Show that the Jacobian of the transformation to spherical coordinates is ρ^2sin∅

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- Sep 29th 2009, 05:31 AMsinni8jacobian (multivariable calculus) plz help!
Show that the Jacobian of the transformation to spherical coordinates is ρ^2sin∅

- Sep 29th 2009, 05:48 AMpomp

Show some working and it will be easier to help you out. Do you know how to find the Jacobian in general? Where is it that you are stuck?

For spherical coordinates you have,

$\displaystyle x = \rho \sin{\phi} \cos{\theta}$ , $\displaystyle y = \rho \sin{\phi} \sin{\theta}$ and $\displaystyle z = \rho \cos{\phi}$.

Just plug in the correct derivatives into the formula you have to calculate the Jacobian. Let me know where you get stuck.