History of ODE and PDE reference request

Is there any reference (book or articles) which made the history (up to the modern times) and the conceptual development of Ordinary Differential Equations and Partial Differential Equations? It will be great if it will be mentioned the key ideas and people of the past, the problems which are to be solved nowadays and the principal directions of the present research in these fields.

Thanks a lot!

4 Answers
4

Another useful reference on the history of PDE theory is "The Prehistory of The Theory of Distributions" by Jesper Lützen.

As J. Dieudonné eloquently pointed out in Chapter A V of A panorama of pure mathematics (as seen by N. Bourbaki), this is an extremely broad question:

The theory of partial differential equations has been studied incessantly
for more than two centuries. By reason of its permanent symbiosis with
almost all parts of physics, as well as its ever closer connections with many other branches of mathematics, it is one of the largest and most diverse regions of present-day mathematics, and the vastness of its bibliography defies the imagination.

For a long time, the theory of ordinary differential equations served more
or less consciously as a model for partial differential equations, and it is only rather recently that it has come to be realized that the differences between the two theories are much more numerous and more profound than the
analogies.

However, I'd like to mention at least a couple of very interesting surveys and a well-known graduate textbook:

The article by Klainerman PDE AS A UNIFIED SUBJECT could be helpful too.

You might consider reading Hairer, Wanner: Analysis by Its History, which includes differential equations in its treatment, and Bertil Gustafsson Scientific Computing which focuses on the history of computational mathematics and its applications. The latter book will be published in about two months.

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