Complex Number System and Exponents Tutorial Sheet
1.
Let
zl
=2+4j,
z2
=1j,z3
=23jand
z4
=34j.Expresseach ofthefollowing
in
the form
of
a+bj.where a,be$
1
32+
()1
22
(c, [2 32 i /z.
ell-2i
2.
Find all the complex roots of each of the following equations
(
School of Mathematics, Computer Science and
Engineering
BEng in Biomedical Engineering
EE1460: General Mathematics A
Part 1 Examination
[day][month] 2016
XXXX XXXX
Answer FIVE of the SEVEN questions.
Only FIVE questions will be marked.
Division of marks:
The University for business
and the professions
School of Engineering and Mathematical Sciences
BEng in Biomedical Engineering
EE1460: General Mathematics
Part 1 Examination
Monday 16th January 2012
1430 - 1630
Answer FIVE of the SEVEN questions
Only FIVE
Solutions to Exercises
Exercise 1. Express each of the following angles in radian measure: (Hint: See
Example 8.)
1) 20
2) 35
3) 140
4) 400
5) 1080
Solution: Equation 1 suggests that:
20
20
r rad
=
so that r rad =
1)
rad = 6. 092 3 103 rad.
180
180
The University for business
and the professions
SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES
BEng in Biomedical Engineering
GENERAL MATHEMATICS A
Module: EE1460
Part 1 Examination
Date: Thursday 14 January 2010
Answer FIVE of the SEVEN questions
BEGIN
The University for business
and the professions
School of Engineering and Mathematical Sciences
BEng in Biomedical Engineering
BEng in Multimedia
EE1460: General Mathematics A
Part 1 Examination
Tuesday 4th January 2011
1430 - 1630
Answer FIVE of the SEVE
The University for business
and the professions
SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES
BSc / BEng in Biomedical Engineering
BSc in Electrical and Electronic Engineering
BSc in Computer Systems Engineering
GENERAL MATHEMATICS A
Module: EE1460
Part
Farmulas and
Trig Sheet
identities
Tangent and Cotangent Identities
.
.
.
.
Definition of the Trig Functions
,
this definition we assume that
Unit circle definition
g < E
For this definition
0 < H <90 _
0
is any angle.
.
CW9 = cf);
cos
,
,
1
Sin: 9 = 7(1-
The University for business
and the professions
School of Engineering and Mathematical Sciences
BEng in Biomedical Engineering
EE1460: General Mathematics
Part 1 Examination
Thursday 17th January 2013
1430 - 1630
Answer FIVE of the SEVEN questions
If more
Problem 5.1. Explain what happens
when an investor shorts a certain
share.
Problem 5.6. Explain carefully the
meaning of the terms convenience yield
and cost of carry. What is the
relationship between futures price, spot
price, convenience yield, and cost
Maths Methods solutions 2009-2010
1. Let f be the 2 periodic function dened on [, ) by
f (x) = sin
x
.
2
(a) First of all, note that f is odd so
an = 0 , n N .
Then,
1
bn =
sin
x
sin nxdx .
2
A convenient way to compute bn is to integrate by parts twice
x
MA2603
CITY UNIVERSITY
London
BSc Honours Degree in Mathematical Science
Mathematical Science with Statistics
Mathematical Science with Computer Science
Mathematical Science with Finance and Economics
Mathematics and Finance
Part 2
Mathematical Methods So
Solutions Complex Variable
All the questions cover standard material seen in the lectures and/or
in the coursework. Only minor changes have been made compared to seen
examples.
1. (a) Let f be analytic inside and on a closed simple contour C (oriented
pos
Calculus and Vector Calculus
1. (a) Using the standard trigonometric identiy sin2 + cos2 = 1, we can
set z = 4 cos and x2 + y 2 = 4 sin . Applying it a second time for
x
the second equality, we see that we can set (formally) 4 sin = cos
y
and 4 sin = sin
City University
London
MA2604: Calculus and Vector Calculus
Time allowed: 3 hours
Full marks may be obtained for correct answers to
FIVE of the EIGHT questions.
If more than FIVE questions are answered,
the best FIVE marks will be credited.
At least TWO q
Calculus and vector calculus set task
Please notice that you must attempt all questions.
1. (a) Find and classify the stationary points (maxima, minima and saddle points) of
the function
f (x, y ) = 2x3 6xy + y 2 .
(b) Compute the Taylors expansion of the
City University
London
MA2603: Mathematical Methods
Time allowed: 3 hours
Full marks may be obtained for correct answers to
FIVE of the EIGHT questions.
If more than FIVE questions are answered,
the best FIVE marks will be credited.
Turn over . . .
1. Let
MA2603
CITY UNIVERSITY
London
BSc Honours Degree in Mathematical Science
Mathematical Science with Statistics
Mathematical Science with Computer Science
Mathematical Science with Finance and Economics
Mathematics and Finance
Part 2
Mathematical Methods
20
MA2602 Linear Algebra - 2012 Set Task
Answer ALL questions
1. (a) Determine whether the following subsets are subspaces (giving reasons for your answers):
i. U = cfw_(x1 , x2 , x3 , x4 ) | x1 = 2 x2 R4 ;
ab
ii. V =
ad bc = 0 M (2, 2);
cd
iii. W = cfw_a0
1
An investor wishes to borrow 30,000 from a bank at an effective rate of interest of
7.5% per annum to finance the expansion of his business. The project is expected to
generate net revenues of 6,340 per annum payable in arrears for the next 8 years.
(a)
City University
London
MA2600: Complex Variable
Time allowed: 2 hours
Full marks may be obtained for correct answers to
THREE of the FOUR questions.
If more than THREE questions are answered,
the best THREE marks will be credited.
Turn over . . .
1. (a) S
Supplement 12
Implicit Differentiation and the Chain Rule
1.
An offshore oil well is leaking oil onto the ocean surface, forming a circular oil slick about .005 meters
thick. If the radius of the slick is r meters, then the volume of oil spilled is cubic