side of this equation is the Laplace operator, and the entire equation Δu = 0 is known as Laplace's equation. Solutions of the Laplace equation, i.e. functions...

second-order linear constant coefficient partial differential equation of elliptic type, the Laplace equation: ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 = 0. {\displaystyle {\frac...

In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics...

incompressible flow. An additional equation, which was called the adiabatic condition, was supplied by Pierre-Simon Laplace in 1816. During the second half...

the Laplace transform or Fourier transform of the time domain variables or they can be taken to be phasors. The resulting frequency domain equations are...

laws of diffusion. Taking the Laplace transform of Fick's second law yields an ordinary second-order differential equation (here in dimensionless form):...

applications, such as when solving Laplace's equation in polar coordinates. The second order Cauchy–Euler equation is x 2 d 2 y d x 2 + a x d y d x +...

H(s)={V_{\rm {out}}(s) \over V_{\rm {in}}(s)}} . Taking the Laplace transform of our differential equation and solving for H ( s ) {\displaystyle H(s)} we get...

Helmholtz equation in spherical coordinates. Bessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical...

the Laplace transform. This is a technique that maps differential or integro-differential equations in the "time" domain into polynomial equations in what...

a mixed boundary condition was solved by Stanisław Zaremba for the Laplace equation: according to himself, it was Wilhelm Wirtinger who suggested him to...

In differential equations, the Laplace invariant of any of certain differential operators is a certain function of the coefficients and their derivatives...

representation. It can be considered a discrete-time equivalent of the Laplace transform (the s-domain or s-plane). This similarity is explored in the...

Paris firm to undertake it, and it was issued under the supervision of Laplace, Cousin, Legendre (editor) and Condorcet in 1788. Lagrange's lectures on...

mathematical term symbolizing a change (Δ) in pressure (P). Young–Laplace equation Given that the head loss hf expresses the pressure loss Δp as the height...

same as those obtained via Laplace transforms. For short circuit evaluation, RL circuit is considered. The more general equation is: v i n ( t ) = v L (...

operator, box operator or sometimes quabla operator (cf. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician...

solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential equation where two of the three regular singularities...

translation of Laplace's work. Instead it endeavoured to explain his method ". . . by which these results were deduced from one general equation of the motion...

assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations. A simple...

{\displaystyle g(x)} is the Coulomb kernel or Green's function of the Laplace equation in d {\displaystyle d} dimensions, so g ( x ) = { − log ⁡ | x |  if ...

Young of the United Kingdom and Pierre-Simon Laplace of France. They derived the Young–Laplace equation of capillary action. By 1830, the German mathematician...

carried out in the time domain using differential equations, in the complex-s domain with the Laplace transform, or in the frequency domain by transforming...

equazioni generali di grado superiore al quarto ("General Theory of equations, in which the algebraic solution of general equations of degree higher than...

showed that the theory is not concerned by Laplace's critique, because due to the structure of the Maxwell equations only effects in the order v2/c2 arise...

of several variables. Solutions of boundary value problems for the Laplace equation satisfy the Dirichlet's principle. Plateau's problem requires finding...

this equation like in the mass on a spring example above, this section will analyze the frequency response of this circuit. Taking the Laplace transform...

the nth powers of deviations was noticed by several earlier, including Laplace, Kramp, Gauss, Encke, Czuber, Quetelet, and De Forest. Torque (or moment...

symbol ∇2 ≡ ∇ · ∇ is the Laplace operator. Aharoni 1996, chapter 6 Brown 1962 Griffiths 1999, chapter 6 For tables or equations for the magnetizing factors...

method of steepest descent or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral...