Editing Heat equation (section)

{{Short description|Partial differential equation describing the evolution of temperature in a region}}
{{More citations needed|date=August 2024}}
[[Image:Heat eqn.gif|thumb|upright=1.8|Animated plot of the evolution of the temperature in a square metal plate as predicted by the heat equation. The height and redness indicate the temperature at each point.  The initial state has a uniformly hot hoof-shaped region (red) surrounded by uniformly cold region (yellow). As time passes the heat diffuses into the cold region.]]

In [[mathematics]] and [[physics]] (more specifically [[thermodynamics]]), the '''heat equation''' is a [[parabolic partial differential equation]]. The theory of the heat equation was first developed by [[Joseph Fourier]] in 1822 for the purpose of modeling how a quantity such as [[heat]] diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental in many parts of both pure and applied mathematics.