/sci/ - Science & Math

[ЯR !!qSRZhfCxFtq No.2259336]

hey sci I ran into some trouble with a few calculations, and I was looking for some help...
does <span class="math">\nabla \cdot \vec{E}=\vec{E} \cdot \nabla[/spoiler]? because I know the dot product is commutative, but the divergence is possibly a special case.

also, if anyone could explain this identity to me, because it's throwing me off:
<div class="math">\frac{1}{2} \nabla {E^2}=\vec{E} \times (\nabla \times \vec{E})+\vec{E} (\vec{E} \cdot \nabla)</div>
I'm using the identity <span class="math">\vec{A} \times (\vec{B} \times \vec {C}) = \vec{B}(\vec{A} \cdot \vec{C}) - \vec{C} (\vec{A} \cdot \vec{B})[/spoiler], which keeps giving me <span class="math">\vec{E} \times (\nabla \times \vec{E}) = \nabla (E^2) - \vec{E}(\vec{E} \cdot \nabla)[/spoiler], so I can't figure out how to get that. Help much appreciated.

[Anonymous No.2259345]

The "del" operator (that triangle is called a nabla) is just a mnemonic device for curl, div, and gradient. It has no meaning besides that.

[Anonymous No.2259349]

\nabla {E^2} = 2\vec{B}(\vec{E} \cdot \vec{grad(E)})

[Anonymous No.2259351]

Hey, how do you produce such arcane symbols on 4chan? I don't even know what it's called. Someone point me in the right direction?

[Anonymous No.2259353]

>>2259349
Damn I always fail at latex.

Well, nabla(E) = (dE/dx, dE/dy, dE/dz)
and nabla(E²) (dE²/dx, dE²/dy, dE²/dz) = (2*E*dE/dx, 2*E*dE/dy, 2*E*dE/dz) = 2*E*grad(E), so you have your equation.

[Anonymous No.2259355]

Wolfram Alpha gives this faggot trying to bitchfuck another faggot for A(BC)=B(AC)−C(AB)

[Anonymous No.2259360]

>>2259355

[ЯR !!qSRZhfCxFtq No.2259367]

>>2259345
thanks captain obvious

>>2259351
pic related

>>2259355
A, B and C are vectors, not scalars as your picture implies

[ЯR !!qSRZhfCxFtq No.2259395]

ok, wikipedia just saved the day on my first question
http://en.wikipedia.org/wiki/Del#Precautions

and I have a feeling that might have something to do with the second one, but i suppose that'll have to wait till tomorrow to figure out

[Anonymous No.2259424]

Gotta keep your derivatives in the right order, because <span class="math">\nabla(A B)[/spoiler] is different from <span class="math">A \nabla(B)[/spoiler].

<div class="math">\vec{A} \times (\vec{B} \times \vec {C}) = \sum_{i=1}^3 A_i \vec{B} C_i - (\vec{A} \cdot \vec{B}) \vec{C}</div>
<div class="math">\vec{E} \times (\nabla \times \vec{E}) = \sum_{i=1}^3 E_i \nabla E_i - (\vec{E} \cdot \nabla) \vec{E} = \frac{1}{2} \nabla \left(\sum_{i=1}^3 E_i E_i\right) - (\vec{E} \cdot \nabla) \vec{E}</div>

[Montreal Guy !!tHbqytpCk+g No.2259625]

I'd think the Levi-Civita method would help you greatly. Here's a little thing I figured out in second year physics.

http://www.physicsforums.com/showthread.php?t=257144