The Heat Equation is a fundamental partial differential equation that describes how heat diffuses through a given region over time. It mathematically models the distribution of temperature in a material, taking into account factors like thermal conductivity and initial temperature conditions. 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 how temperature changes in different environments, aiding in applications such as climate modeling and material design.