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Thread: Evaluate the closed contour integral

  1. #1
    lpd
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    Evaluate the closed contour integral

    Consider a piecewise smooth contour $\displaystyle \Gamma$ which is a triangle with vertices at $\displaystyle z = 0, 1 + i, i$. Evaluate the closed contour integral,

    $\displaystyle $\int_\Gamma\bar{z}^3 dz$

    around the triangle $\displaystyle \Gamma$ by suitably parametrizing the segments of the piecewise smooth contour $\displaystyle \Gamma$.

    Why doesn’t Cauchy’s theorem apply to this integral?
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  2. #2
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    Quote Originally Posted by lpd View Post
    Consider a piecewise smooth contour $\displaystyle \Gamma$ which is a triangle with vertices at $\displaystyle z = 0, 1 + i, i$. Evaluate the closed contour integral,

    $\displaystyle $\int_\Gamma\bar{z}^3 dz$

    around the triangle $\displaystyle \Gamma$ by suitably parametrizing the segments of the piecewise smooth contour $\displaystyle \Gamma$.

    Why doesn’t Cauchy’s theorem apply to this integral?

    Because $\displaystyle f(z)=\bar{z}^3$ isn't analytic...

    Tonio
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