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Laplace's equation - Wikipedia


In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often ...

Differential Equations - Laplace's Equation - Pauls Online Math Notes


We can see that Laplace's equation would correspond to finding the equilibrium solution (i.e. time independent solution) if there were not sources. So, this is an ...

Laplace's Equation -- from Wolfram MathWorld


A solution to Laplace's equation is uniquely determined if (1) the value of the function is specified on all boundaries (Dirichlet boundary conditions) or (2) the ...

Laplace's Equation


Laplace's Equation. • Separation of variables – two examples. • Laplace's Equation in Polar Coordinates. – Derivation of the explicit form. – An example from ...

LaPlace's and Poisson's Equations - HyperPhysics


LaPlace's and Poisson's Equations. A useful approach to the calculation of electric potentials is to relate that potential to the charge density which gives rise to it.

5.4 Solutions to Laplace's Equation in CartesianCoordinates - MIT


Having investigated some general properties of solutions to Poisson's equation, it is now appropriate to study specific methods of solution to Laplace's equation ...

3 Laplace's Equation


to solve Poisson's equation. Given the symmetric nature of Laplace's equation, we look for a radial solution. That is, we look for a harmonic function u on Rn such ...

The Laplace Equation and Harmonic Functions - MathPages


Typically we are given a set of boundary conditions and we need to solve for the ( unique) scalar field j that is a solution of the Laplace equation and that satisfies ...

Analytic Solutions to Laplace's Equation in 2-D


1. Analytic Solutions to Laplace's Equation in 2-D. Cartesian Coordinates. When it works, the easiest way to reduce a partial differential equation to a set of ...

Lecture 24: Laplace's Equation


Key Concepts: Laplace's equation; Steady State boundary value problems in two or more dimensions; Linearity;. Decomposition of a complex boundary value ...