Definition
Plain language
A type of equation that describes how something — like heat, air, or a wave — changes across space and time.
As stated in the literature
Partial Differential Equation — an equation relating a multivariable function to its partial derivatives; the governing form for fluid flow, diffusion, and wave problems, solved numerically by the methods benchmarked throughout scientific-computing work.
Also called: PDEs, partial differential equation
Why it matters: These equations govern fluids, heat, and waves, so solving them well underpins everything from weather forecasts to aircraft design.
For example, a PDE can describe how heat spreads through a metal bar over time, with temperature changing at every point.