Harmonic Function

A harmonic function is a type of mathematical function that is smooth and well-behaved, meaning it has no abrupt changes or breaks. In physical terms, it often describes systems in balance, such as how heat spreads in a material or how fluid flows without turbulence. Mathematically, harmonic functions satisfy specific equations (Laplace's equation) that make them equal to the average value of their values in nearby locations. This property leads to applications in areas like physics, engineering, and even finance, where understanding equilibrium and smooth behavior is essential.