u,w are scalar functions of 3 variables(adsbygoogle = window.adsbygoogle || []).push({});

the book says you can verify by direct computation:

[tex]u\nabla^{2}w = \nabla \bullet\left(u\nabla w\right) - \left(\nabla u\right)\bullet\left(\nabla w \right)[/tex]

and

[tex]\nabla^{2}w[/tex] is [tex]\Delta w[/tex], the Laplacian operator.

Every time I've worked this, I just can't seem to come close. Can someone get me started on this? It's out of a PDE book so of course they don't bother expounding on this and I haven't looked at vector calculus in years...

My first thoughts were:

[tex]u \nabla ^{2}w [/tex]

= [tex]u \nabla \nabla w [/tex]

= [tex] u \ div \ grad \ w [/tex]

=[tex]u \left(\frac{\delta^{2}w}{\delta x^{2}} [/tex] [tex] + \frac{ \delta^{2}w}{ \delta y^{2}} + \frac{ \delta^{2}w}{ \delta z^{2}}} \right) [/tex]

I can't get that RHS parens in there, sorry :-/

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# Vector calculus

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