Math 4150/6150
Fall 2013
Exam 2
No calculators. Show your work. Give full explanations. Good luck!
1. (15 points) Let C denote the straight line segment joining the points z = i and z = 2 in the
complex plane. Evaluate that following:
z 2 dz
(a)
|z |2 dz
Math 4150/6150 Assignment 8
and
Practice Exam 3
* indicates Math 6150 questions
Due date: Thursday 14th of November 2013
1. Let C be the circle of radius 3 centered at the origin and oriented positively. Evaluate the following
integrals:
(a)
C
z5
dz
1 z3
Math 4150/6150
Fall 2013
Exam 3
No calculators. Show your work. Give full explanations. Good luck!
1. (15 points) Let C denote the circle of radius 2 centered at the origin with positive orientation.
Show that
3z 2 + 1
dz = 3i.
C z (z + 1)(2z 1)
2. (15 po
Math 4150/6150
Fall 2013
Practice Exam 2
* indicates Math 6150 questions
1. Evaluate
z 2 dz
and
Re(z ) dz
C
C
for the following curves C :
(a) C (t) = 2eit , /2 t /2
(b) C (t) = t + it2 , 0 t 1.
(feel free to use the Fundamental theorem of calculus where
Math 4150/6150
Fall 2013
Practice Exam 1
* indicates Math 6150 questions
Examinable Sections from Churchill and Brown
1-11, 12-15, 16* & 18*, 19-21, Statement of Theorem in 22, 24-25, 29-33
|2 + i |
and ( 3 + i)4 in the form x + iy , with x, y R.
3 + 4i
(
Math 4150/6150
Fall 2013
Exam 1
No calculators. Show your work. Give full explanations. Good luck!
1. (30 points) Express each of the following in the form x + iy , with x, y R:
|3 i|
2+i
(b) (1 + i)8
(c) all cube roots of i
(d) all solutions of the equat
Math 4150 / 6150
Fall 2011
Review of Innite Series from 3100
just the basics - no powers series, Taylors theorem, or uniform convergence
1. Important infinite series
n
n=1 r
Geometric series:
converges |r| < 1. If |r| < 1, then
n=1
The p-series:
n
n=1 r
=
Math 4150/6150
Fall 2012
Exam 3
No calculators. Show your work. Give full explanations. Good luck!
1. (15 points) In each case, write down the principle part of the function
at its isolated singular point and determine whether that point is a
pole, an ess
Math 4150/6150
Fall 2012
Exam 2
No calculators. Show your work. Give full explanations. Good luck!
1. (30 points) Dierentiate the following functions, giving an appropriate
region on which the functions are analytic.
(a)
(b)
(c)
(d)
f (z ) = z 3 + z 1
g (
Math 4150/6150
Fall 2012
Exam 1
No calculators. Show your work. Give full explanations. Good luck!
1. (15 points)
|2 + i|
and ( 3 + i)4 in the form x + iy , with x, y R.
3 + 4i
(b) Find all values of z C for which z 1 = z .
(a) Express
2. (20 points) Give
Math 4150/6150: Bonus Problems Spring 2011 Instructor: Dr. Shuzhou Wang Each problem is worth an extra 1% of the course. Note: If you turn in solutions of these problems for credit, you must work independently and must not discuss them with anyone else ex