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Math Help - Domain & formula - curve

  1. #1
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    Domain & formula - curve

    Hi guys, 1st post here.

    Anyway, I've missed a month of uni and now I got this assignment due. I have no idea how to go about it. I'll post the first question and see what you guys can do.

    If I'm not mistaken, its just asking for the domain U? not sure about the formula part though.

    Problem 1.

    Let U be a simply connected domain with a simple closed boundary curve C orientated couterclockwise, and define:

    g(w)=\oint\frac{\sin(z)}{(z-w)^2}dz for all w \in C \ C

    Find a formula for g(w) not involving integration.

    Thanks!
    Last edited by pseudoace; August 17th 2009 at 03:54 AM. Reason: maths tags, latex instruction said use [\math] which is meant to be [/math]
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  2. #2
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    Quote Originally Posted by pseudoace View Post
    Hi guys, 1st post here.

    Anyway, I've missed a month of uni and now I got this assignment due. I have no idea how to go about it. I'll post the first question and see what you guys can do.

    If I'm not mistaken, its just asking for the domain U? not sure about the formula part though.

    Problem 1.

    Let U be a simply connected domain with a simple closed boundary curve C orientated couterclockwise, and define:

    g(w)=\oint\frac{\sin(z)}{(z-w)^2}dz for all w \in C \ C

    Find a formula for g(w) not involving integration.

    Thanks!
    If the closed curve does not enclose the point z = w then you should know that the integral is equal to zero.

    If the closed curve DOES enclose the point z = w, then read Cauchy's integral formula - Wikipedia, the free encyclopedia and apply the appropriate formula.

    NB: Try to negotiate an extension on the due date of your assignment due to the circumstances that caused you to miss a month of uni.
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