List of named differential equations


In mathematics, differential equation is a fundamental concept that is used in many scientific areas. Many of the differential equations that are used have received specific names, which are listed in this article.

Pure mathematics

Classical mechanics

So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion. Classical mechanics for particles finds its generalization in continuum mechanics.

Electrodynamics

are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. They are named after the Scottish physicist and mathematician James Clerk Maxwell, who published an early form of those equations between 1861 and 1862.

General relativity

The Einstein field equations are a set of ten partial differential equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature with the local energy and momentum within that spacetime.

Quantum mechanics

In quantum mechanics, the analogue of Newton's law is Schrödinger's equation for a quantum system. It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system's wave function.

Fluid dynamics and hydrology

Biology and medicine

Predator–prey equations

The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order, non-linear, differential equations frequently used to describe the population dynamics of two species that interact, one as a predator and the other as prey.

Chemistry

The rate law or rate equation for a chemical reaction is a differential equation that links the reaction rate with concentrations or pressures of reactants and constant parameters. To determine the rate equation for a particular system one combines the reaction rate with a mass balance for the system. In addition, a range of differential equations are present in the study of thermodynamics and quantum mechanics.

Economics and finance