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

hypergeometric series Euler rotation equations, a set of first-order ODEs concerning the rotations of a rigid body. Euler–Cauchy equation, a linear equidimensional...

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

incompressible and compressible flows. The incompressible Euler equations consist of Cauchy equations for conservation of mass and balance of momentum, together...

Cauchy–Euler equations are examples of equations of any order, with variable coefficients, that can be solved explicitly. These are the equations of...

corresponding eigenfunctions xn. Cauchy–Euler equation Sturm–Liouville theory Ross, Clay C (2004). Differential Equations: An Introduction with Mathematica...

differential equation Cauchy–Euler equation Riccati equation Hill differential equation Gauss–Codazzi equations Chandrasekhar's white dwarf equation Lane-Emden...

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

Cauchy's convergence test Cauchy (crater) Cauchy determinant Cauchy distribution Cauchy's equation Cauchy–Euler equation Cauchy's functional equation...

assumption of an inviscid fluid – no deviatoric stress – Cauchy equations reduce to the Euler equations. Assuming conservation of mass, with the known properties...

distribution Log-Cauchy distribution Wrapped Cauchy distribution Cauchy–Euler equation Cauchy's functional equation Cauchy filter Cauchy formula for repeated...

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

equation Wave equation Types of boundary conditions Dirichlet boundary condition Neumann boundary condition Robin boundary condition Cauchy problem Various...

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

a unique solution. It is also known as Picard's existence theorem, the Cauchy–Lipschitz theorem, or the existence and uniqueness theorem. The theorem...

In mathematics, the Euler–Poisson–Darboux(EPD) equation is the partial differential equation u x , y + N ( u x + u y ) x + y = 0. {\displaystyle u_{x,y}+{\frac...

eigenvalues of the stress tensor, which are called the principal stresses. The Euler–Cauchy stress principle states that upon any surface (real or imaginary) that...

discovered the three-dimensional wave equation. The Euler–Lagrange equation was developed in the 1750s by Euler and Lagrange in connection with their...

study of elastic deformations of solid objects. Euler formulated the partial differential equations for the motion of inviscid fluid, and laid the mathematical...

surface has Euler characteristic   χ = V − E + F = 2   . {\displaystyle \ \chi =V-E+F=2~.} This equation, stated by Euler in 1758, is known as Euler's polyhedron...

solve the PDE we recognize that it is a Cauchy–Euler equation which can be transformed into a diffusion equation by introducing the change-of-variable transformation...

This constant, χ, is the Euler characteristic of the plane. The study and generalization of this equation, specially by Cauchy and Lhuillier, is at the...

Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body. Traditionally the Newton–Euler equations is the grouping...

Leonhard Euler publishes his method. 1824 - Augustin Louis Cauchy proves convergence of the Euler method. In this proof, Cauchy uses the implicit Euler method...

equation. The qualities of the Euler's characteristic equation were later considered in greater detail by French mathematicians Augustin-Louis Cauchy...

Magnitude" extended the Euler definition to a complex variable, proved its meromorphic continuation and functional equation, and established a relation...

differential equations, the Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental...

decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form. Bernoulli's principle can be derived...

logarithm, also commonly written as ln(x) or loge(x). Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually...

{e^{z/n}}{1+z/n}}} where γ is the Euler–Mascheroni constant. Evaluated at ⁠ z = 1 2 {\displaystyle z={\tfrac {1}{2}}} ⁠ and squared, the equation ⁠ γ ( 1 2 ) ) 2 = π...