Heat equation
Scientists have found many different ways to use the heat equation. For example, it can be used to study random walks and Brownian motion in probability theory, and it can help to resolve pixelation in image analysis. In addition, variants of the heat equation are used in financial mathematics and quantum mechanics. Scientists have also found that solutions of the heat equation are helpful in understanding hydrodynamical shocks. People have been studying the heat equation for a long time, and it is a very important topic in mathematics and physics.