RE: LeoThread 2026-03-15 20-27
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Mathematical Review: Partial Differential Equations (PDE), Laplace's Equation, Gradient, Divergence
#math #sphericalharmonics #calculus #partialdifferentialequation #multivariablecalculus
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In this video I go over a quick math review of the terms involved in the Laplace equation in 3D rectangular coordinates. Laplace's equation is defined as the divergence of the gradient of a function set equal to zero. This is also written using the Laplace Operator or Laplacian (∇² or Δ). The gradient gives the direction and rate of fastest increase of a scalar function, while the divergence measures the net flux out of a point (or the extent to which a vector field acts as a source or sink at that point).