MATH 406: Additional Problems for PS 9

1. Evaluate the following integrals around the curve defined by :

a)    b)    c)

2. Find

Res

3. Evaluate:

4. Find the real and imaginary parts of :

a)    b)

5. Show that the integral of a 2-analytic function

around a closed simple loop is not identically zero (note that and are analytic). Evaluate the contour integral explicitly for the curve defined by , with

and

Andrew L. Belmonte 2005-03-22