Something about exterior algebra

[ltd5241]

1.how to prove div(A × B) = (rot A)· B - A ·(rot B)
2.d(ω1(A) × ω1(B))=?

 

[HallsofIvy]

The simplest way to do 1 is just to go ahead and write out the component by component formula for both sides (I assume that "rot A" is what I would call "curl A": [itex]\nabla \times A[/itex].

For 2, use the product rule.

 

[ltd5241]

For 2, use the product rule.[/QUOTE]

What's the rule?

 

[HallsofIvy]

If you are working with exterior algebras and "differentials", surely you have taken Calculus I- and all I am talking about is the extension of the "product rule" from Calculus I extended to vectors. You should have seen that in multi-variable Calculus.