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Math Help - regular surface

  1. #1
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    regular surface

    Show that the cylinder { (x,y,z) in R^3; x^2+y^2=1} is a regular surface, and find parametrizations whose coordinate neighborhoods cover it.

    Please help.
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  2. #2
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    I won't do it for you but..

    Parameterize it using cylindrical coordinates into some parameterization S.

    To show it is regular you can
    -Show the first partial derivative of S are independant.
    or
    -Show that the cross product of the first partial derivatives of S is non zero

    there are many other ways to show it is regular.
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