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Analysis (implicit and inverse func thrms)

  1. Feb 16, 2008 #1
    1. The problem statement, all variables and given/known data

    The equations:

    uz - 2e^(vz) = 0
    u - x^2 - y^2 = 0
    v^2 - xy*log(v) - 1 = 0

    define z (implicitly) as a function of (u,v) and (u,v) as a function of (x,y),
    thus z as a function f (x,y)

    Describe the role of the inverse and implicit function theorems in the
    above statement and compute

    [tex]\partial[/tex]z/[tex]\partial[/tex]x(0,e).

    (Note that when x=0 and y=e, u=e^2, v=1 and z=2)



    2. Relevant equations

    Implicit and inverse function theorems

    3. The attempt at a solution

    I'm finally starting to get a grasp on the 2 theorems and their
    respective proofs (I hope), but as far as explaining their role in this
    concrete example I'm a little lost.
    If anyone can put me on the right path, it would be greatly appreciated.
    (This is for an undergrad analysis course)
     
    Last edited: Feb 16, 2008
  2. jcsd
  3. Feb 16, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Perhaps it would be a good idea to check on exactly what the "implicit function theorem" and ""inverse function theorem" say!

    In particular you might want to determine where, if ever, the Jacobian is zero.
     
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