Gnome Mathematical Interface

sorry for the earlier mail. i have changed the character thier names..

Q1. Show that
u(r,theta) = Brn Sin n*theta .
Satisfy the laplace equation in polar coordinate.

u rr +1/r u r + 1/r2 u thetatheta = 0

Q2. A circular plate given by 0 <= r <= 1, pi <= theta <= pi kept at 50 Centigrade and a portion r =1 , -pi <= theta <= 0 kept at &#8211; 50 Centigrade, show that the steady state temp u (in centigrade) at (r,theta) is given by u (r,theta) = &#931; Bnrn sin ntheta , n= 1 to infinity
Where Bn ={0 (even)
{200/n*pi (odd)