Divergence and curl example

### Multivariable calculus and vector analysis

### Divergence and curl example

#### Back to Lectures #14 Back to Exercises #14

For F : R3 → R3, the formulas for the divergence and curl are

div F | = + + |  |
curl F | = . |  |

(The formula for curl was somewhat motivated in an earlier reading.)

Given these formulas, there isn’t a whole lot to computing the divergence and curl. Just “plug and chug,” as they say.

#### Example

Calculate the divergence and curl of F = (-y,xy,z).

Solution: Since

= 0, = x, = 1 |  |

we calculate that

div(F) = 0 + x + 1 = x + 1. |  |

Since

= -1, = y, |  |
= = = = 0, |  |

we calculate that

curl(F) = (0 - 0, 0 - 0,y + 1) = (0, 0,y + 1). |  |

Good things we can do this with math. If you can figure out the divergence or curl from the picture of the vector field (below), you doing better than I can.