Divergence and curl example

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### Multivariable analysis

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### Divergence and curl example

Back to Lecture #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).