Laplace's equation

Laplace's equation is a partial differential equation named after its discoverer Pierre-Simon Laplace.

Laplace's equation for a scalar variable φ(x,y,z) in a 3D space with unit basis vectors i, j and k can be written as

∇² φ = 0

where the operator ∇ stands for (∂/∂x i + ∂/∂y j + ∂/∂z k)

Expanding this into its full component form, we have:

∂²/∂x² φ(x,y,z) + ∂²/∂y² φ(x,y,z) + ∂²/∂z² φ(x,y,z) = 0

Solutions of Laplace's equation are important in many fields of science, notably the fields of electromagnetism and astronomy.

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External links:

• Biography of Pierre-Simon Laplace