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