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partial differential equation

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partial differential equation

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.


partial differential equation [′pär·shəl ‚dif·ə′ren·chəl i‚kwā·zhən]
(mathematics)
An equation that involves more than one independent variable and partial derivatives with respect to those variables.


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The textbook and accompanying software is significantly more detailed than typical introductions to partial differential equations, they say, and provide examples on setting up physical problems as mathematical ones, solving partial differential equations under different types of boundary conditions, working with special functions, and carrying out a Fourier analysis using these functions.
Numerical methods for partial differential equations use different discretizations of space and time and have different mathematical properties, like convergence and accuracy.
And so this ease of use is one of the notable features of the latest release, Maple 12-which also has improvements to solvers for differential equations, partial differential equations, and algebraic equations.
 
 
 
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