EG4012 Coursework Assignment 1 Module: EG4012 Setter: Dr Peter Soan Title of Assignment: Coursework 1 Deadline: 07/01/19Module weighting 25% Module Learning Outcomes assessed in this piece of coursework This assessment is designed to assess your ability in the following module learning outcomes: · apply differential and integral calculus in an engineering context and appreciate practical applications with the use of a suitable Computer Algebra System · evaluate statistical data and probability both manually and with the application of computing software such as Excel Assignment Brief and assessment criteria (these will be discussed within a timetabled class) This assignment is designed to assess your ability to formulate simple mathematical problems in engineering and to use the computer algebra package Maple and Excel for solving them. You must use Excel for Tasks 1 and 2 and Maple for Task 3. Marks will be lost if you carry out calculations on paper or with a calculator and type in the results. Please make sure your answer to each question is very clear to the marker and use comments as necessary to describe important intermediate steps in the solutions. Marks will be given for the worksheets functioning correctly and will also be awarded for clarity of the work. Please do not share files, or email worksheets to each other. Any attempt to do so will be treated as academic misconduct. Be aware of the University rules on plagiarism: https://mykingston.kingston.ac.uk/myuni/academicregulations/Pages/plagiarism.aspx Submission details The deadline for submitting this assignment is 7th January 2019. Late submissions within one week will be capped at 40%. Please use new worksheets within a single spreadsheet in Excel as specified in Tasks 1 and 2, and a separate Maple worksheet file, so a total of two files should be submitted. Start each file by entering your name and ID number then save your files in your normal directory. Your files should be named as follows: i. Excel file – as (your) ‘kunumberTask12.xlsx’, submitted via Canvas before the deadline. ii. Maple file – as (your) ‘kunumberTask3.mw’ file, submitted via Canvas before the deadline. Important - once you have submitted your files to Canvas, do NOT open that file again until you have been given your mark for the coursework. This is a safeguard against the event that the files are not readable by the marker. Feedback Date. You will receive initial feedback in the form of solutions to the questions soon after the due date and written feedback on your coursework in Teaching Week 16. Further guidance. In the coursework we will be looking for clearly laid-out solutions to the problems posed, with fully worked solutions within the scope as indicated by the question. 1. Aircraft engines manufactured and used by WaterCoach Industries are known to have a probability of failing of 0.1 in a given period (which may be regarded, pessimistically, as the length of a typical .

1. EG4012 Coursework Assignment 1
Module: EG4012 Setter: Dr Peter
Soan Title of Assignment: Coursework 1
Deadline: 07/01/19Module weighting 25%
Module Learning Outcomes assessed in this piece of coursework
This assessment is designed to assess your ability in the
following module learning outcomes:
· apply differential and integral calculus in an engineering
context and appreciate practical applications with the use of a
suitable Computer Algebra System
· evaluate statistical data and probability both manually and
with the application of computing software such as Excel
Assignment Brief and assessment criteria (these will be
discussed within a timetabled class)
This assignment is designed to assess your ability to formulate
simple mathematical problems in engineering and to use the
computer algebra package Maple and Excel for solving them.
You must use Excel for Tasks 1 and 2 and Maple for Task 3.
Marks will be lost if you carry out calculations on paper or with
a calculator and type in the results. Please make sure your
answer to each question is very clear to the marker and use
comments as necessary to describe important intermediate steps
in the solutions. Marks will be given for the worksheets
functioning correctly and will also be awarded for clarity of the
work. Please do not share files, or email worksheets to each
other. Any attempt to do so will be treated as academic
misconduct. Be aware of the University rules on plagiarism:
https://mykingston.kingston.ac.uk/myuni/academicregulations/P
ages/plagiarism.aspx
Submission details
The deadline for submitting this assignment is 7th January

2. 2019. Late submissions within one week will be capped at 40%.
Please use new worksheets within a single spreadsheet in Excel
as specified in Tasks 1 and 2, and a separate Maple worksheet
file, so a total of two files should be submitted. Start each file
by entering your name and ID number then save your files in
your normal directory. Your files should be named as follows:
i. Excel file – as (your) ‘kunumberTask12.xlsx’, submitted via
Canvas before the deadline.
ii. Maple file – as (your) ‘kunumberTask3.mw’ file, submitted
via Canvas before the deadline.
Important - once you have submitted your files to Canvas, do
NOT open that file again until you have been given your mark
for the coursework. This is a safeguard against the event that
the files are not readable by the marker.
Feedback Date. You will receive initial feedback in the form of
solutions to the questions soon after the due date and written
feedback on your coursework in Teaching Week 16.
Further guidance. In the coursework we will be looking for
clearly laid-out solutions to the problems posed, with fully
worked solutions within the scope as indicated by the question.
1. Aircraft engines manufactured and used by WaterCoach
Industries are known to have a probability of failing of 0.1 in a
given period (which may be regarded, pessimistically, as the
length of a typical flight). On any given aircraft this probability
is independent of any other engine failures.
It may be assumed that a WaterCoach aircraft can land

