Does anyone know what is the history of PDEs in GENERAL?
i.e. does it back to 400 years ago or 300, 200 or less or more.
any refe. in this matter. I'm sure there an expert mathematician out there.
Since Newton only introduced the calculus in the mid to late 1600's (the Principia was around 1686) the concept of a pde cannot predate this date. Many of the ideas for pdes actually arise from problems in differential geometry (Riemann, Guass, Riccati,...). There was also a considerable amount of work in what is now refered to a classical mechanics by Lagrange, Euler and others.
There's quite a bit of historical discussion in
Applications of Lie groups to differential equations by P. J. Olver.
While discussions of pdes with relevant references can be found in volume II of Courant and Hilbert and the book "Partial differential equations" by Garabedian.
The book on differential geometry by Struik also has a lot of historical references,
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