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==Coordinate Conversions for the Laplace Operator==
 
==Coordinate Conversions for the Laplace Operator==
  
It is most common to use the Laplace Operator <math>\Delta<math> in three-dimensions, as that is the dimensionality of our physical universe. Thus, the Laplace Operator is often used in 3-D Cartesian coordinates, cylindrical coordinates, and spherical coordinates.
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It is most common to use the Laplace Operator <math>\Delta<\math> in three-dimensions, as that is the dimensionality of our physical universe. Thus, the Laplace Operator is often used in 3-D Cartesian coordinates, cylindrical coordinates, and spherical coordinates.
  
 
<math>
 
<math>
 
\Delta f=\frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}+\frac{\partial^{2} f}{\partial z^{2}}\
 
\Delta f=\frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}+\frac{\partial^{2} f}{\partial z^{2}}\
 
<\math>
 
<\math>

Revision as of 15:04, 6 December 2020

Coordinate Conversions for the Laplace Operator

It is most common to use the Laplace Operator $ \Delta<\math> in three-dimensions, as that is the dimensionality of our physical universe. Thus, the Laplace Operator is often used in 3-D Cartesian coordinates, cylindrical coordinates, and spherical coordinates. <math> \Delta f=\frac{\partial^{2} f}{\partial x^{2}}+\frac{\partial^{2} f}{\partial y^{2}}+\frac{\partial^{2} f}{\partial z^{2}}\ <\math> $

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