هموگش ِ لاپلاس hamugeš-e Laplace
*Fr.: équation de Laplace*
A → *linear differential equation* of the second order
the solutions of which are important in many fields of science, mainly in electromagnetism,
fluid dynamics, and is often used in astronomy. It is expressed by:
∂^{2}*V*/ ∂*x*^{2} +
∂^{2}*V*/ ∂*y*^{2} +
∂^{2}*V*/ ∂*z*^{2} = 0.
Laplace's equation can more concisely expressed by: ∇^{2}*V* = 0.
The function *V* may, for example, be the potential at any point in the electric field where
there is no free charge. The general theory of solutions to Laplace's equation is
known as *potential theory*. → *Laplace*; → *equation*. |