/b].[/*][/list]