3. safely if at least half of its engines are working.
Which is safer a two-engine plane or a four-engine plane?
(i) Answer the above question using Excel as your calculator.
Explicitly calculate the probability of each type of plane
crashing – highlight the cells in which you obtain these results
and write a brief explanation of your calculations and
conclusions in neighbouring cells. Credit will be awarded for an
easy to read spreadsheet (assume that you are presenting it as a
very brief electronic report).
(ii) Answer the above question by carrying out a simple Monte
Carlo Simulation exercise – use a new worksheet inside your
spreadsheet file. Simulate 2000 flights. Use a random number
generator based on a uniform distribution to represent the
operation/failure of each engine and calculate the number of
crashes in your sample of 2000 flights. Explicitly calculate the
proportion of flights which crash for each type of plane (this
can be compared with the probabilities calculated earlier) –
highlight the cells in which you obtain these results and write a
brief explanation of your calculations and conclusions in
neighbouring cells (ensure that this is in cells near the top of
your spreadsheet – in the first 10 rows). Credit will be awarded
for an easy to read spreadsheet (assume that you are presenting
it as a very brief electronic report).
(Please note the actual probability of an aircraft engine failing
in flight is reported to be less than 0.000001 – the reason for
choosing a larger probability in the questions is so that sensible
results may be obtained with only 2000 simulated flights.)
(30 marks)
2. A certain manufacturer of LED light bulbs finds that in
normal usage their 10W bulbs have a lifespan which is
approximately normally distributed with a mean of 15,000 hours
and a standard deviation of 2,000 hours. Use the built in

4. functions in Excel to help you perform the following
calculations:
(i) Find the probability that a bulb fails after 10,000 hours
normal usage;
(ii) Find the probability that a bulb lasts for longer than 18,000
hours normal usage;
(iii) Find the probability that a bulbs lasts for between 14,000
and 16,000 hours.
(iv) The manufacturer wishes to advertise that their bulbs are
guaranteed to last for longer than x hours. What is the highest
value can they give for x if they wish to be sure that 98% of
their bulbs will last longer than x hours?
Highlight the cells in which you obtain these results and write a
brief explanation of your calculations and conclusions in
neighbouring cells. Credit will be awarded for an easy to read
spreadsheet (assume that you are presenting it as a very brief
electronic report).
(15 marks)
3. During a manufacturing process a component is to be
machined in the shape of a hollow torus (a torus is a ring-
doughnut shape). The manufacturer wishes to model this torus
to calculate the surface area as this determines the quantity of
steel required for each component.
Use Maple to create plots of the graphs of the circles and (take
care with the + and - signs) and display both on the same axes
according to the following specifications (it is easier to use the
mouse activated plot editing features in Maple rather than
separate plot command options):

5. · Label the horizontal and vertical axes ‘x values’ and ‘y
values’ respectively and make sure that the horizontal axis runs
from -4 to 10 while the vertical axis runs from -7 to 7.
·
For the curve use a green dotted line.
·
For the curve use orange + signs (size 20).
· Give the plot the title ‘Torus Cross Section’.
· Create a legend which labels the curves, Cross Section 1 and
Cross Section 2 respectively.
· Superimpose a grid on the plot (with gridlines at axes tick
marks – this is the default).
(Marks are available for the specifications above – if you
cannot plot everything requested then at least plot something
with these specifications. Typing the command: with(plots);
will activate the implicitplot command which you will need to
plot the circles above.)
(For safety, to back-up your formatting amendments, export the
plot (when complete) to a Graphics Interchange Format file and
save it on your H: drive with your username as the file name.)
(30 marks)
The implicit definition of the circle may be split into 2
explicit formulae for y in terms of x (for the top half of the
circle) and (for the bottom half of the circle). (You may wish to
create appropriate functions for these.) Use Maple to obtain a
formula for for each of these.

6. (10 marks)
If the curve is rotated around the x-axis it forms a ‘surface
of revolution’ in the shape of the surface of a torus (a ring-
doughnut shape). In fact the pair of circles which you have
plotted represent the cross section shown if the torus is cut in
half.
The area of a surface of revolution obtained when a curve
between and is rotated about the x-axis is given by the value
of the integral . Apply this formula to the given curves
representing the circle to evaluate the total surface area of the
torus.
(15 marks)
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