Solving a PDE with Polar coordinates

Does

Thanks.

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- Dec 24th 2010, 07:22 PMdwsmithPolar Coordinates
Solving a PDE with Polar coordinates

Does

Thanks. - Dec 25th 2010, 07:04 AMJester
You need to use the chain rule

or if you use Jacobians (the way I'd do it)

. - Dec 25th 2010, 12:56 PMdwsmith
Danny,

I haven't done anything with the Jacobian in a long time. Could you show me how it is done?

Thanks.

The solution I am supposed to conclude is , f arbitrary.

How do I finish off from

Thanks. - Dec 25th 2010, 03:05 PMzzzoak
From

- Dec 25th 2010, 03:08 PMdwsmith
- Dec 25th 2010, 03:40 PMzzzoak
- Dec 25th 2010, 03:42 PMdwsmith
And making the change from u(r, theta) to u(x,y) is fine?

- Dec 25th 2010, 04:01 PMzzzoak
We convert

and

and have finally

We may check inserting it to the initial equation.