Divergence and curl example
For
F : R3
R3, the formulas for the divergence and curl
are
| div F | = |
|
| curl F | = |
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
| div(F) = 0 + x + 1 = x + 1. |
| 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.
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