In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as ∇ ∇ 2 f = 0 or Δ Δ f = 0 , where Δ Δ = ∇ ∇ ⋅ ⋅ ∇ ∇ = ∇ ∇ 2 is the Laplace operator, ∇ ∇ ⋅ ⋅ is the divergence operator (also symbolized "div"), ∇ ∇ is the gradient operator (also symbolized "grad"), and f ( x , y , z ) is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function.