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Not a simply connected contour

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data

    I have a contour in the complex plane it is not simply connected, because it looks like two figure eights that overlap and intersect eachother. Now how do i evaluate an integral for such a contour?

    2. Relevant equations

    The question asks to evalute the contour shown for ∫dz/z-1.
    But the contour is not simply connected and we are not given a function for the contour only a picture. In addition the discontinuity at z=1 is inside the contour. So how can i evaluate it?

    Is this a trick question or something?
    I thought we could only evaluate integrals when the contour is simply connected and we use a contour that does not contain the discontinuity?



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 20, 2009 #2
    "Simply connected" would describe the domain, not the contour. I bet you mean the contour is not simple. You have to figure out the winding number of the contour around the point z=1. How many times does the contour wrap around z=1. Then you probably have a formula in your notes or book involving winding number.
     
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