Talk:Vector calculus identities

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The other vector identities can be found in the apendices of a lot of textbooks. These particular ones came from "Advanced Engineering Electromagnetics" by Constantine A. Balanis.

[edit] Restate identities using div, grad, curl (names) ?

Hello. I wonder if anyone is opposed to rewriting the identities as curl grad foo = 0, etc, i.e., using the words curl, div, and grad. As Wikipedia is a reference work, it seems safe to assume that we are going to get many readers who are capable of understanding the identities, but are only occasional users of the notation. Yes, no, maybe? Keep up the good work, 64.48.158.121 03:59, 19 May 2006 (UTC)

[edit] Collect identities from other pages here

Another thing to think about -- it would be a good idea to look at the other pages in Category:Vector calculus and see if there are some identities which can be copied here. 64.48.158.121 04:01, 19 May 2006 (UTC)

[edit] Reversions of identities using Feynman notation

Hello User talk:Crowsnest: You reverted these entries; why?

In simpler form, using Feynman subscript notation:

\nabla(\mathbf{A} \cdot \mathbf{B})= \nabla_A(\mathbf{A} \cdot \mathbf{B}) + \nabla_B (\mathbf{A} \cdot \mathbf{B}) \ ,
where the notation ∇A means the subscripted gradient operates on only the factor A.
\mathbf{A \ \times } \left( \mathbf{ \nabla \times B} \right) =\nabla_B \left( \mathbf{A \cdot B} \right) - \left( \mathbf{A \cdot \nabla } \right) \mathbf{ B} \ ,
where the Feynman subscript notation ∇B means the subscripted gradient operates on only the factor B.

Point 1: The notation is defined and is useful - why delete it? It's only notation - use it or don't; suit yourself. So why not show how it works and give the reader a choice?

Point 2: Feynman's notation is used; for example, see: "following Feynman , introduce a partial operator ∇A in the latter identity (14), where the subscript denotes the quantity to be differentiated. p. 4

Point 3: Quote from Feynman: "Here is our new convention: we show by a subscript, what a differential operator works on; the order has no meaning." etc. The guy introduced it in his undergrad lectures - he must think its useful. Hey, he's a Nobel Prize winner; why trust his judgment, eh?? Reference: R P Feyman, & Leighton & Sands (1964). The Feynman Lecture on Physics. Addison-Wesley, Vol II p. 27-4. ISBN 0805390499. 

Point 4: They are identities, for Pete's sake. They are here for reference only - no great wisdom attaches. You can prove them yourself, there is no question of validity. It's just to save some time, or provide a little smörgåsbord for browsing when solving a problem. What possible purpose or rationale is there for these reverts??? Brews ohare (talk) 05:35, 23 April 2008 (UTC)

Hello Brews. I reverted them because they are not common vector calculus and unreferenced. Not because they are wrong, not useful, etc. This article starts with "...in vector calculus". So that says something of what people may expect on this page. Different branches of science develop different tools and notation they use, depending on their needs (which may spread out to other branches later on).
You cannot expect everybody to know Feynman notation, and things have to be verifiable on Wikipedia: "The threshold for inclusion in Wikipedia is verifiability, not truth".
So please re-instate them, with the references mentioned above (or others). And if you like, start an article on Feynman notation and its use (that sounds at least interesting to me, I came across some variational problems in fluid dynamics where use of Feynman notation would have shortened the writing-up considerably). Best regards, Crowsnest (talk) 09:51, 23 April 2008 (UTC)
OK - I've done that. I think you'll find that the overdot notation is the convenient one. I stumbled across it yesterday by accident. Brews ohare (talk) 15:23, 23 April 2008 (UTC)