Something about exterior algebra

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Homework Help Overview

The discussion revolves around proving a vector calculus identity involving the divergence of the cross product of two vector fields, as well as exploring a differential expression related to exterior algebra.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the proof of the identity div(A × B) and suggest writing out the component formulas. There is also a query regarding the product rule in the context of exterior algebra and its relation to previous calculus knowledge.

Discussion Status

Some participants have offered guidance on how to approach the proof and have referenced the product rule, while others are seeking clarification on the specifics of this rule as it applies to the current context.

Contextual Notes

There is an assumption that participants have a background in Calculus I and multi-variable calculus, which may influence their understanding of the concepts being discussed.

ltd5241
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1.how to prove div(A × B) = (rot A)· B - A ·(rot B)
2.d(ω1(A) × ω1(B))=?
 
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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": \nabla \times A.

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

What's the rule?
 
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.
 

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