The Laplace operator, often denoted as ∆ or ∇², is a second-order differential operator used in mathematics and physics. It measures the rate at which a quantity changes in space, providing insights into various phenomena such as heat conduction, fluid flow, and electromagnetic fields. The operator is defined as the divergence of the gradient of a function, making it a crucial tool in calculus and partial differential equations. In Euclidean space, the Laplace operator can be applied to scalar functions, resulting in a new function that describes how the original function behaves around a point. It plays a significant role in potential theory and is essential in solving problems related to harmonic functions, which are functions that satisfy the Laplace equation (∆f = 0).