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    asder's Avatar
    asder Posts: 2, Reputation: 1
    New Member

    Nov 20, 2005, 04:10 AM
    Contour Integral
    is there anybody there who is interested in complex calculus?
    Is the theorem right?
    When you integrate f on a closed loop, you may or may not get 0 as the total integral. It depends a lot on what f is, and what the loop is. If f has an anti-derivative on the loop, then the integral is guaranteed to be 0 by the fundamental theorem of calculus. If f is analytic on the loop and inside the loop, then Cauchy's theorem guarantees that the integral is 0. In all other cases it is very unlikely that the integral vanishes completely.
    f(z)=Logz=lnr+i@ then the antiderivative is exist is 1/z and by calculation the integral yields "2pi*i". But according to the theorem above shouldn't it be 0.
    Where am I wrong?
    CroCivic91's Avatar
    CroCivic91 Posts: 729, Reputation: 23
    Senior Member

    Nov 20, 2005, 04:04 PM
    I remember this vaguely from my university. I believe Log(z) is not defined on the whole set C. I believe there is a line going from (0, 0) under the angle "fi" (for different Log(z) functions or something) that Log(z) is not defined for points on that line. Am I correct? If true, and if your loop intersects that line, I believe that might be causing the problem. Then again, I remember that an integral is not affected if a function is not defined in a single point, but I don't know if that means anything. Is that any help?

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