Math 3D03
Short solutions to assignment #1
1. Compute the Taylor, respectively Laurent series expansion and determine the region of convergence of the following functions around the point z = 0:
1
(a) f (z ) =
log
2i
(a)
1
2i
(log(1 + iz ) log(1 iz ) =
1
INVESTIGATING RATIONAL FUNCTIONS
What is a Rational Function?
Just as a rational number is the ratio of two integers, a rational function is the ratio of two polynomial functions.
a
Rational Numbers have the form r = where a ], b ], b 0 (a and b are inte
ANSWERS TO LOGARITHM PRACTICE TEST
Multiple Choice Questions
1.
6.
11.
16.
d
d
d
c
2.
7.
12.
17.
c
b
d
c
3.
8.
13.
18.
a
a
c
a
4.
9.
14.
19.
d
d
a
b
5.
10.
15.
20.
b
c
c
b
Short Answer Questions
21. D = cfw_ x \ : x < 5
22. x = 4
R=\
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30.
Solution Graphing Exercise on Page 14 of Unit 1
Given f ( x ) = log 2 x , sketch the graph of g ( x ) = 3 f ( 2( x + 1) ) 4 .
Equation of g
g ( x ) = 3log 2 ( 2 ( x + 1) ) 4
Transformations of f expressed in Words
Horizontal
1
1. Compression by a factor o
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Math 3D03
Short answers to assignment #2
1. (8 marks) Evaluate the following denite (real-valued) integrals:
(i)
0
(ii)
log(x)
(iii)
(log(x)2
dx
1 + x2
dx
3
4
(iv )
x (1 + x)
0
0
eax
dx
1 + ex
dx
1 + xn
for 0 < a < 1
where n 2 is an integer
(i) This is pr
Math 3D03
Short answers to assignment #4
1.
Problem 30.26 on page 1216 in the textbook
Suppose you have x dollars in your hand. If you play one more time your expected wealth after that
is 0.2 0 + 0.5 (x + 1) + 0.3 (x + 2) = 1.1 + 0.8 x The optimal strate
Math 3D03
Short Answers to Assignment #3
#1. The complex potential
1
i log(z)
z
where is a positive real number, describes a uid ow around a cylinder with circulation. Locate
the stagnation points (as a function of ) and sketch the streamlines of the ow,