MA 340 (1) (a) Let the ends of a copper rod 100cm long be maintained at 0 degrees Celsius. Suppose that the center of the bar is heated to over 100 degrees Celsius by an external heat source and that this situation is maintained until a steady state results. Find this steady state temperature distribution. (b) At t=0 [after steady state part (a) has been reached], let the heat source be removed. At that the same instant let the end x=0 be placed in thermal contact with a reservoir at 20 degrees Celsius, while the other end remains at 0 degree Celsius. Find the temperature as a function of time u(x,t).