Homework 4

1. Contour integrals

Integrate[z,{z,I,I+1}]

Integrate[1/(1-(z^2)),{z,0,I Infinity}]

s1={z,-1-I,-1+I};
s2={z,-1+I,1+I};
s3={z,1+I,1-I};
s4={z,1-I,-1-I};
results=Map[Integrate[Abs[z]^2,#]&,{s1,s2,s3,s4}]
Total@results

3. Laurent series

Use Mathematica to compute the Laurent series for
	f(z) = 1/(z(z -i)(z -1))
in the following annuli
	(Subscript[A, 1])= {z|0< |z| <1}
(Subscript[A, 2])= {z|0< |z-1| <1}
(Subscript[A, 3])= {z|0< |z-i| <1}
(Subscript[A, 4])= {z|1< |z|}.

f[z_]:=1/(z (z-I) (z-1))
n=5;
Series[f[z],{z,0,n}]
Series[f[z],{z,1,n}]
Series[f[z],{z,I,n}]
Series[f[z],{z,Infinity,n}]