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Inverse Laplace Transform

  • Thread starter NT123
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Homework Statement

I need to find the inverse Laplace transform of s/(s^2+a^2), where a is a constant, by the method of residues. I need to prove the part of the contour not actually relating to the desired integral tends to zero as R---> infinity.



Homework Equations





The Attempt at a Solution

I have calculated the residues, however I am having trouble proving the integral of the contour which isn't the straight line from -R to R vanishes. Any help would be appreciated.
 

Answers and Replies

  • #2
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You need to use the same methods here that are used in the proof of Jordan's theorem. The large s behavior is like 1/s, while the radius of the circle will be proportional to s, so a more straightforward way of estimating the integrand won't do.
 

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