I don't understand what I am doing wrong here.(adsbygoogle = window.adsbygoogle || []).push({});

I'm supposed to show that this function is divergence free.

[tex] \vec v = \left( \frac{x}{x^2+y^2}, \frac{y}{x^2+y^2} \right) [/tex]

I ran the divergence through with my TI-89 at it equals 0. But, I want to calculate it by hand, so it would be easier to do this in polar coordinates (and this is my problem).

[tex] \vec v(r,\theta) = \left ( \frac{\cos \theta}{r}, \frac{\sin \theta}{r} \left) [/tex]

Standard divergence in cylindrical coordinates (dropping the z component)

[tex] div\,\, \vec u = \frac{1}{r} \left( \frac{\partial}{\partial r} (rF_r) +\frac{\partial}{\partial \theta} (F_\theta) \right) [/tex]

[tex] div\,\, \vec v = \frac{1}{r}\left( \frac{\partial}{\partial r} (\cos \theta ) + \frac{\partial}{\partial \theta}\left (\frac{\sin \theta}{r} \right) \right) [/tex]

Now this is obviously not 0, since the [itex] \sin \theta [/itex] is not going anywhere with the partials. So what am I doing wrong?

Thanks,

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# Homework Help: Divergence what am I doing wrong

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