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Contour Integration

  1. Mar 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the poles for the integrals:
    [tex]
    \int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})}
    [/tex]

    One pole is at [tex] -(\gamma+\gamma_{n}) [/tex].

    Is there another one?


    Also
    [tex]
    \int_{c}ds e^{st} \frac{1}{(s + \kappa + \frac{g^{2}}{s+\gamma+\gamma_{n}})} \frac{1}{s+\gamma+\gamma_{n}} [/tex]
    Similiarly, one pole is at [tex] -(\gamma+\gamma_{n}) [/tex].

    Is there another one? I just need to be sure.

    Thanks

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 2, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    Poles are the values of the integration variable s where the denominator vanishes, right? I don't think -(gamma+gamma_n) is a pole. In both cases, it looks to me like you are getting a relatively complicated quadratic in s.
     
  4. Mar 3, 2009 #3
    Can you tell me what technique of integration I should use to evaluate this integral?

    [tex]
    \noindent\(\frac{e^{s t}}{g^2+(s+\text{yn}+\gamma ) (s+\kappa )}\)
    [/tex]
     
  5. Mar 3, 2009 #4

    Dick

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    Homework Helper

    The ordinary residue theorem, I think. You can write that as e^(st)/((s-p1)(s-p2)) where p1 and p2 are the poles you get from solving the quadratic equation. It's straightforward in principle, but I don't know a simple way to write the nasty expressions you get from solving the quadratic. Where are you getting these problems??
     
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