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Thread: Countour Integral

  1. #1
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    Countour Integral

    I have no idea where should I start. I have only learned line integration, Cauchy's Integral theorem and formula.

    Please give me some hints on where should I begin. Do note that I have not learned very detail in this topic.

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  2. #2
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    Hello,

    Since $\displaystyle w\in\mathbb{C}\backslash\mathcal{C}$, the function $\displaystyle f(z)=\frac{\sin(z)}{(z-w)^2}$ has no singularity within $\displaystyle \mathcal{C}$
    Hence it's a holomorphic function in $\displaystyle \mathcal{C}$ and we can apply Cauchy's integral theorem...


    Cauchy's integral formula wouldn't work because w is not within $\displaystyle \mathcal{C}$
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  3. #3
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    Hi, I dont quite get what you mean

    I understand that w covers all complex number except C

    What does the C stand for?
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  4. #4
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    Quote Originally Posted by wzseow View Post
    I have no idea where should I start. I have only learned line integration, Cauchy's Integral theorem and formula.

    Please give me some hints on where should I begin. Do note that I have not learned very detail in this topic.

    Two cases:
    (1) If $\displaystyle w $ is in the domain, $\displaystyle g(w)=?$
    (2) else if $\displaystyle w $ is outside the domain, $\displaystyle g(w)=?$
    Last edited by mr fantastic; Sep 19th 2009 at 12:18 AM. Reason: Restored original reply
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  5. #5
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    Quote Originally Posted by luobo View Post
    Two cases:
    (1) If $\displaystyle w $ is in the domain, $\displaystyle g(w)=?$
    (2) else if $\displaystyle w $ is outside the domain, $\displaystyle g(w)=?$
    Hi luobo

    Is this what you meant?

    1) If $\displaystyle w $ is in the domain, then I have to use Cauchy's Integral theorem and calculate the integral

    2) If $\displaystyle w $ is outside of the domain, then g(w) = 0 from Cauchy's integral formula


    Am I correct in doing so?
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