The branch of mathematics concerned with changes in a dependent variable due to discrete changes in the independent variable.
To Lagrange, perhaps more than to any other, the theory of differential equations is indebted for its position as a science, rather than a collection of ingenious artifices for the solution of particular problems. To the calculus of finite differences he contributed the beautiful formula of interpolation which bears his name; although substantially the same result seems to have been previously obtained by Euler.
The general method of constructing formulae of this kind involves the use of the integral calculus and of the calculus of finite differences.
Formulae of the calculus of finite differences enable us from the chronograph records to infer the velocity and retardation of the shot, and thence the resistance of the air.