| The OED gives an 1816 reference to a text for the earliest usage of
| "partial differential equations". My question is, when did the various
| equations become a single field of study, which we now call partial
| differential equations. (Obviously, not necessarily in English.) A
| textbook or treatise would be a good enough marker for my purposes.
| ...
Dear Martin,
Demidov's papers on the subject might be a good place to start, I think.
There are a few essays on the works of Ivan Georgievich Petrovskij on
PDE and their role in the modern development of the theory of differential
equations - they are written in Russian.
=======
Handy references are:
Demidov, Serghei S:
"The Study of Partial Differential Equations of the First Order in
the 18th and 19th Centuries", _Archive for History of Exact Sciences_,
vol 26, no 4, pp 325-350, 1982.
Demidov, Serghei S:
"Creation et developpement de la theorie des equations differentielles
aux derivees partielles dans les travaux de J. d'Alembert" [Creation
and Development of the Theory of Partial Differential Equations in the
Works of J. d'Alembert], _Revue d'histoire des sciences et de leurs
applications_, vol 35, no 1, pp 3-42, 1982.
Luetzen, Jesper:
"The Solution of Partial Differential Equations by Separation of
Variables: A Historical Survey" (pp 242-277) in "Studies in the
History of Mathematics", edited by Esther R. Phillips, MAA Studies
in Mathematics, vol 26, Washington, DC, 1987.
Engelsman, SB:
"Lagrange's Early Contributions to the Theory of First-order Partial
Differential Equations", _Historia Mathematica_, vol 7, no 1, pp 7-23,
1980.
With best regards,
Julio Gonzalez Cabillon