A computer component of length L = 1 is insulated at the end x = 1, so ux(1, t) = 0

and cooled to u(0, t) = 0. Assume that the temperature is described

by the equation

u/t=²u/x², t>0, 0<x<1

where u(x, t) is the temperature, t is time. Assume that the initial temperature is u(x, 0) = 1.

(a) Draw a sketch in the (x, t) plane that shows the equation and boundary/initial conditions.

(b) Solve for u(x, t)) using separation of variables and Fourier series.