Homework Help: Inverse Laplace Transform

1. Mar 28, 2010

NT123

1. The problem statement, all variables and given/known data 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.

2. Relevant equations

3. 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.

2. Mar 28, 2010

Count Iblis

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.