partial differential equation


partial differential equation

noun

Definition of PARTIAL DIFFERENTIAL EQUATION

:  a differential equation containing at least one partial derivative

First Known Use of PARTIAL DIFFERENTIAL EQUATION

1845

partial differential equation

noun    (Concise Encyclopedia)

In mathematics, an equation that contains partial derivatives, expressing a process of change that depends on more than one independent variable. It can be read as a statement about how a process evolves without specifying the formula defining the process. Given the initial state of the process (such as its size at time zero) and a description of how it is changing (i.e., the partial differential equation), its defining formula can be found by various methods, most based on integration. Important partial differential equations include the heat equation, the wave equation, and Laplace's equation, which are central to mathematical physics.

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