mathematics, an Euler–Cauchy equation, or Cauchy–Euler equation, or simply Euler's equation, is a linear homogeneous ordinary differential equation with variable...

been given simple yet ambiguous names such as Euler's function, Euler's equation, and Euler's formula. Euler's work touched upon so many fields that he is...

In mathematics, Euler's differential equation is a first-order non-linear ordinary differential equation, named after Leonhard Euler. It is given by: d...

variations and classical mechanics, the Euler–Lagrange equations are a system of second-order ordinary differential equations whose solutions are stationary points...

science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with...

for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their...

In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives...

dynamics, the Euler equations are a set of partial differential equations governing adiabatic and inviscid flow. They are named after Leonhard Euler. In particular...

In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a...

characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given nth-order differential equation or...

Lane-Emden equation Emden–Chandrasekhar equation Hénon–Heiles system Equation of motion Euler's rotation equations in rigid body dynamics Euler–Lagrange...

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other...

backward Euler method (or implicit Euler method) is one of the most basic numerical methods for the solution of ordinary differential equations. It is similar...

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution...

Eruditorum, 1744 The title page of Euler's Methodus inveniendi lineas curvas Euler's 1760 world map Euler's 1753 map of Africa Euler is listed by an academic genealogy...

valid if x is a complex number, and is also called Euler's formula in this more general case. Euler's formula is ubiquitous in mathematics, physics, chemistry...

Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary...

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...

In mathematics, a linear differential equation is a differential equation that is linear in the unknown function and its derivatives, so it can be written...

an extension of the Euler method for ordinary differential equations to stochastic differential equations named after Leonhard Euler and Gisiro Maruyama...

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its...

The sine-Gordon equation is a second-order nonlinear partial differential equation for a function φ {\displaystyle \varphi } dependent on two variables...

constant. With this time-dependent loading, the beam equation will be a partial differential equation: ∂ 2 ∂ x 2 ( E I ∂ 2 w ∂ x 2 ) = − μ ∂ 2 w ∂ t 2 ....

g(0) = I and the lines t ↦ tv are geodesics through 0. Euler's equations imply the matrix equation g(v)v = v, a key result, usually called the Gauss lemma...

In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named after mathematicians...

Hamilton–Jacobi–Bellman equation from dynamic programming. The Hamilton–Jacobi equation is a first-order, non-linear partial differential equation − ∂ S ∂ t = H...

A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when...

Bernoulli equation may refer to: Bernoulli differential equation Bernoulli's equation, in fluid dynamics Euler–Bernoulli beam equation, in solid mechanics...

mechanics and information theory, the Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability...

The Cauchy momentum equation is a vector partial differential equation put forth by Augustin-Louis Cauchy that describes the non-relativistic momentum...