Ex Sheet
2
2C Feedback Exercise 201415
Feedback exercises
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1
Ex Sheet
2C Applied Mathematics 201516
.
Tutorial exercises
T1
Find the dimensions of the following expressions.
a) mgh where m is mass, g is acceleration due to gravity and h is
distance.
p
/ (r ) where is density, r is radius and is surface tension.
b
Ex Sheet
3
2C Applied Mathematics 20142015
.
Tutorial exercises
T1 For each of the following ODEs, nd the equilibrium point(s),
the linearization about each of these points and whether or not they
are stable
(a)
dN
= a bN
dt
(b)
dN
= a( N b) N
dt
(c)
dN
=
Ex Sheet
3
2C Feedback Exercise 201415
.
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially forma tted paper for your solution, use one cover sheet and
additional continuation sheets if required. Su bmit your so
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your solutions to
the wooden submission cabinet in
Ex Sheet
6
2C Feedback Exercise 201415
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your soluti
2
Ex Sheet
2C Feedback Exercise 201415
.
Feedback exercises
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specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your solu
Ex Sheet
5
2C Feedback Exercise 20142015
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your solu
Review exercises
It is very important that you are competent with the material in
level-1 mathematics (1RSXY) and from 2A and 2B. In particular for
2C we will make use of vector algebra, differentiation, integration
and the solution of ordinary differenti
Ex Sheet
2C Feedback Exercise 201415
6
.
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your solu
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your solutions to
the wooden submission cabinet in
1
Ex Sheet
2C Feedback Exercise 201415
.
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your solu
Mathematics 2C Vector functions of a single variable
Review of vector algebra.
In this document vectors are elements of R3 and the scalars are elements of R.
For vectors a, b, c and scalars and
a+b=b+a
a + (b + c) = (a + b) + c
(a + b) = a + b
( + ) a =
Ex Sheet
9
2C Applied Mathematics 201415
.
Tutorial exercises
T1
A billiard ball A of mass 2m moving to the right with speed
v collides with a second ball B of mass m moving in the opposite
direction with speed 2v. If the ball A rebounds with speed v to t
Ex Sheet
2C Applied Mathematics 201415
4
.
Tutorial exercises
T1 The environment for an isolated population changes as a result
of radiation poisoning. We model the population using the exponential model but with variable birth and death rate. The radiati
Ex Sheet
2C Feedback Exercise 201415
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially formatted paper for your solution, use one cover sheet and
additional continuation sheets if required. Submit your solution
Review exercises
It is very important that you are competent with the material in
level-1 mathematics (1RSXY) and from 2A and 2B. In particular for
2C we will make use of vector algebra, differentiation, integration
and the solution of ordinary differenti
Ex Sheet
3
2C Applied Mathematics 20142015
.
Tutorial exercises
Lectures 68
T1 For each of the following ODEs, find the equilibrium point(s),
the linearization about each of these points and whether or not they
are stable
(a)
dN
= a bN
dt
(b)
dN
= a( N b)
Review exercises
It is very important that you are competent with the material in
level-1 mathematics (1RSXY) and from 2A and 2B. In particular for
2C we will make use of vector algebra, differentiation, integration
and the solution of ordinary differenti
Tuesday, 13th May, 2014
2:00 p.m. to 3:30 p.m.
EXAMINATION FOR THE DEGREES OF
M.A. AND B.Sc.
Mathematics 2C - Topics in Applied Mathematics
An electronic calculator may be used provided that it does not have
a facility for either textual storage or displa
2C degree exam 2013 annotated solutions
1.
(i) The equation is separable
M
dN =
N (M N )
0 dt.
We use partial fractions to represent the integrand on the
LHS,
M
A
B
=
+
N (M N )
N
M N
or
M = A(M N ) + BN
set N = 0 to nd that A = 1 and set N = M to nd that
Wednesday, 12th December, 2012
09:30 a.m. to 11:30 a.m.
EXAMINATION FOR THE DEGREES OF
M.A. AND B.Sc.
Mathematics 2C - Topics in Applied Mathematics
An electronic calculator may be used provided that it does not have
a facility for either textual storage
2C degree exam 2012 annotated solutions
1.
(i) Newtons second law for the constant mass particle is
m = F.
x
(ii) Take the scalar product of Newtons second law with the velocity and integrate from t = 0 to T = T ,
x (m ) = x F
x
mx x = x F
m
T
0
d
dt
1
Class test 2C1 , Tuesday 6th November 2012. Solutions.
1.
(i) The radius is conjectured to depend on u, m and E so
R = ku m E
where k, , and are dimensionless constants. The dimensions of the quantities are:
radius [L]; speed of impacter [L][T ]1 ; mass
Tuesday, 6th November, 2012
9:10 a.m. to 9:55 a.m.
University of Glasgow
School of Mathematics and Statistics
Mathematics 2C1 - Topics in Applied Mathematics
Class Test
An electronic calculator may be used provided that it does not have
a facility for eit
Ex Sheet
3
2C Feedback Exercise 201415
Feedback exercises
Answer all the questions. Show your working clearly. Use only the
specially forma tted paper for your solution, use one cover sheet and
additional continuation sheets if required. Su bmit your solu
1
Ex Sheet
2C Applied Mathematics 201415
.
Tutorial exercises
T1
Find the dimensions of the following expressions.
a) mgh where m is mass, g is acceleration due to gravity and h is
distance.
b)
/ (r ) where is density, r is radius and is surface tension.
Ex Sheet
2
2C Applied Mathematics 201415
.
Tutorial exercises
T1 It is observed that a population of size N0 doubles in size after
D units of time. Using the exponential model
dN
= N,
dt
where N is the population at time t, show that
N = N0 2t/D .
The con
Ex Sheet
10
2C Applied Mathematics 201415
.
Tutorial exercises
T1
A mass M rests on a plane that is inclined at an angle to the
horizontal. It is connected by a light inextensible string which passes
over a pulley xed at the top of the plane to a mass m >
11
Ex Sheet
2C Applied Mathematics 201415
.
Further exercises
F1 Consider N 1 masses, each of mass L/N, lying in a straight
line on a smooth table between two walls, one at x = 0 and the other
at x = L. The masses are connected in series by linear springs