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I would like to know something like what's the first PDE etc.

Could you recommend book on the history of PDE/ODE?

thanks.

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    Have you read the men of mathematics by bell? I mean this subject is so big, that history could mean a lot of things! If you mean the history involving the big names like euler and newton, then this book is perfect. http://books.google.com/books?id=BLFL3coT5i4C&printsec=frontcover&dq=men+of+mathematics&hl=en&ei=riZ8TJ7LJYK0lQeys7XrCw&sa=X&oi=book_result&ct=book-thumbnail&resnum=1&ved=0CDUQ6wEwAA#v=onepage&q&f=false2010-08-30
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    A recent post on MathOverflow with a similar topic: [History of ODE and PDE reference request](https://mathoverflow.net/q/308880).2018-08-22

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You can refer to these articles:

1) http://www.jstor.org/pss/2298771

2) www.johnsasser.com/pdf/article13.pdf

3) http://www.math.niu.edu/~rusin/known-math/index/34-XX.html#HIST

Bit of surfing yourself for things should help you out!

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    Community wiki?2010-08-30
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SIAM (The Society for Industrial and Applied Mathematics) has collected some oral interviews and other materials that have some bearing on the history of ordinary and partial differential equations:

http://history.siam.org/

There is also a lot of material on this topic that is related to more specialized historical studies:

History of Hydraulics by Hunter Rouse and Simon Ince

A History of the Theory of Elasticity and of the Strength of Materials ... by Isaac Todhunter

and work on the Euler equations and the Navier-Stokes equations.

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If I were you I would start by looking for similar threads.. ;)

Could you recommend some classic textbooks on ordinary/partial differential equation?

Good 1st PDE book for self study