Frederick Robinson
Math 410-3: Complex Analysis
Homework 2
Frederick Robinson
11 April 2011
Chapter 2
1
Problem 3
1.1
Question
Let U C be an open disc with center 0. Let f be holomorphic on U . If
z U , then define z to be the path
0 t 1.
z (t) = tz,
Defi
Frederick Robinson
Math 410-3: Complex Analysis
Homework 5
Frederick Robinson
16 May 2011
Chapter 5
1
1.1
Problem 1
Question
Let f be holomorphic on a neighborhood of D(P, r). Suppose that f is not
identically zero on D(P, r). Prove that f has at most fin
Frederick Robinson
Math 410-3: Complex Analysis
Homework 1
Frederick Robinson
4 April 2011
Chapter 1
1
Problem 29
1.1
Question
Compute each of the following derivatives:
1.
2
(x y)
z
2.
(x + y 2 )
z
3.
4
(xy 2 )
zz 3
4.
2
(zz 2 z 3 z + 7z)
zz
1.2
Answer
Frederick Robinson
Math 410-3: Complex Analysis
Homework 5
Frederick Robinson
25 May 2011
Chapter 6
1
1.1
Problem 1
Question
Does there exist a holomorphic mapping of the disc onto C? [Hint: The
holomorphic mapping z 7 (z i)2 takes the upper half plane on
Frederick Robinson
Math 410-3: Complex Analysis
Homework 4
Frederick Robinson
27 April 2011
Chapter 4
1
Problem 5
1.1
Question
Let P = 0. classify each of the following as having a removable singularity
, a pole, or an essential singularity at P .
1.
1
z
Frederick Robinson
Math 410-3: Complex Analysis
Homework 3
Frederick Robinson
20 April 2011
Chapter 3
1
1.1
Problem 1
Question
It was shown (Corollary 3.5.2) that if fj are holomorphic on an open set
U C and if fj f uniformly on compact subsets of U , the