Would you mind helping me out with another problem in this textbook... #23 from the same section. It says:

The heat conduction in two space dimensions may be expressed in terms of polar coordinates as

(alpha)^2 (Urr + (1/r)Ur + (1/r^2)U(theta)(theta)) = Ut

Assuming that u(r, theta, t) = R(r)(phi)(theta)T(t), find ordinary differential equations that are satisfied by R(r), (phi)(theta), and T(t).

If you could, I'm also a little confused by the insulated heat conduction problems. For example,

Find the steady-state equation fo the heat conduction equation (alpha)^2 * Uxx = Ut that satisfies the given set of boundary conditions.

U(0,t) = 10 , u(50,t)=40

Thanks

*Also, what's LaTeX? (that you mentioned before PerfectHacker)