Let u(x, y) be a twice differentiable function. Show that in polar coordinates the Laplacian of u takes the form...

.

Should be an easy Q but i cant remember how to do the second derivative.

= .

But then how do you take the second derivative?

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- April 24th 2009, 05:18 PMDeadstarLaplacian Differentiation
Let u(x, y) be a twice differentiable function. Show that in polar coordinates the Laplacian of u takes the form...

.

Should be an easy Q but i cant remember how to do the second derivative.

= .

But then how do you take the second derivative? - April 24th 2009, 06:04 PMCalculus26
http://www.mathhelpforum.com/math-he...12bc8738-1.gif = http://www.mathhelpforum.com/math-he...87deb5a7-1.gif

replace x = rcos(theta) y = rsin(theta)

This won't be pleasant but:

Uxx = (Ux)x so in http://www.mathhelpforum.com/math-he...12bc8738-1.gif replace U with Ux

similarly for Uyy