harmonic functions

Harmonic functions are mathematical functions that satisfy a specific condition called Laplace's equation. They are smooth and continuous, meaning they don't have abrupt changes. In practical terms, harmonic functions can describe various physical phenomena, such as the distribution of heat in a solid or the flow of fluids. They are important in fields like physics and engineering because they help us understand how things behave in balance, like the surface of a stretched membrane or the potential energy in a gravitational field. Essentially, they provide insights into systems where equilibrium is achieved.