Cars
An introduction to cars
In 1769 French inventor Nicolas-Joseph Cugnot (1725 1804) is known to have built
the automobile that could carry a human passenger; this was run by a steam engine, it
also had three wheels and could carry four people.
It was
Cars
A typical car-driver uses about 40 kWh per day.
Only about 14%26% of the energy from the fuel you put in your tank gets used to move
your car down the road, depending on the drive cycle. The rest of the energy is lost to engine
and driveline ineffici
Cars
Travelling by car, van or taxi is by far the most common mode of transport in Britain with up
to 75% of households owning at least one car. However we are going to see how efficient it is
to use these automobiles.
To work out how efficient a cars eng
We used Maple and an SIR model to plot a flu outbreak across a period of 12 months.
(1)
(2)
(3)
We use = 0.001 and = 3
The initial conditions we used were I(0) = 1, R(0) = 0 and S(0) = N - I(0).
The unit of time is one month and we used a time step of t =
Now I am going to look at which is more dominant, the swirling air energy or breaking
energy. We will work out the distance between stop signs, for which if the if a cars distance is
greater than this value the swirling air energy is more dominant and if
This graph shows us that as the susceptible individuals become infected the more removed
individuals there are. At the peak of Infected individuals the Susceptible and Removed
Individuals intercept. From our graph we can tell that the infection lasts betw
From this graph we can see that as the number of susceptible individuals decrease the amount
of removed individuals increases and these two lines intercept shortly after the point of
highest infection. This tells us that once the peak of infected individu
Now I am going to look at which is more dominant, the swirling air energy or breaking
energy. We will work out the distance between stop signs, for which if the cars distance is
greater than this value the swirling air energy is more dominant and if the c
1) Using the model with the acid the p-value is 0.07657>0.01 which is not significant. However if we
2)
transform this variable using the log function the p-value is 0.01969 which is much more significant so
we will now use the variable log(acid).
We star
MAS3111/PHY4006/MAS8111
Problems, Part 3
Second-Order Partial Differential Equations: The Method of Eigenfunction Expansions
Question 1
Find a finite solution of 2 u = f (r, ) in 0 < r < a, 0 2, subject to the boundary condition u(a, ) = 0, where f (r, )
MAS3111/PHY4006/MAS8111
Problems, Part 2
Second-Order Partial Differential Equations: Separation of Variables
Question 1
Solve the Laplace equation in 0 < x < a, 0 < y < b, subject to u(0, y) = 0 , 2u 2u + =0 x2 y 2 u(x, 0) = 0 , u(x, b) = f (x) .
u (a, y
MAS3111/PHY4006/MAS8111
Problems, Part 1
Linear and Quasilinear First-Order Partial Differential Equations
Question 1
Consider x u u y + (x2 + y) + -x u=1. x y x
(a) Using the parametric method, solve this equation subject to the condition u = 0 on x = 1.
MAS3214/8214 Cryptography
Answers to Homework Exercises III
1. Plaintext and ciphertext digraphs are encoded in (2 1)-matrices x with entries
in Z26 . Encryption and decryption are given by
D(x) = A1 x A1 B
E (x) = Ax + B,
where K = (A, B ) is the key. No
MAS3214/8214 Cryptography
Answers to Homework Exercises IV
1. Alice must (1) compute the encryption EKB (1345) and (2) compute the ciphertext signature DLA (EKB (1345).
(1) We have EKB (1345) = 13457 mod 9167. We compute this using the method of
squares.
MAS3214/8214 Cryptography
Answers to Tutorial Questions V
1. One way of solving the problem is to reduce the ciphertext units modulo 89,
then determine whether the reductions are squares in Z89 . If a reduction is a square
then the decryption is 0; if it
MAS3210 Geometries and Designs
Assignment Exercises
1
1.1
Solution Suppose that there is a 2 (24, 4, 2) design. Then
r=
But
46
3
23
46
(v 1)
=2
=.
(k 1)
3
3
Z, a contradiction. Hence there is no 2 (24, 4, 2) design.
/
1.2
Solution Suppose that there is a
MAS3214 Number Theory (2009) Examples Sheet 1
M.C.W.
Qu. 6(iv) was by far the least correctly answered question. Most who made an attempt got as far as 20012001 1, but did not realise that 2001 1 as well. Qu. 7 Ive dropped a lot of people the 2 method mar
MAS3214 Number Theory (2012)
M.C.W.
Assignment Sheet 2
Qu. 2 Hardly anyone thought of dening h rst and then using its prime factorisation inside
the prime factorisations of m and n, and consequently lots got stuck deciding what to
cancel out in the totien
MAS3214 Number Theory (2009) Examples Sheet 3
M.C.W.
Qu 2: Very few people explicitly dealt with the fact that m and n are coprime. If someone wrote down CPFs for m and n, then wrote down a separate line giving the CPF of mn as the composition of those, I
MAS3214 Number Theory (2009) Examples Sheet 4
M.C.W.
This homework seemed to be found a little harder than the previous exercices. Qu 2: A few people had trouble showing f was multiplicative, but most managed. A number of people did far, far too much work
MAS3214 Number Theory (2009) Examples Sheet 5
M.C.W.
Qu 2: Most people got this right, but a few had trouble finding inverses and some just made calculator errors. Qu 4: A lot of people didn't check the case n = 1. Most people followed the method in the n
MAS3214/8214 Cryptography
Answers to Homework Exercises I
1. (1) We have 29 5 = 24 = 2 2 2 3 and 109 57 = 52 = 2 2 13. The greatest
common divisor is 4 which is a good guess for the length of the keystring.
(2) We presume that the most common letter in th
GROUP 5
Group report:
We liked your bright and clear slide designs and the talk had a logical structure. You gave a deta iled
introduction which set the scene for what was to come and how the parts interlinked. Throughout the
talk, you used a good selecti
Economic Forecasting
Running Head: Economic forecasting
Economic Forecasting
[Name of the student]
[Name of the instructor]
[Date]
1
Economic Forecasting
2
Economic Forecasting
Economic data is of utmost importance in many circumstances and that is the re