Contour Integration

  • Thread starter Nusc
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  • #1
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Homework Statement


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

Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
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Homework Helper
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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.
 
  • #3
753
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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]
 
  • #4
Dick
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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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