The heat equation is of fundamental importance in diverse scientific fields.

The heat equation is used to determine the change in the function u over time.

The heat equation is used in probability and describes random walks.

Let us consider the heat equation for one space variable.

The (time) stationary heat equation is not dependent on time.

A physical interpretation of this principle comes from the heat equation.

Replace by and divide through by to yield the heat equation.

This is an explicit method for solving the one-dimensional heat equation.

In 1822, Fourier first used this technique to solve the heat equation.

This law forms the basis for the derivation of the heat equation.