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The Laplace operator, represented by <math>\Delta</math>, is defined as the divergence of the gradient of a function. | The Laplace operator, represented by <math>\Delta</math>, is defined as the divergence of the gradient of a function. | ||
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\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}}} | \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> | </math> | ||
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| + | [[Walther_MA271_Fall2020_topic9|Back to main page]] | ||
Revision as of 23:12, 5 December 2020
Definition of the Laplace Operator
The Laplace operator, represented by $ \Delta $, is 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}}} $
