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]] $

Alumni Liaison

Prof. Math. Ohio State and Associate Dean
Outstanding Alumnus Purdue Math 2008

Jeff McNeal