rhizoverbBeta
DictionaryharmonicFunctions satisfying Laplace’s equation
adjective

harmonic

Describing a mathematical function that satisfies Laplace’s equation.

The solution was a harmonic function on the region.

Etymology
harmonGreekfitting together; harmony
+icEnglishrelating to

Greek harmonia meant a fitting together or agreement. Mathematics extended the musical family of meanings through the analysis of oscillations; harmonic became a technical label for functions satisfying Laplace’s equation.

More examples

  • A harmonic function satisfies Laplace's equation.
  • The proof examined the boundary values of a harmonic function.
  • The potential was harmonic away from the sources.

Forms

harmonic

Similar words

analytic
Analytic functions have a stronger local power-series property; real and imaginary parts of complex analytic functions are harmonic.