In mathematics, the Euler–Poisson–Darboux equation is the

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similarly to ...

u_+\frac=0.

This equation is named for Siméon Poisson,

Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...

, and

Gaston Darboux Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician. Life According this birth certificate he was born in Nîmes in France on 14 August 1842, at 1 am. However, probably due to the midnig ...

. It plays an important role in solving the classical

wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and s ...

. This equation is related to :

u_+\fracu_r-u_=0,

x=r+t

y=r-t

, where

N=\frac

and some sources quote this equation when referring to the Euler–Poisson–Darboux equation.

References

External links

* Differential calculus Partial differential equations Leonhard Euler {{mathanalysis-stub