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Math Help - Multivariable Calculus Parametrization

  1. #1
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    Multivariable Calculus Parametrization

    I am trying to find the surface area.

    So I know that once I have the parameters, I can find Tu, Tv and cross them to find the normal vector.

    However, I seem to have trouble whenever the function isn't given in terms of u and v.

    This is the problem I am looking at:-

    Calculate [Double Integral] f(x,y,z)dS for the given surface and function

    y=9-z^2, 0<=x<=3, 0<=z<=3, f(x,y,z) = z
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  2. #2
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    Re: Multivariable Calculus Parametrization

    The surface is defined by y= 9-  z^2 with no condition on x. So use x and z as parameters. x= u, y= 9- v^2, z= v.
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  3. #3
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    Re: Multivariable Calculus Parametrization

    Thanks!

    That works.

    I've got a new problem.

    Verify Stokes Theorem for the given vector field and surface, oriented with an upward pointed normal.

    F = <2xy, x,y+z>, the surface z = 1 - x^2 -y^2 for x^2 +y^2<=1

    For using line integrals, what should I use my c(t) as?

    For the Stokes theorem part, I can calculate the curl, but again I don't know how to go from there (as in find the boundaries and dS).

    Thanks!
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  4. #4
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    Re: Multivariable Calculus Parametrization

    Quote Originally Posted by federernadal View Post
    Thanks!

    That works.

    I've got a new problem.

    Verify Stokes Theorem for the given vector field and surface, oriented with an upward pointed normal.

    F = <2xy, x,y+z>, the surface z = 1 - x^2 -y^2 for x^2 +y^2<=1

    For using line integrals, what should I use my c(t) as?

    For the Stokes theorem part, I can calculate the curl, but again I don't know how to go from there (as in find the boundaries and dS).

    Thanks!
    please start a new problem w/ a new thread.
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