My Math Forum proof by using greens theorem or stokes theorem

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 May 14th, 2011, 11:30 AM #1 Newbie   Joined: May 2011 Posts: 8 Thanks: 0 proof by using greens theorem or stokes theorem Let f(x,y) have continous partial derivatives of first and second order in a area in the xy-plane. The area is determinded by a closed smooth curve C. Show that if: $\frac{\part^2f}{\part x^2}+\frac{\part^2f}{\part x^2}=0$ in A then $\oint\frac{\part f}{\part x}dy=\oint\frac{\part f}{\part y}dx$ answertext: http://bildr.no/view/882973 Where do they find F in the answer text?
 May 14th, 2011, 12:18 PM #2 Senior Member   Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0 Re: proof by using greens theorem or stokes theorem They're defining F to be that vector field and depends on what f is.
 May 14th, 2011, 12:29 PM #3 Newbie   Joined: May 2011 Posts: 8 Thanks: 0 Re: proof by using greens theorem or stokes theorem But if i wanted to solve that assignment where would i start to get this F-vector. I mean if it had not had minus in front of x-term then curlvector had become something else
 May 14th, 2011, 01:10 PM #4 Senior Member   Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0 Re: proof by using greens theorem or stokes theorem In order to know what the vector F is, you need to know what f is. In this problem, f is not defined. However, it does tell you that the curl of F is zero. That's the only information you know about f.
 May 14th, 2011, 01:17 PM #5 Newbie   Joined: May 2011 Posts: 8 Thanks: 0 Re: proof by using greens theorem or stokes theorem where does it in the assignment say that curl F is zero, not in the answer that is
 May 14th, 2011, 02:13 PM #6 Senior Member   Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0 Re: proof by using greens theorem or stokes theorem Says from the information given in the text. I assume it means in the problem.

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