Laplace's equation (redirected from Harmonic equation)

Laplace's equation

In mathematics, a partial differential equation whose solutions (harmonic functions) are useful in investigating physical problems in three dimensions involving gravitational, electrical, and magnetic fields, and certain types of fluid motion. Named for Pierre-Simon Laplace, the equation states that the sum of the second partial derivatives (the Laplace operator, or Laplacian) of an unknown function is zero. It can apply to functions of two or three variables, and can be written in terms of a differential operator as ΔF = 0, where Δ is the Laplace operator.

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Laplace's equation [lə′pläs·əz i‚kwā·zhən]

(acoustics)

An equation for the speedcof sound in a gas; it may be writtenc= √(γp/ρ), wherepis the pressure, ρ is the density, and γ is the ratio of specific heats.

(mathematics)

The partial differential equation which states that the sum of all the nonmixed second partial derivatives equals 0; the potential functions of many physical systems satisfy this equation.