Talk:Del

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Contents 1 page title 2 Coordinates 3 So what is ∇? 4 Confusing? 5 Etymology 6 error in identity 4. ?

[edit] page title

Is "del" really the most common name of the operator? I have heard the names "nabla", "grad" and "gradient" before, but never "del". Maybe the page should be renamed to "Nabla" and just mention "del" as an alternative name for the operator? -- Jochen

The formal operator was certainly called "del" in all of my mathematics and physics courses, which also mentioned the (infrequently used) name "nabla operator". The operations it is typically used to construct are called "div", "grad" and "curl". "Del" is one syllable, "nabla" two, so when you have to speak a lot of equations, it's more natural to use "del". It's also easier to say "del squared" than "laplacian of". -- Karada 11:17, 7 Nov 2004 (UTC)

Asking Google for "del operator" gives 1620 hits, asking for "nabla operator" gives 2380. This would indicate that "nabla" is more common. -- J.Voss 13:50, 7 Nov 2004 (UTC)

But, then, most people say "del", not "the del operator," so it's not clear that this is meant. As below, the google fight for "del+math" vs. "nabla+math" shows del+math on top. So I'm not willing to say either is definitive proof. 24.59.199.228 09:40, 23 November 2006 (UTC)

Just to add to this, the del symbol itself isn't the same as the "grad" operation; you only get the grad operation by "multiplying" a scalar field by del. -- Karada 11:21, 7 Nov 2004 (UTC)

Perhaps it could also be notes that sometimes the Δ symbol is used for . And even the tex editor you use here for math editing uses nabla instead of del. --Jaap 20:00, 18 Apr 2005 (UTC)

It's always been del to me, from calculus to physics at umass. also: phi is 'fee'

See http://www.googlefight.com/index.php?lang=en_GB&word1=del+math&word2=nabla+math

But compare http://www.googlefight.com/index.php?lang=en_GB&word1=%22nabla+operator%22&word2=%22del+operator%22 --Jochen 10:09, 29 September 2005 (UTC)

I am also in favour of a move of del to nabla. I think "del" is a manifestation of loss of culture (so we should fight against this). There is no sense imho of calling this "del". The symbol is a reversed delta, OK, but then call it "led" or "atled". (Besides the fact that many other things would deserve the WP "Del" page much more than this one...) — MFH:Talk 15:13, 16 March 2006 (UTC)

Wikipedia isn't a forum for the preservation of culture. Nabla is the symbol, del is the operator, that makes sense, and the rest is nothing to fret over. 24.59.199.228 09:40, 23 November 2006 (UTC)

PS: if you add Ostrogradsky, it's 27 against 4 - as I said, a problem of culture... (I better don't mention the result for Ostrogradski... ;-) — MFH:Talk 15:44, 16 March 2006 (UTC)

[edit] Coordinates

Is it best to expand on how to convert del to different coordinate systems here or in the other coordinate systems? This is done very poorly at them moment, from new unit vectors (and relationship to i,j,k), why you get (1/r).(d/d theta) e.t.c. --rex_the_first 18:30, 05 Nov 2005 (GMT)

Yeah, sorry about that; I know it's not incredibly obvious. Sadly, there are easy ways to do it (h-factors), but they look way too handwavy for wikipedia, and there are rigorous ways to do it (actual coordinate substitution), but they look way too imposing and deep for Wikipedia. Unless people have proofs that I haven't seen, I don't think anything like that is coming to wikipedia. 24.59.199.228 09:40, 23 November 2006 (UTC)

[edit] So what is ∇?

The page defines ∇ beautifully, without actually saying what it is/does. In other words, unless you're a mathematician, the page is meaningless.

There must be a real life example that will clarify what ∇ does. I believe it could be applied to the surface of an irregular hill, in which case, what do ∇, d/dx, etc, represent? Do the d/dx, etc represent the slopes in three different coordinates, in which case ∇ is what? The direction in which a ball will roll? Something else? --Iantresman 13:28, 13 June 2006 (UTC)

Del is an operator. It does different things depending on what you ask it to do. Gradients of potential energy fields are forces. The divergence of the electric field is related to the charge density at a point. Et cetera.

[edit] Confusing?

The article says:

Since del does not really have a direction, this is hardly expectable

How does del 'not really have a direction'? It's a product of basis vectors, right, so isn't it just another vector? -- Ornette 10:39, 22 June 2006 (UTC)

Thanks, I cut out that part. Oleg Alexandrov (talk) 23:30, 22 June 2006 (UTC)

I added what I believe this was talking about to the end of the article. Del *doesn't* have a direction -- not in the same way that k does. kx has the same direction as ky, but ∇x and ∇y are orthogonal. Real directions don't act that way under scalar multiplication. 24.59.199.228 09:40, 23 November 2006 (UTC)

[edit] Etymology

I think it would be nice to know where the name "del" came from. (My guess is likely because it looks like a delta upside-down...perhaps?)

[edit] error in identity 4. ?

I guess there is, as I write this, since I don't see an equality sign in 4. Correction please? Thanks

Identities (3) and (4) did not actually make any formal sense and were eliminated in my most recent edit. 24.59.199.228 09:26, 23 November 2006 (UTC)