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Green's Theorem & Line Integrals

  1. Mar 25, 2008 #1
    1. The problem statement, all variables and given/known data
    [​IMG]
    Note:
    path-connected means arcwise-connected
    C^0 means continuous
    ⊿f=Laplacian=(f)xx+(f)yy
    df/dn = grad f . n

    2. Relevant material
    Green's theorem, line integrals, ...


    3. The attempt at a solution
    The only part I can finish is part (ii):
    (ii) follows from the vector version of Green's theorem [​IMG] by letting F=grad f

    How can I do parts (i) and (iii)?
    And provided that I have proved (i), (ii), and (iii), how would these results aid me in proving the actual problem?

    Any help or hints would be greatly appreciated![​IMG]
     
    Last edited: Mar 25, 2008
  2. jcsd
  3. Mar 26, 2008 #2
    I seriously need help with parts (i) and (iii)...
     
  4. Mar 26, 2008 #3
    Well, I've solved part (i) as well:
    [​IMG]
    Then use squeeze theorem...


    And now I am stuck only on part (iii), please help!
     
  5. Mar 26, 2008 #4
    Provided that I have proved (i), (ii), and (iii), how would these results aid me in proving the actual problem? (i.e. to prove that f is constant on U)
     
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