Homework assignments for Math 618

This will be updated as the semester progresses.

Due Tuesday Feb 1

• Do Ch 6, exercises 12, 17, 18

Due Thursday Feb 10

• Do Ch 6, exercises 19, 20, 21

Due Thursday Feb 17

• Do Ch 6, exercises 23, 24; and Ch 8, exercise 5.

Due Tuesday Feb 29

• Do Ch 8, excersises 3, 11, 12.

• Hint for #3: Reduce to the case when R=1. Let F(z) be the infinite product on the left. Examine the relationship between F(z) and F(z²) and show that there is only one function that can satisfy this relationship.

Due Tuesday Mar 7

• Do Ch 8, excersises 15, 17; Ch 7 exercise 1.

Due Thursday Mar 24

• Do Ch 7, excersises 10 and 20. Also hand in the following problem:

• Suppose U is an open set; suppose a_n is a discrete sequence in U with no limit point in U; and suppose A_n and B_n are any two sequences of complex numbers. Show that there exists a holomorphic function f with f(a_n)= A_n and f'(a_n) = B_n for all n. Generalize this problem to one that specifies a finite order Taylor expansion of f at each point a_n.

Due Thursday April 20

• Do Ch 10, exercises 9, 11 and 12. Do problem 12 as stated in the text.

• This is the last homework assignment. The rest of the term, you should be working on your project, which is due May 2 (the last day of class).