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Partial differential: partial scalar partial vector 
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#1
Sep3009, 01:39 AM

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Hi,
I have a problem to find the meaning of a special partial differential: partial scalar partial vector. i.e. dF/dn where F is a scalar and n is a i.e. normal vector. This is a partial diff. n could be a vector consisting of partial differentials, (dT/dx,dT/dy) I have looked in literature but found nothing. Can someone help me? Thank you very much /Andreas 


#2
Sep3009, 08:31 AM

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Hi Andreas! Welcome to PF!
(have a curly d: ∂ ) But (for example, when calculating flux) you can have ∂F/∂n or d(F.n^)/dn, where n^ is the unit vector in the normal direction, and n is the distance in that direction. 


#3
Sep3009, 01:14 PM

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[tex]\frac {\partial F}{\partial \hat v} = D_{\hat v}(F) = \nabla F \cdot \hat V[/tex] where [tex] \hat V[/tex] is a unit vector in the direction of V. 


#4
Oct109, 02:43 AM

P: 2

Partial differential: partial scalar partial vector
Hi tinytim and LCKurtz,
This is exactly the explaination I am looking for! I had a hard time to understand the meaning of such partial derivative. And it with [tex]\partial[/tex] it should be It is the rate of F in the direction of some unit vector n that is normal to an arbitrary surface. I have no problem to find the growth rate of F in x and y but when it came to a other direction depending on other things, it became a problem. But now I understand how to do it! I actually did not think of the thing that n must be a unit vector. I will make it a unit vector! Thank you very much for your help on this problem, I have been struggling to find the answer for a long time! 


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