Separation of Variables - Spherical Coordinates (Part 1)

We setup the problem of separation of variables for spherical coordinates by studying the steady-state temperature of a spherical ball with some temperature specified on its boundary. The solution involves Legendre Polynomials.

[giovannimariotte]

This is exacly the video that i was looking for

[jazzbuckeye]

Working through the hydrogen atom in my quantum class now. This is really helpful, thanks!

[hollywilson]

I don't understand at 4:10 when you divide by R*Theta where the r^2 goes in both terms

[briannguyen]

How do you check the solution at 7:48 ?

[pt-au-hg]

I'm sure I'm missing something, but a question or thought on how the temperature is calculated; cosine of zero, at the top, would be one multiplied by 1/2 Uo ?; cosine of pi (at the bottom of the sphere) cosine is -1 so wouldn't the temperature at the bottom of the sphere be -1/2Uo ?;