# Book: Partial Differential Equations (Walet)


A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. A special case is ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalized similarly in terms of PDEs.

Thumbnail: A visualization of a solution to the two-dimensional heat equation with temperature represented by the third dimension (Public Domain; Oleg Alexandrov). The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.​​

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