Talk:Vector calculus
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[edit] Note to author
To the author of the page: Don't you think that the description of vector calculus as a "collection of formulas and techniques" is somewhat oversimplified? Indeed, its origin is _not_ a compillation of formulas for use in engineering, but rather the search for the composition structure of "higher order numbers", started by Gauss (and Argand and others) applied to the complex numbers and then Hamilton, Grasmann, Gibbs (and others) to "3rd and 4th order" numbers (what we call today 3-vectors and quaternions, respectively). And this is a "trascendental" motivation, compared to the development of formulas for engineering! But this is just a comment. Cheers!
Jose A. Vallejo Faculty of Sciences UASLP (Mexico)
'Most of the results are more easily understood using the concepts of differential geometry' - well, not using the ideas as currently expressed on WP they're not.
A statement that curl is just dF is NOT going to solve any fluid mechanics! There is a real problem here (yes, it may be ME) but the differential geometry concepts are not sufficiently handlable by a non-graduate mathematician, given present WP presentations.
Interestingly, from errors made in some classical formulae (eg confusion of total & partial time derivatives in Liouville's theorem) by those using diff geom techniques, the mathematicians would be wise to swot up the old techniques too! Linuxlad 17:11, 11 Apr 2005 (UTC)
What about Green's Theorem? Shouldn't that be included as an important theorem of vector calculus? Begreen 01:48, 6 March 2006 (UTC)
[edit] That's It?
This seems to be a pitifully inadequate description of vector calculus to me. It looks like a good lead in, but the article about the techniques is missing! (Arundhati Bakshi (talk • contribs)) 12:34, 20 March 2006 (UTC)
[edit] weird link
Did anyone read that article about the improper use of nabla, written by Chen-to Tai? What a weird, pretentious article. Tai comes across as a bastard. His point is that you can't take a dot-product of nabla with a vector. But his quotes from literature are bizarre. Kreyszig, a well-respected author, comments himself on this (correctly), but Tai doesn't think Kreyszig has commented well enough, so Tai's response (my paraphrase): "the further Kreyszig explains, the more the student becomes confused". Almost no author escapes from Tai's wrath. Well, good for you Tai.
So, I suggest that link be removed, or at least demoted to the talk page (with a warning next to it).Lavaka 23:14, 16 February 2007 (UTC)
- I agree that the link is not very useful, so I removed it. I guess the article is meant to be read in conjunction with Tai's other article, which appears to be interesting reading. By the way, Chen-To Tai also seems to be well respected; the IEEE has an award named after him. -- Jitse Niesen (talk) 01:13, 17 February 2007 (UTC)
[edit] Conventional vector algebra
I moved this section to Talk:Cross product#Conventional vector algebra. Paolo.dL 09:21, 25 July 2007 (UTC) --Physis 04:26, 10 November 2007 (UTC)
[edit] Hypercorrect verbalization of divergence theorem
The article summarizes the divergence theorem like this:
| Divergence theorem |  |
The integral of the divergence of a vector field over some solid equals the integral of the flux through the surface bounding the solid. |
My emphasis added, typeset with red.
I conjecture that the formula is correct, but the verbalization contains a "hypercorrect", overlapping invocation of notion integral. Maybe the correct verbalization would be,
| “ | The integral of the divergence of a vector field over some solid equals the |
” |
In summary; the notion of flux already contains the notion of integral.
I am new in this field, maybe I am not right.
Physis 04:26, 10 November 2007 (UTC)....pp
