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Contour Integrals in complex analysis questions

  1. Dec 8, 2013 #1
    I am confused as to what we are obtaining when taking these contour integrals.

    I know that the close loop contour integral of a holomorphic function is 0. Is this analogous to the closed loop of integral of a conservative force which also gives 0?

    Also when I am integrating around a function and there is a singularity in my contour, it gives me a value according to Cauchy integral theorem and 0 if no singularity is inside. Why is this? In this case does the function still have to be holomorphic and is there a relation to dirac delta function, since it looks somewhat similar. What is the difference whether there is a singularity inside or not and exactly WHAT am i getting when I calculate the integral (Area under something? or what..).

    A lot of questions, but I'd like to know what I'm doing since the math itself is not too hard but I have no idea the physical meaning.
  2. jcsd
  3. Dec 9, 2013 #2
    What I recall from doing those was that when you do the contour integral, you're basically finding something analogous to flux.
    This is one of those hazy areas for me, but I hope it helps. I think we talked about those for a week in one of my calculus classes and I haven't seen them since.
  4. Dec 9, 2013 #3


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    Have you been able to follow proof of Cauchy's Integral Theorem? Because that pretty much answers the "why" question.
  5. Dec 10, 2013 #4
    No, I am trying to follow it in my text book but it is not clear to me. Do you have a good link or text book you can refer?
  6. Dec 10, 2013 #5
    Yes the function still must be holomorphic everywhere except at the pole
    Thinking of an integral as an area under something is a clutch. A clutch might help you walk but you might have to get rid of it if you want to run.
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