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Residue Theorem Applications

  1. Aug 10, 2014 #1
    Hi, first post here. I'm having some trouble with contour integration. Basically here's the question:

    Contour Integral of

    1+z dz
    (z-1)(z2+9)

    There are three cases:

    l z l = 2
    l z+1 l = 1
    l z-[itex]\iota[/itex] l = 3

    Is each case a straightforward application of the residue theorem? Also, reading up in my textbook the poles should be contained within the contour so does on the boundary count?

    Thanks in advance.
     
  2. jcsd
  3. Aug 10, 2014 #2

    vela

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    You should take a little time and learn LaTeX. It's not very difficult.
    $$\int_C \frac{1+z}{(z-1)(z^2+9)}\,dz$$
    There's a good tutorial here: https://www.physicsforums.com/showthread.php?p=3977517#post3977517

    Yup.

    No, the pole needs to be inside the contour. If it's on the contour, you have to treat it differently.
     
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