LetT(x, y) satisfy Laplace’s equation in the square 0 < x < ¼ and

0 < y < ¼. Let T = 1 on the side y = ¼, 0 < x < ¼, and let T = 0 on

the other three sides. Show that

T(x, y) = big expression involving sinhs (I can derive this)

and, by considering three similar problems, thatT = 1/4at the centre of the square.

Which other 3 problems would I consider and then what would I do with these to get the solution at the centre of the square?

many thanks