Understanding Vector Integrals: A Closer Look at Integral Identity 1

[coverband]

1. By considering each component of the vector A show that $$\iint A(u.n)ds = \iiint{(u.nambla)A+A(nambla.u)}dV$$ (A,u and n are vectors)

Homework Equations

3. Let A = ai + bj + ck. L.H.S: $$\iint ai (u.n)ds + \iint bj (u.n)ds +\iint ck (u.n)ds$$
R.H.S. = $$\iiint(u.nambla)ai dV+ \iiint(u.nambla)bj dV+ \iiint(u.nambla)ck dV + \iiinta(nambla.u)i dV ...$$

Sorry my latex is all over the place maybe just ignore this

 

[hgfalling]

That gradient symbol is called "nabla." "nambla" is something else entirely.