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Homework Help: Implicit function theorem

  1. Aug 4, 2007 #1
    1. The problem statement, all variables and given/known data

    Understanding the proof of the implicit function theorem.

    2. Relevant equations

    May assume the inverse function theorem.

    3. The attempt at a solution

    I'm following a proof given on the net:

    http://ocw.mit.edu/NR/rdonlyres/Mathematics/18-994Fall-2004/5A4796E8-2EFB-493C-8201-4743AA4EB1EE/0/chapter4.pdf [Broken]

    since I'm unhappy with my lecturer's explanation.

    The only thing I'm not clear about in this proof is the fact that the inverse function h is of the form [itex]h(x,y) = (x,k(x,y))[/itex] for some differentiable function k. Apparently this is clear but I just don't see it.

    Any help would be appreciated.
    Last edited by a moderator: May 3, 2017
  2. jcsd
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