Rotational

### 13.7.5 Rotational

The curl of a three-dimensional vector field F=[F1,F2,F3] with variables [x1,x2,x3] is

curl F= | ⎡ ⎢ ⎢ ⎣ |
∂ F3
∂ x2
| − |
∂ F2
∂ x3
| , |
∂ F1
∂ x3
| − |
∂ F3
∂ x1
| , |
∂ F2
∂ x1
| − |
∂ F1
∂ x2
|  | ⎤ ⎥ ⎥ ⎦ | .

The curl command computes the curl of a three dimensional vector field (note that it must be three dimensional).

- curl takes two arguments:
  - F, a three-dimensional vector field, given as a list of three expressions depending on three variables.
  - vars, a list of the three variable names.
- curl(F,vars) returns the curl of the vector field.

#### Example

curl([x*z,-y^2,2*x^y],[x,y,z])

| ⎡ ⎣ | 2 lnx· xy,x−2 y xy−1,0 | ⎤ ⎦