Talk:Vector calculus
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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)