Math 461A -- Advanced Seminar in Complex Analysis -- Fall 2010

Homework Assignments:

Assignment
Chapter
 Problems
Due Date
1
1
 1.3, 1.4, 1.5, 1.9, 1.10, 1.13, 1.15, 1.17
9-14-10
2
1
 1.18, 1.19, 1.22.3, 1.22.4, 1.23, 1.26, 1.27.2, 1.27.3, 1.28.2, 1.28.3, 1.30
9-21-10
3
2
 2.5, 2.6, 2.7, 2.10, 2.14, 2.15, 2.17, 2.19
10-5-10
4
2
 2.25, 2.26, 2.27, 2.29, 2.36
10-21-10
5
2

Lemma 2.37.5  Prove by induction on n:  For all z0 in C, and for all n in N, the limit of z^n, as z approaches z0, equals (z0)^n.

Also:  2.40, 2.41b, 2.41e, 2.47, 2.48

10-28-10
6
3
 Review sequences and series in R (handout)
12-2-10
7
3
  • Exercise 3def
  • Exercise 4
  • Prove Theorem 9
  • Exercise 10.5:  Consider the series ∑ (c)^n, where c is a complex number.  For which values of c is the series absolutely convergent?  Conditionally convergent?  Divergent?  Justify your answers.
  • Prove Theorem 12
  • Exercise 13:  For which complex numbers z is the series ∑ (z^n)/n! absolutely convergent?  Justify your answer.
12-9-10

 

Course Notes:

Other Handouts: