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
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