As a precursor to carrying out calculus operations such as derivatives and integrals, a mathematical expression will have to be placed in the differential form for the application of the methods of continuous variables. For example, a finite difference expression occurs in the development of the relationship for radioactive decay:Application to radioactive decay
It is standard practice to use the Greek letter to represent a finite difference. Often the finite difference relationship is only approximately true and is exactly true only in the limit where the differences become infinitesmally small. In this limit, the time interval t becomes vanishingly small and as a result, the number of decays N also becomes vanishingly small. The is replaced by the differential symbol d and the resulting form
is said to be the differential form of the expression.