Help With Partial Derivatives and Infinite Sums

by Tenenbaum3r
Tags: infinite summation, partial derivatives, substitution
Tenenbaum3r is offline
Dec14-12, 02:16 PM
P: 2
I'm working on a calculus project and I can't seem to work through this next part...
I need to substitute equation (2) into equation (1):

(1): r[itex]\frac{\partial}{\partial r}[/itex](r[itex]\frac{\partial T}{\partial r}[/itex])+[itex]\frac{\partial ^{2}T}{\partial\Theta^{2}}[/itex]=0

(2): [itex]\frac{T-T_{0}}{T_{0}}[/itex]=A[itex]_{0}[/itex]+[itex]\sum[/itex] from n=1 to infinity of ([itex]\frac{r}{R}[/itex])[itex]^{n}[/itex](A[itex]_{n}[/itex]cos(n[itex]\Theta[/itex])+B[itex]_{n}[/itex]sin(n[itex]\Theta[/itex]))

I know I have to solve for T in the second equation and then substitute but I don't really know the rules for infinite sums... The whole point of this is to prove that equation (2) is a solution to equation (1). Any help or advice would be appreciated!
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mfb is offline
Dec14-12, 05:50 PM
P: 10,809
You can multiply an infinite sum with T0, this is no problem. You don't need to modify the sum itself to solve equation (2) for T.
Tenenbaum3r is offline
Dec14-12, 10:22 PM
P: 2
Thank you! that helped me figure it out

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