1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex Analysis: countour integral

  1. Jan 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Compute the contour integral I around the following curve $\Gamma$:

    $ I = \int_\Gamma \dfraq{dz}{z^2 +1} $

    see picture:
    http://dl.dropbox.com/u/26643017/Screen%20Shot%202012-01-07%20at%2010.39.58.png [Broken]


    2. Relevant equations


    3. The attempt at a solution

    $\Gamma$ is an open curve, but even if you close it with a line from A to B an the real axis, you may not use cauchy's theorem and calculate it with the residue theorem, because it is not a "smooth curve"...
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jan 7, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The curve doesn't have to be "smooth" to apply Cauchy's theorem. It only has to be rectifiable. Piecewise smooth is plenty good enough.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Complex Analysis: countour integral
  1. Countour integral (Replies: 1)

Loading...