Re: [HM] Jacobian, implicit (and inverse) function theorems

Julio Gonzalez Cabillon (jgc@adinet.com.uy)
Wed, 17 Mar 1999 18:10:01 -0300

At 05:36 PM 16/03/1999 -0500, you wrote:
> Dear Colleagues,
> I'm looking for sources on the history of the Jacobian, the Implicit
> Function theorem, and the Inverse Function theorem. Thanks.
> Israel Kleiner
>

Dear Israel,

The term JACOBIAN was coined by James Joseph Sylvester (1814-1897), who used
it as early as 1853:

"In Arts. 65, 66, I consider the relation of the Bezoutiant
to the differential determinant, so called by Jacobi, but
which for greater brevity I call the Jacobian."

Cf. The Philosophical Transactions of the Royal Society of London, vol
CXLIII, part III, pp 407-548, London 1853. Also in Sylvester's _Collected
Mathematical Papers_, vol 1, Cambridge (At the University Press), 1904.

An extensive and original study of the topic was first carried out by
Carl Gustav Jacob Jacobi (1804-1851) in "De determinantibus functionalibus",
_Journal fuer die reine und angewandte Mathematik_ (Crelle's Journal),
vol 22, pp 319-352, 1841. Needless to say, you will not find there math
terms and symbols as we use them today; anyhow the intellectual seeds and
mathematical flowers to the point are all there (and no weeds whatsoever!).

Regards,
Julio Gonzalez Cabillon

>
> --------------------------------------------------------
> Israel Kleiner
> Department of Mathematics & Statistics
> York University
> Toronto, Ontario M3J 1P3
> Tel: 416-736-5250
> Fax: 416-736-5757
> email: kleiner@home.com
>