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...

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...

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...

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

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

Laplace transform or Fourier transform of the time domain variables or they can be taken to be phasors in which case the frequency domain equations can...

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

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...

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

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...

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...

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

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

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

periodic functions, on Laplace transforms in one and several dimensions, and on the theory of elliptic partial differential equations. A selection of Luigi...

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

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...

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

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...

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

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 +...

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...

Named after Pierre-Simon Laplace, the graph Laplacian matrix can be viewed as a matrix form of the negative discrete Laplace operator on a graph approximating...

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...

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 (...

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

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...

specific element denoted i, called the imaginary unit and satisfying the equation i 2 = − 1 {\displaystyle i^{2}=-1} ; every complex number can be expressed...

The Lorentz force on a macroscopic current is often referred to as the Laplace force. Consider a conductor of length ℓ, cross section A, and charge q...

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...