The first lecture course that was devoted solely to PDEs that I
know of was Riemann's 2-part course of the mid-1850s.
Transcriptions were not published until the mid-1870s, with the
titles "Schwere, Elektrizitaet und Magnetismus" and "Partielle
Differentialgleichungen". The first of these is basically about
potential theory, and is indebted to Dirichlet's lectures on action-at-
a-distance forces from the 1840s, also published much later.
Potential theory was much closer to being a free-standing research
specialty in the 1830s and 1840s than was the case for PDEs as
such. If you look at the organization of treatises and lectures they
tend to much more oriented around the physical problems than
around the equations. Thus Airy's text on the figure of the earth,
various papers of Liouville (see Lutzen's book), Green's Essay,
lectures and papers of Dirichlet etc etc fit in a pattern in which the
mathematical tools are presented and developed in a particular
context.
By Riemann's time there is a critical mass of results and a basic
subdivision of the subject into gravitation/electrostatics/steady-
state heat conduction; non-steady state heat conduction; and
waves. This course eventually became Riemann-Weber.
In any case forgive this rather hasty comment. A more detailed
account in necessary to convey much nuance here.
Best for 1999
Tom Archibald
On 29 Dec 98, at 20:59, Martin Krieger wrote:
>
> Further looking gives credit to DuBois Raymond, 1889, for the division.
> Euler for PDEs, Bernstein for apriori estimates.
> There is a good article by Brezis and Browder in the current Advances in
> Math. Still, it is hard to be sure when it was seen as a subject, as
> such--but it must be by 1800 or so.
> MK
>
>
> On Wed, 30 Dec 1998, J F Harper wrote:
>
> > On Sat, 26 Dec 1998, Roger Cooke wrote:
> >
> >> I believe the classification of pde's as hyperbolic, elliptic, and
> >> parabolic is due to IG Petrovsky (1901--1973).
> >>
> >
> > When? It's in Hadamard's "Lectures on Cauchy's problem in linear partial
> > differential equations" (written 1921 publ. 1923 Yale) with no indication
> > it wasn't already well-known then.
> >
> > John Harper, School of Mathematical and Computing Sciences,
> > Victoria University, Wellington, New Zealand
> > e-mail john.harper@vuw.ac.nz phone (+64)(4)471 5341 fax (+64)(4)495 5045
>
>
>
**********************************************************
Tom Archibald
Head, Dept. of Mathematics and Statistics
Acadia University, Wolfville, N. S. B0P 1X0
Tel: 902-585-1475 Fax: 902-585-1074
email: Tom.Archibald@acadiau.ca
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