COMPLEX ANALYSIS HOMEWORK ASSIGNMENT 1
Due Friday, January 25, 2013, at the beginning of class.
Please write clearly, and staple your work !
1. Problem
Assume that the power series aj z j has converge
COMPLEX ANALYSIS MIDTERM 1 SOLUTIONS
1. Problem
Assume that f H(C) is an entire function whose imaginary part is bounded. Prove that
f must be a constant.
Hint: Consider eif .
Solution: Let f = u + iv
M361 FALL 2015 UNIQUE NUMBER 53490 HOMEWORK 7
This homework is due on Friday, October 23, 2015, before lecture begins. Late
homework is not accepted. In order to receive credit for this assignment you
Hossein Namazi
Department of Mathematics
1 University Station C1200
Austin, TX 78712-0257
(512) 471-1184
E-mail: [email protected]
http:/www.ma.utexas.edu/users/hossein
Education
Stony Brook Un
M361 FALL 2012
UNIQUE NUMBER 56205
SECOND IN-CLASS EXAM
No books or calculators allowed. Just paper and pen.
Exercise 1. (8 points) Solve the equation sin(z) = 0, and the compute the line integral
z
d
M361 FALL 2013 UNIQUE NUMBER 57350 SECOND IN-CLASS EXAM
This exam is graded 0-50 points. In order to receive credit for it you must: write
your name and UT eid at the top of the first page of your tur
M361 FALL 2013 UNIQUE NUMBER 57350 THIRD IN-CLASS EXAM
This exam is graded 0-50 points. In order to receive credit for it you must: write
your name and UT eid at the top of the first page of your turn
M361 FALL 2012
UNIQUE NUMBER 56205
FIRST IN-CLASS EXAM
Exercise 1. Draw all the solutions to the equation z 5 = 32.
Exercise 2. Compute the line integrals
z+7
dz ,
2
C1 (z + 1)(z 2i)
C2
z+7
dz ,
(z +
COMPLEX ANALYSIS PRACTICE PROBLEMS
1. Problem
1
(a) Prove that if f H(), then g (z ) := f ( z ) is holomorphic in = cfw_z C | z . In
particular,
g (z ) = f (z ) .
P
(b) What is the general form of a r
COMPLEX ANALYSIS PRACTICE SOLUTIONS
1. Problem
1
(a) Prove that if f H(), then g (z ) := f ( z ) is holomorphic in = cfw_z C | z . In
particular,
g (z ) = f (z ) .
P
(b) What is the general form of a
COMPLEX ANALYSIS HOMEWORK ASSIGNMENT 6
Due Friday, March 8, 2013, at the beginning of class.
Please write clearly, and staple your work !
1. Problem
What can you say about an entire function whose rea
COMPLEX ANALYSIS HW 2 SOLUTIONS
1. Problem
(a) For which A =
ab
cd
GL(2, C) are the Mbius transformations
o
TA : z
az + b
cz + d
automorphisms of C, respectively automorphisms of C ?
Solution: The M
COMPLEX ANALYSIS HOMEWORK ASSIGNMENT 2
Due Friday, February 1, 2013, at the beginning of class.
Please write clearly, and staple your work !
1. Problem
(a) For which A =
ab
cd
GL(2, C) are the Mbius
COMPLEX ANALYSIS HW 3 SOLUTIONS
1. Problem
Expand
2z +3
z +1
in powers of z 1. What is the radius of convergence?
Solution:
2z + 3
1
1
1
1
1
(1)n
=2+
=2+
=2+
=2+
(z 1)n
z+1
z+1
2 + (z 1)
2 1 + z 1
2
2
COMPLEX ANALYSIS HOMEWORK ASSIGNMENT 3
Due Friday, February 8, 2013, at the beginning of class.
Please write clearly, and staple your work !
1. Problem
Expand
2z +3
z +1
in powers of z 1. What is the
COMPLEX ANALYSIS HW 4 SOLUTIONS
1. Problem
Find all automorphisms of D, H, and C.
Hint: For an arbitrary automorphism f : D D, show that you can assume f (0) = 0
via composition with a fractional line
COMPLEX ANALYSIS HOMEWORK ASSIGNMENT 4
Due Friday, February 15, 2013, at the beginning of class.
Please write clearly, and staple your work !
1. Problem
Find all automorphisms of D, H, and C.
Hint: Fo
COMPLEX ANALYSIS HW 5 SOLUTIONS
1. Problem
Assume that f H( \ cfw_z0 ), and that limz z0 (z z0 )f (z ) = 0. Dene g (z ) := (z z0 )f (z )
for z \ cfw_z0 , and g (z0 ) := 0. Prove that g is holomorphic
COMPLEX ANALYSIS HOMEWORK ASSIGNMENT 5
Due Friday, February 22, 2013, at the beginning of class.
Please write clearly, and staple your work !
1. Problem
Assume that f H( \ cfw_z0 ), and that limz z0 (
M361 FALL 2015 UNIQUE NUMBER 53490 FIRST IN-CLASS EXAM
This exam is graded 0-110 points. In order to receive credit for it you must: write
your name and UT eid at the top of the first page of your tur