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Math Help - Surface Integrals

  1. #1
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    Surface Integrals

    Hi,

    is the formula for ds equal to

    <br />
ds = sqrt(( (pz/px)^2 + (pz/py)^2 + 1))
    where p = partial derivative

    many thanks


    Problem:
    For the parametrically defined surface S given by , find each of the following differentials.



    In , dS = ________ du dv In , dS = ___________ du dv

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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by althaemenes View Post
    Hi,

    is the formula for ds equal to

    <br />
ds = sqrt(( (pz/px)^2 + (pz/py)^2 + 1))
    where p = partial derivative

    many thanks


    Problem:
    For the parametrically defined surface S given by , find each of the following differentials.



    In , dS = ________ du dv In , dS = ___________ du dv

    d\vec S =\vec n \cdot dS=\frac{(\vec r_u \times\vec  r_v)}{|\vec r_u \times \vec r_v|} |\vec r_u \times \vec r_v|dA=(\vec r_u \times \vec r_v)dA
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    d\vec S =\vec n \cdot dS=\frac{(\vec r_u \times\vec r_v)}{|\vec r_u \times \vec r_v|} |\vec r_u \times \vec r_v|dA=(\vec r_u \times \vec r_v)dA
    okay, So I got <0,0,0> for the first ds and 0 for the second ds

    Given,


    <br />
r_u=-vsin(uv)i + vcos(uv)j + 0k<br /> <br />

    <br />
r_v=-usin(uv)i + ucos(uv)j + 0k<br /> <br />

    (\vec r_u \times \vec r_v)dA = 0dA

    but its wrong!!!
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  4. #4
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    sorry!!!

    I did it wrong the first time....

    Now I got it... Thanks a lot ..... YOU ROCK
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  5. #5
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    I am working on the same question. I got the answer to the first part:

    <vcos(uv),vsin(uv),0>

    but I cant figure out the answer to the second part. Any help would be greatly appreciated.
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  6. #6
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    reply

    for the second part the answer is: v
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