# Definition:Partial Differential Equation/Historical Note

## Historical Note on Partial Differential Equation

The first partial differential equation to be recognised as such was the one which defines the form of a vibrating string.

It was discussed by Leonhard Paul Euler and Jean le Rond d'Alembert in $1747$.

Joseph Louis Lagrange completed the solution of that equation.

Between $1772$ and $1785$ he also addressed the partial differential equation of the first order.

He established the general solution of the linear equation, and classified the various kinds of non-linear equation.

These theories are still being developed.

Others who have contributed include George Chrystal and Micaiah John Muller Hill.

Other methods were given by Paul Charpit and Carl Gustav Jacob Jacobi.

Higher order partial differential equations have been investigated by Pierre-Simon de Laplace, Gaspard Monge, André-Marie Ampère and Jean-Gaston Darboux.

Work is still being done on these equations.

## Sources

- 1952: H.T.H. Piaggio:
*An Elementary Treatise on Differential Equations and their Applications*(revised ed.) ... (previous) ... (next): Historical Introduction