Differential equations

Abstract

Differential equations arise frequently in mathematical and physical theory because the calculus limit so often gives simple relations. In physical theory we may have simple relations for the rates of change with time, distance or temperature of such quantities as energy (thermal conductivity, heat capacity), momentum (force, viscosity) or amount of substance (fluid flow, reaction kinetics, heat of reaction). These theories give rise to equations containing derivatives, and comparison with experiment requires the solution of such equations by integration, the purpose of which is to eliminate the differentials.