## 17Calculus Partial Differential Equations - The Wave Equation

##### 17Calculus

The Wave Equation

The wave equation is a 2nd-order partial differential equation which describes waves.

The Wave Equation 1-Space

For $$u(x,t)$$, the 1D wave equation is $$\dfrac{\partial^2 u }{\partial t^2} = c^2 \dfrac{\partial^2 u}{\partial x^2}$$ where $$c$$ is a constant.

The Wave Equation 2-Space

For $$u(x,t)$$, the 2D wave equation is $$u_{tt} = c^2(u_{xx} + u_{yy} )$$ where $$c$$ is a constant.

Deriving The Wave Equation

### Christopher Lum - Derivation of the 1D Wave Equation

video by Christopher Lum

Other wave equation videos

video by MIT OCW

### Michel vanBiezen - The 1-D Wave Equation

video by Michel vanBiezen

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