Laplacian: Difference between revisions

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imported>Gemma E. Mason
m (also linked to 'Cartesian coordinates')
imported>Milton Beychok
m (Added a {{subpages}} template to top of page to create a proper Citizendium article. Also bolded '''Laplacian''' in first sentence.)
 
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The Laplacian is a differential operator of the form<br />
{{subpages}}
The''' Laplacian''' is a differential operator of the form<br />
<math>\sum_{i}\frac{\partial^{2}}{\partial x_{i}^{2}}</math><br />
<math>\sum_{i}\frac{\partial^{2}}{\partial x_{i}^{2}}</math><br />
where <math>x_{i}</math> are [[Cartesian coordinates]].  The Laplacian is usually denoted by the symbol <math>\Delta</math> or written as the gradient squared <math>\nabla^{2}</math>.
where <math>x_{i}</math> are [[Cartesian coordinates]].  The Laplacian is usually denoted by the symbol <math>\Delta</math> or written as the gradient squared <math>\nabla^{2}</math>.

Latest revision as of 21:40, 3 September 2010

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The Laplacian is a differential operator of the form

where are Cartesian coordinates. The Laplacian is usually denoted by the symbol or written as the gradient squared .

In cylindrical coordinates, the Laplacian takes the form

In spherical coordinates, the Laplacian is