1. ## Divergence and Curl

Need to find divergence and curl of:
$F(x)=(x^{2}+y^{2}-xyz,xz^{2}\cos y,z^{2}e^{(x^{2}+y^{2})})$

I know divergence is the sum of partials w.r.t x,y, and z. But this looks so complicated! Could somebody walk me thru it?

And for curl am I setting this up correctly?
i(partial P to y - partial N to z) - j(partial P to x - partial M to z) + k(partial N to x - partial M to y)

where F(x) = (M,N,P)

Many thanx.

2. Originally Posted by thepongofping

And for curl am I setting this up correctly?
i(partial P to y - partial N to z) - j(partial P to x - partial M to z) + k(partial N to x - partial M to y)

where F(x) = (M,N,P)
Correct!

3. Originally Posted by thepongofping
Need to find divergence and curl of:
$F(x)=(x^{2}+y^{2}-xyz,xz^{2}\cos y,z^{2}e^{(x^{2}+y^{2})})$

I know divergence is the sum of partials w.r.t x,y, and z. But this looks so complicated! Could somebody walk me thru it?
What "complicated" answer did you get? Does NOT look like it should be terribly complicated to me. Remember that you take the dervivative of only the x-component with respect to x, the derivative of the y-component with respect to y, and the derivative of the z-component with respect to z.

And for curl am I setting this up correctly?
i(partial P to y - partial N to z) - j(partial P to x - partial M to z) + k(partial N to x - partial M to y)

where F(x) = (M,N,P)

Many thanx.

4. ## Curl & Divergence

Thanks for both your tips... Here's what I got. Look right?

div F
= (∂/∂x)(x² + y² - xyz) + (∂/∂y)(xz² cos y) + (∂/∂z)(z² e^(x² + y²))
= 2x - yz - xz² sin y + 2z e^(x² + y²).

Curl F
= (2yz² e^(x²+y²) - 2xz cos y, -(2xz² e^(x²+y²) - (-xy)), z² cos y - (2y - xz))
=(2yz² e^(x²+y²) - 2xz cos y, -2xz² e^(x²+y²) - xy, z² cos y - 2y + xz).

5. The divergence is certainly correct. I'll leave the curl to pickslides!

6. The CURL is correct as well.

You could have checked both the div and the curl, as well as all your integrations on WolframAlpha.

Using WolframAlpha to compute INTEGRALS
Using WolframAlpha to compute DIFFERENTIALS
Using WolframAlpha to compute CURL
Using WolframAlpha to compute DIVERGENCE

Any many more... Highly recommend it.

In fact, I was surprised to learn that most of our forum experts use these links or Mathematica software (same functionality - different packaging - not free) to check their own answers.

But of course, you must learn to do everything by hand as well. Otherwise you'll be too dependent on Mathematica/WolframAlpha.