Differential equations are a basic tool for understanding the physical world. Indeed, since Newton's laws of motion all the description of the physical world is done in the language of differential equations. In this page, we list some of the most important equations in mathematical physics. In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ... Newtons laws of motion are three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ...

• Laplace's equation

• Heat equation

• Wave equation

• Maxwell's equations

• Einstein's field equation

• Schrödinger equation

• Navier-Stokes equations

• Euler-Lagrange equations

Laplaces equation is a partial differential equation named after its discoverer Pierre-Simon Laplace. ... The heat equation or diffusion equation is an important partial differential equation which describes the variation of temperature in a given region over time. ... The wave equation is an important partial differential equation which generally describes all kinds of waves, such as sound waves, light waves and water waves. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... In physics, the Einstein field equation or Einstein equation is a differential equation in Einsteins theory of general relativity. ... In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ... In fluid dynamics, the Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes are a set of nonlinear partial differential equations that describe the flow of fluids such as liquids and gases. ... In physics, the action principle is an assertion about the nature of motion, from which the trajectory of an object subject to forces can be determined. ...

Bibliography

• A. D. Polyanin and V. F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Chapman & Hall/CRC Press, 2004. ISBN 1584883553.
• A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, 2002. ISBN 1584882999.
• Refaat El Attar, Ordinary Differential Equations, Lulu Press, Morrisville NC, 2005. ISBN 1-41163-920-0. [1].

External links

• Linear Equations of Mathematical Physics - from EqWorld
• Nonlinear Equations of Mathematical Physics - from EqWorld