Testwiki:Reference desk/Archives/Mathematics/2012 June 14

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June 14

n in definition of Green's theorem

In the following identity, $\int \int \underset{V}{\int }\varphi div(grad(\psi ))+grad(\varphi )\cdot grad(\psi )dV=\int \underset{S}{\int }\varphi \frac{\partial \psi }{\partial n}dS$, what does $n$ represent? ? Widener (talk) 20:40, 14 June 2012 (UTC)

It represents a normal -- this is the directional derivative in the direction perpendicular to the surface. Looie496 (talk) 21:18, 14 June 2012 (UTC)