# Definition:Heat Equation

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## Contents

## Equation

The **heat equation** is a second order PDE of the form:

- $a^2 \left({\dfrac {\partial^2 w} {\partial x^2} + \dfrac {\partial^2 w} {\partial y^2} + \dfrac {\partial^2 w} {\partial z^2}}\right) = \dfrac{\partial w} {\partial t}$

## Also known as

Some sources refer to this equation as **Fourier's equation**, for Joseph Fourier, but while the attribution is clear, this usage is rare.

## Also see

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VI}$: On the Seashore - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 1.1$: Introduction - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**heat equation**