| Line 1: | Line 1: | ||
[[Category:MA271Fall2020Walther]] | [[Category:MA271Fall2020Walther]] | ||
| + | ==Vector Laplacian== | ||
| + | |||
| + | The Laplace operator is originally an operation where you input a scalar function and it returns a scalar function. However, there is an alternate version of the Laplace operator that can be performed on vector fields. | ||
| + | |||
| + | The vector Laplacian is defined as: | ||
| + | |||
| + | <math>\Delta F = \nabla^2 F = \nabla (\nabla \cdot F) - \nabla \times (\nabla \times F) \\</math> | ||
| + | |||
| + | where F is a vector field. In Cartesian coordinates, the vector Laplacian simplifies to the following: | ||
| + | |||
| + | <math> | ||
| + | \Delta F = | ||
| + | \left[\begin{array} {1} | ||
[[Walther_MA271_Fall2020_topic9|Back to main page]] | [[Walther_MA271_Fall2020_topic9|Back to main page]] | ||
Revision as of 00:03, 7 December 2020
Vector Laplacian
The Laplace operator is originally an operation where you input a scalar function and it returns a scalar function. However, there is an alternate version of the Laplace operator that can be performed on vector fields.
The vector Laplacian is defined as:
$ \Delta F = \nabla^2 F = \nabla (\nabla \cdot F) - \nabla \times (\nabla \times F) \\ $
where F is a vector field. In Cartesian coordinates, the vector Laplacian simplifies to the following:
$ \Delta F = \left[\begin{array} {1} [[Walther_MA271_Fall2020_topic9|Back to main page]] $
