The heat equation is a fundamental partial differential equation that describes how heat diffuses through a given region over time. It models the distribution of temperature in a material, showing how it changes in response to initial conditions and external influences. The equation is typically expressed as ∂u/∂t = α∇²u, where u represents temperature, t is time, and α is the thermal diffusivity of the material. This equation is widely used in various fields, including physics, engineering, and mathematics, to analyze heat transfer in solids, liquids, and gases. Solutions to the heat equation help predict temperature changes, which is crucial for applications like thermal management in electronics and climate modeling.