Definition:Harmonic (Analysis)

This page is about harmonic in the context of analysis. For other uses, see harmonic.

Definition

A harmonic is a solution $\phi$ to Laplace's equation in $2$ dimensions:

$\nabla^2 \phi = 0$

that is:

$\dfrac {\partial^2 \phi} {\partial x^2} + \dfrac {\partial^2 \phi} {\partial y^2} = 0$

Also see

• Results about harmonics in the context of analysis can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): harmonic: 1.