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The Laplace Operator is an operator defined as the divergence of the gradient of a function. | The Laplace Operator is an operator defined as the divergence of the gradient of a function. | ||

− | + | <math>{\large\Delta=\nabla\cdot\nabla=\nabla^{2}=\bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg]\cdot\bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg]=\sum\limits_{n=1}^{N}\frac{\partial^{2}}{\partial x^{2}_{n}}}</math> | |

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[[Walther_MA271_Fall2020_topic9|Back to main page]] | [[Walther_MA271_Fall2020_topic9|Back to main page]] |

## Latest revision as of 23:24, 5 December 2020

**Introduction**

The Laplace Operator is an operator defined as the divergence of the gradient of a function. $ {\large\Delta=\nabla\cdot\nabla=\nabla^{2}=\bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg]\cdot\bigg[\frac{\partial}{\partial x_{1}},\cdots,\frac{\partial}{\partial x_{N}}\bigg]=\sum\limits_{n=1}^{N}\frac{\partial^{2}}{\partial x^{2}_{n}}} $