(Created page with "The Laplace operator, represented by <math>\Delta</math>, is defined as the divergence of the gradient of a function. <math> {\large\Delta = \nabla\cdot\nabla = \nabla^{2} =...")
 
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==Definition of the Laplace Operator==
 
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 00:12, 6 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}}} $

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Abstract algebra continues the conceptual developments of linear algebra, on an even grander scale.

Dr. Paul Garrett