Homework+Set+12.solutions

# Homework+Set+12.solutions - Residue at z=3i Residue at z=2i...

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Homework Set 12 Find the values of the following integrals 1) The second integral on the right side is zero (odd integrand) and the third integral approaches zero as R approaches infinity if a>0. Therefore There is a second order pole at (inside the contour if b>0) with residue

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2) The integrand is an even function, therefore Using the same contour shown above The last integral approaches zero as R approaches infinity, therefore There is a simple pole at z=3i and a second order pole at z=2i.

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Unformatted text preview: Residue at z=3i: Residue at z=2i: 3) Using the same contour as before As R approaches infinity the last integral approaches zero, hence There is a simple pole at z = -2+i with residue Hence 4) The first pair of integrals on the right hand side sum to zero (odd function) and the last integral approaches zero as R approaches infinity. As (residue at the simple pole at z = 0). The residue at z = 0 is 1. Therefore...
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Homework+Set+12.solutions - Residue at z=3i Residue at z=2i...

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