Laplace's Equation is a second-order partial differential equation that describes the behavior of scalar fields, such as temperature or electric potential, in a given region. It is expressed as ∇²φ = 0, where φ represents the scalar field and ∇² is the Laplacian operator. This equation is fundamental in various fields, including physics and engineering, as it characterizes steady-state solutions where there are no local maxima or minima. Solutions to Laplace's Equation are known as harmonic functions. These functions exhibit smoothness and are often used in problems involving potential theory, fluid dynamics, and electrostatics. The equation plays a crucial role in understanding how physical quantities distribute themselves in space under equilibrium conditions.