The faces of the thin square plate with side a = 24 are perfectly insulated.

(a) the upper side is kept at 25c and the other sides are kept at 0c. find the steady-state temperature u(x; y) in the plate.

(b) find the steady-state temperature in the plate speci ed in (a) if the lower side is kept at u 0c, the upper side at u 1c, and the other sides are kept at 0c. hint: split into two problems in which the boundary temperature is 0c on three sides for each problem. one more hint: the solutions to the two problems are so similar that you only need to solve at most one problem.

(c) find the steady-state temperature in the plate speci ed in (a) with the upper and lower sides perfectly insulated (i. e. ty = 0), the left side kept at 0c, and the right side kept at f(y)c.