Results 1 to 2 of 2

Math Help - Evaluate the closed contour integral

  1. #1
    lpd
    lpd is offline
    Member
    Joined
    Sep 2009
    Posts
    100

    Evaluate the closed contour integral

    Consider a piecewise smooth contour \Gamma which is a triangle with vertices at z = 0, 1 + i, i. Evaluate the closed contour integral,

    $\int_\Gamma\bar{z}^3 dz

    around the triangle \Gamma by suitably parametrizing the segments of the piecewise smooth contour \Gamma.

    Why doesn’t Cauchy’s theorem apply to this integral?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by lpd View Post
    Consider a piecewise smooth contour \Gamma which is a triangle with vertices at z = 0, 1 + i, i. Evaluate the closed contour integral,

    $\int_\Gamma\bar{z}^3 dz

    around the triangle \Gamma by suitably parametrizing the segments of the piecewise smooth contour \Gamma.

    Why doesn’t Cauchy’s theorem apply to this integral?

    Because f(z)=\bar{z}^3 isn't analytic...

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contour integral, limiting contour theorem with residue
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: May 23rd 2011, 10:00 PM
  2. Contour Integrals (to Evaluate Real Integrals)
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: January 17th 2011, 09:23 PM
  3. Replies: 2
    Last Post: August 31st 2010, 07:38 AM
  4. [SOLVED] Though contour integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 6th 2010, 07:54 AM
  5. contour integral-need help
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: October 27th 2009, 09:48 AM

Search Tags


/mathhelpforum @mathhelpforum