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Partial using the chain rule

  1. Sep 25, 2008 #1
    [tex] u^{*}(r^{*},\theta^{*},\phi^{*}) = \frac{a}{r^{*}}u(\frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}) [/tex]

    [tex] \frac{\partial u^{*}}{\partial r^{*}}= \frac{a}{r^{*}}u_{r^{*}} \left( \frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}\right) \left( -\frac{a^{2}}{r^{2*}} \right) - \frac{a}{r^{*2}} u \left( \frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}\right) [/tex]

    where [tex] u_{r^{*}} [/tex] is the partial of u w.r.t r*

    Did I do this right? Is there a better way of representing [tex]u_{r^{*}} \left( \frac{a^{2}}{r^{*}},\theta^{*},\phi^{*}\right) [/tex]
    Last edited: Sep 25, 2008
  2. jcsd
  3. Sep 25, 2008 #2
    Calculation is right but pedantically speaking you mean derivative of u with respect to its first argument which is a^2/r* not r*.

    I don't know what kind of notations mathematicians use for that, symbolic programs like Mathematica would denote it like Derivative[1,0,0].
  4. Sep 25, 2008 #3
    well I'm trying to crank out the laplacian in spherical to show it u* is harmonic. So I'm just trying to differentiate with respect to each component and sub it into the laplacian in spherical and HOPEFULLY get zero.
  5. Sep 28, 2008 #4
    I still need help with this. Is there anybody out there who can help me?
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