Partial differential equation

A Partial differential equation is a type of differential equation which relates a multivariable function to its partial derivatives. They are very commonly used in engineering and physics.

Examples

• $ \frac{\part U}{\part x}+\frac{\part U}{\part y}+U=0 $
• $ \frac{\part^2U}{\part x^2}+\frac{\part U}{\part x}+xU=\frac{\part U}{\part y} $
• $ \frac{\part^2U}{\part x^2}+\frac{\part^2U}{\part y^2}=xy $

The Diffusion Equation

$ \frac{\partial u}{\partial t} = \alpha \bigtriangledown^2 u $

The Laplace Equation

$ \bigtriangledown^2 u =0 $

The Wave Equation

$ \frac{\partial^2 u}{\partial t^2} = \alpha \bigtriangledown^2 u $

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