(Question with partial differentiation, gradient, and polar coordinates)

http://f.imgtmp.com/VWq59.jpg

How do I start?

Question

(Question with partial differentiation, gradient, and polar coordinates)

http://f.imgtmp.com/VWq59.jpg

How do I start?

turingtest · Answer

bookmark*
I'll be back for this one...

turingtest · Answer

@JamesJ feel like deriving the gradient in polar coordinates?
I'm quite stuck.

s3a · Answer

( http://f.imgtmp.com/PRW03.jpg) The gradient in polar coordinates: http://math.mit.edu/classes/18.013A/HTML/chapter09/section04.html Does that get you unstuck?

turingtest · Answer

That is the exact page I was looking at, but I don't think I understand why u_(theta) is perpendicular to u_rm and what they say about$$\vec \nabla\cdot \vec ds=df$$is news to me, so I wanted another way...
after looking for a while though, it seems most proofs of this look about the same, so I think this is your best bet

turingtest · Answer

*perpendicular to u_r

s3a · Answer

But I know less than you so I'm more screwed! Does this somehow help?: http://www.youtube.com/watch?v=uFOqAMuXrg8 It didn't do anything for me but maybe I missed something important?