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Math Help - Divergence and Curl

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by thepongofping View Post

    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!
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  3. #3
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    Quote Originally Posted by thepongofping View Post
    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.
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  4. #4
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    Curl & Divergence

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

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

    Curl F
    = (2yz e^(x+y) - 2xz cos y, -(2xz e^(x+y) - (-xy)), z cos y - (2y - xz))
    =(2yz e^(x+y) - 2xz cos y, -2xz e^(x+y) - xy, z cos y - 2y + xz).
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  5. #5
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    The divergence is certainly correct. I'll leave the curl to pickslides!
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  6. #6
    Newbie sherryl's Avatar
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    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.
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