Math 3364 Exam 2.
Sanders Fall 2012
This exam has ve problems, and all ve will be graded. Use my supplied paper only.
Return your solution sheets with the problems in order. Put your name, last name rst,
and student id number on each solution sheet you tu
Math 3364 Exam 1.
Sanders Fall 2012
This exam has ve problems, and all ve will be graded. Use my supplied paper only.
Return your solution sheets with the problems in order. Put your name, last name rst,
and student id number on each solution sheet you tu
Math 3364: Homework 3
1. Factor the following polynomials.
(a) z 4 + (2 + 2i)z 3 + 2iz 2
(b) z 3 + z 2 + z + 1
(c) z 4 16
(d) z 4 + 16
2. Perform a partial fraction expansion on the following.
z+1
1
(a) 2
(c) 3
z + 2iz 1
z 2z 2 + z
2z + 1
z2 + 1
(b) 2
(d)
The New England,
Middle, and Southern
Colonies
Unit 1, Lesson 3
Essential Idea
The New England colonies were largely
settled for religious reasons.
Following the English Civil War, the Middle
and Southern colonies were settled.
Religious Problems in Engla
Last Name:
First Name:
Signature:
Student I.D. No.:
Math 3364 Practice Midterm 1
Some time in September, 2010
One Hour and twenty minutes
University of Houston
Instructions:
1. Put your name, signature and I.D. No. in the blanks above.
2. Answer the quest
Last Narrlc: A.
First Narrm: M.
Signature: ____M 4m_ ___ m
Student. I. D. No.2 w M-
Nlath 3364 Practice Final
December, 2010
Two hours and twenty minutes
University 01 IlffiStOTl
Instructiong:
3.. Put, your name, signature and 1.1:}. No. in the blank
MATH 3364 Final Exam. Sanders Fall 2012
This exam has 10 problems, and all 10 problems will be graded. Use my supplied paper
only. Return your solution sheets with the problems in order. Put your name, last name
rst, and student id number on each solution
Math 3364: Homework 1
1. The set of complex numbers is a eld when multiplication is given by
z1 z2 = (x1 + iy1 )(x2 + iy2 ) (x1 x2 y1 y2 ) + i (x1 y2 + x2 y1 ),
and the reciprocal of z = 0 is given by
x
y
1
2
+i 2
.
2
z
x +y
x + y2
Show it is always true
Math 3364: Homework 6
1. The function f (z ) = ez is analytic on the whole complex plane. Determine that its
Taylor series around z0 = 0 is given by n=0 z n /n! .
2. Use the result from the previous exercise to compute the Taylor series around z0 = 0
for
Math 3364: Homework 8
Suppose f is a complex function which is analytic on a simply connected and open set
C except at a discrete set of isolated singular points. Let be a simple positive
closed contour in which does not intersect any of the singular poi
A Proof of the Fundamental Theorem of Algebra
Recall Liouvilles Theorem from class: If f is bounded and entire then f must be a
constant function.
From this the Fundamental Theorem of Algebra easily follows. That is, a polynomial p(z )
of degree greater t
Math 3364: Homework 5
1. Use the root test to determine the radius of convergence for the following power series.
2
(a)
(k + 1) z
k
k
(b)
2z
k=0
k
(c)
k=0
k=0
1
zk
k+1
(d)
k=0
k+1 k
z
k2 + 1
2. Use the ratio test to determine the radius of convergence for
Math 3364: Homework 4
1. Recall from calculus: Along a smooth path (x0 , x1 ) in R2 which joins x0 to x1 we
have
( x ) dx =
x dx + y dy = (x1 ) (x0 ).
(x0 ,x1 )
(x0 ,x1 )
Use this together with Cauchy-Riemann to prove that along a smooth path (z0 , z1 )
Math 3364: Homework 2
1. A complex function f is analytic on an open set C if f (z ) exists for every z .
Determine points at which the following are not analytic.
1
iz 3 + 2z
(a)
(b) 2
z 2 + 3i
z +1
3z 1
(d) z 2 (2z 2 3z + 1)2
(c) 2
z +z+4
2. A complex f
Last Name:
First Name:
Signature:
Student I.D. No.:
Math 3364 Practice Final
December, 2010
Two hours and twenty minutes
University of Houston
Instructions:
1. Put your name, signature and I.D. No. in the blanks above.
2. Answer the questions in the space
Homework #5, Math 3364.
due 3.30pm, Thursday March 24th, 2016.
The notation is that used in class or from the text.
Question 1.
Find all the complex zeroes of cosh z
Question 2.
Find a formula for tan (iy) in terms of hyperbolic functions of y.
Question 3
Math 3364 Exam 2. Sanders Fall 2012
1. Recall Greens theorem from calculus:
S
fdx+ gdy = ( gx fy ) dxdy
.
Use this to prove
2. Let
f ( z ) dz=0
when f is analytic.
R denote the positively oriented circle centered at z = 0 which has radius R > 0. Use
Ca
Math 3364 Exam 1.
Sanders Fall 2012
This exam has five problems, and all five will be graded. Use my supplied paper only.
Return your solution sheets with the problems in order. Put your name, last name first,
and student id number on each solution sheet
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