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.

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.

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No references found	Specifically, Laplace's equation is solved in n dimensions to obtain the electric potential, and hence the electric field. Electrostatics in n dimensions with illustrative examples by Journal of the Alabama Academy of Science Anwane gives readers sufficient background in each section and in the appendix to handle vector analysis, the electric field, density of displacement flux, energy and potential, Poisson's and LaPlace's equations, the magnetic field, Maxwell's equations for time-varying fields, the uniform plane wave and the wave guides. Fundamentals of electromagnetic fields. (CD-ROM included) by SciTech Book News For such an "ideal" flow, the conservation of mass equation may be expressed as Laplace's equation, [[nabla]. Real-time prediction of rack-cooling performance by VanGilder, James W.; Shrivastava, Saurabh K. / ASHRAE Transactions	Lapin, Albert Lapin, Albert Ianovich Lapin, Artur Lapin, Artur Ianovich Lapin, Petr Lapin, Petr Ivanovich Lapin, Sergei Lapin, Sergei Georgievich LaPine State Park lapis lapis lazuli Lapita culture Lapitskii, Iosif Lapitskii, Iosif Mikhailovich Laplace Laplace Azimuth Laplace Invariant Plane Laplace irrotational motion Laplace law Laplace Nebular Hypothesis Laplace Operator Laplace Point Laplace Theorem Laplace Transform Laplace's Differential Equation Laplace's equation Laplace's expansion Laplace's irrotational motion Laplace's Law Laplace's measure of dispersion Laplace, Pierre Simon, Marquis de Laplace, Pierre-Simon, marquis de Laplacian Laplacian speed of sound Lapland LapLink LapLink cable LAPM Lapointe, Ernest Laporte selection rule Laporte, Otto Laporte, Roland LaPorte, William Lapouge, Georges Vacher de Lapp Lapparent, Albert-Auguste Lappé, Frances Moore lapped dovetail lapped tenons Lappeenranta lappet	Lapithus Lapitskii, Iosif Lapitskii, Iosif Mikhailovich LAPJ LAPK LAPL Laplace Laplace Laplace Azimuth Laplace domain Laplace equation Laplace Invariant Plane Laplace irrotational motion Laplace law Laplace Nebular Hypothesis Laplace operator Laplace operator Laplace Pierre Simon de Laplace Point Laplace Theorem Laplace transform Laplace transform Laplace Transformation Laplace transformations Laplace transforms Laplace's Coefficients Laplace's differential equation Laplace's differential equation Laplace's equation Laplace's expansion Laplace's irrotational motion Laplace's law Laplace's law Laplace's measure of dispersion Laplace, Pierre Simon, marquis de Laplace, Pierre Simon, marquis de Laplace, Pierre-Simon, marquis de Laplace-Beltrami operator Laplace-Beltrami operator Laplace-Carson Transform Laplace-de Rham operator Laplace-de Rham operator Laplace-Runge-Lenz vector Laplace-Stieltjes transform Laplaces equation Laplacian Laplacian Laplacian Eigenmap Laplacian matrix Laplacian of a Gaussian Laplacian operator Laplacian operator Laplacian plane Laplacian Pyramid Hierarchical Coding Laplacian speed of sound Lapland Lapland Lapland (disambiguation) Lapland (disambiguation)

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Specifically, Laplace's equation is solved in n dimensions to obtain the electric potential, and hence the electric field.

Electrostatics in n dimensions with illustrative examples by Journal of the Alabama Academy of Science

Anwane gives readers sufficient background in each section and in the appendix to handle vector analysis, the electric field, density of displacement flux, energy and potential, Poisson's and LaPlace's equations, the magnetic field, Maxwell's equations for time-varying fields, the uniform plane wave and the wave guides.

Fundamentals of electromagnetic fields. (CD-ROM included) by SciTech Book News

For such an "ideal" flow, the conservation of mass equation may be expressed as Laplace's equation, [[nabla].

Real-time prediction of rack-cooling performance by VanGilder, James W.; Shrivastava, Saurabh K. / ASHRAE Transactions

Lapin, Albert

Lapin, Albert Ianovich

Lapin, Artur

Lapin, Artur Ianovich

Lapin, Petr

Lapin, Petr Ivanovich

Lapin, Sergei

Lapin, Sergei Georgievich

LaPine State Park