Laplace's Equation


Output: Press calculate


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Formula: Δu = 0

Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace. In two or more dimensions, it is represented as Δu = 0, where Δu (the Laplacian of u) is the sum of the second partial derivatives of u with respect to the spatial coordinates. This equation describes the behavior of harmonic functions, and it arises in various areas of physics, including heat conduction, fluid dynamics, and electromagnetism.

Tags: Calculus, Partial Differential Equation, Harmonic Function, Physics