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Help With Partial Derivatives and Infinite Sums

  1. Dec 14, 2012 #1
    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!
     
  2. jcsd
  3. Dec 14, 2012 #2

    mfb

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    Staff: Mentor

    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.
     
  4. Dec 14, 2012 #3
    Thank you! that helped me figure it out
     
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