MATH 406: Problem Set 11

due Friday, April 15, 2005

1. (F 2.6.18) Compute the following integral, using the change of variables to move the lower limit (and the singularity) to :

2. Compute the following integral:

3. Fisher 3.3.5(d)

4. Tell if each function is -analytic, specifying , then if the function is 2-analytic, check that the real and imaginary parts are biharmonic:

a)    b)    c)

5. Decide if the following functions are harmonic or not by checking the first Cauchy-Riemann equation , then check if the functions is biharmonic by checking if the difference is harmonic (as we showed in class):

a)    b)    c)

6. Based on the previous question, is a biharmonic function also harmonic, or not? Explain.

7. Find all points at which the following mappings would not be conformal:

a)    b)    c)    d)

8. Fisher 3.4.8