Homework+Set+12.solutions

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

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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.
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 4

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online