OCR

Physics 515 Homework #1 (math review) 1-1

1. Evaluate the integral

(∫_0^2*π)(d(θ)/(z−sin(θ)))

using residues.
Hint: Pick γ = unit circle z=e(i*θ)
then sin(θ)=1/(2*i)*(z−1/z).

2. evaluate (∫_−∞^∞)((cos(b)*x)/(x2+a2)*d(x))*a>0*b>0

by residues.

3. Evaluate for δ>0

numerically and plot the real and imaginary parts as a function of ω.
Use a principal value integration to do this for |ω|≤2.
If you are brave, you can try to evaluate by residues as well. But that's not needed now.
Plot results for −5≤ω≤5.