This document provides details for an assignment for a mathematics/computation module. It includes 5 questions worth a total of 100 marks. It provides learning outcomes being tested, submission details, formatting instructions, and assessment criteria. The deadline is February 3rd, 2015. References must be included using the Numeric or Harvard style. Questions involve solving differential equations using Laplace transforms, Markov modeling, linear programming, and probabilistic analysis techniques.

1. Assignment Brief 2014/15
Assignment Details
This assignment is a series of five mathematical/computational
questions, some requiring more than one computation and not
all of equal value. The 100 marks for this assignment have been
divided up amongst the series of problems. The marks for each
problem are shown in square brackets at the end of the question.
Attempt all five problems
· You must demonstrate that you have met the learning
outcomes below
· As you construct and present your work, consider the
assessment criteria
Learning outcomes
From the module descriptor the “indicative” assessment criteria
were used to produce this test for you. It was also considered to
focus on materials to be learned in the first block of teaching.
The practice you gain with this assignment should help you to
prepare for the way problems are written and marked in the
final exam.
The learning outcomes being tested here are: 1,2,3
· Apply Transforms to solve differential equations for
engineering problems
· Apply Linear programming and Markov modelling techniques
to the solution of complex engineering problems
· Critically evaluate probabilistic analysis techniques.
These outcomes may be further assessed in the final exam,
along with the remaining outcomes not tested here. Be assured
you will be tested on everything.

2. The deadline for submission is
4.00pm on the 3rd Feb 2015
Every attempt will be made to ensure that the work will be
marked and available for collection by 24th Feb 2015.
The assignment is worth 40% of the total module assessment.
Assessment Criteria
For more information please see the marking guide at Appendix
1
Submission
Your work must be submitted with:
· a front cover sheet (detailing the module code and title,
coursework title, module name and student name, word count,
date submitted).
· a firmly attached and fully completed School Assessment
Cover Sheet. These are available from JBF203. It should not be
submitted in folders, plastic wallets or paper clipped
The assignment should be submitted:
electronically to turn-it-in before the deadline using the link on
the module area on blackboard
Presentation Instructions
The word limit is 2500 words (+/-10%). This excludes footnotes
but includesquotations and appendices.
Remember: You must keep to the word limit of 2500 words
It is your responsibility to ensure that your work is neatly and
accurately presented.

3. The work must be:
· Word-processed
· Single sided
· 1.5 or double line spaced
· Times New Roman or Ariel 12 point font
· Justified
· Page numbered
· On A4 paper
· Margins left and right 3cm
· Stapled together at the top left-hand corner
· Attached to a cover sheet.
Marks may be deducted for failure to follow these instructions.
Please look at the Student Guide to Assessment for more
information.
Referencing
All academic writing must be referenced. If you use other
people’s ideas without referencing them you are plagiarising
their work.
Use either the Numeric or Havard system of referencing
withinyour text.
1
Solve the following initial value problems (IVP) using the
Laplace transform method.

4. (i) , , (equation 1)
[12 marks for this
part]
(ii) , (equation 2)
[8 marks for this
part]
[Total 20 marks for this
question]
2
Your exam could be marked with a range of possible grades,
simplified as on the following state diagram:
Acceptable
To begin with the chances are that you will pass with a standard
result. Each 45 minutes (the time allocated for each answer)
your grade could go up or down to a neighbouring grade or stay
put.
There is a chance that your Genius is so great that the examiner
cannot appreciate what you are saying and incorrectly marks it
as nonsense.
What is your grade most likely to be after the 3 hour exam?
[10 marks]

5. What (if any) are the steady state results for a group of 14
students? [10 marks]
[Total 20 marks for this
question]
3
The Cannon Hill furniture Company produces tables and chairs.
Each table takes five hours of labor from the carpentry
department and three hours of labor from the finishing
department. Each chair requires three hours of carpentry and
two hours of finishing. During the current week, 230 hours of
carpentry time are available and 90 hours of finishing time.
Each table produced gives a profit of £85 and each chair a profit
of £55. How many chairs and tables should be made?
[Total 20 marks for this
question]
4
A very new European “Rapid Reaction Force for Fire” has been
created today and begins operation between three Countries
“A”, “B” and “C”. It’s main resource is a super aircraft
“Funderbird2” with a massive water cannon that even carries a
small mini-submarine for fighting fires at sea. Unfortunately, it
can only be in one Country at a time.

6. What is the matrix representation of this problem?
[5 marks]
The probabilities of going to a fire in another Country, given
that the force are in a given Country to begin with, are shown
on the sketch above (any resemblance to any particular Country
or Nation is purely coincidence and not intended). The
probabilities were obtained as a weekly average using statistics
for fires over many recorded weeks.
When will the plane take up permanent residence in one
Country? [15 marks]
[Total 20 marks for this
question]
5

7. 0.1
A
0.5
0.1
0.3
B C
0.05
Figure 3. State diagram for Question 3.
For the state diagram shown on Figure 3 the initial state is ‘C’
and the time steps are days. Find the following:
i) Find the stochastic transitional probability matrix
[5 marks for this part]
ii) Find the probability of being in state ‘C’ after two time steps
[5 marks for this part]
iii) What is the steady state probability of being in state ‘A’?
[8 marks for this part]
iv) What is the steady state probability of being in either state
‘B’ OR state ‘C’?
[2 marks for this part]
[Total 20 marks for this

8. question]
Plagiarism
The use of work produced for another purpose by you, working
alone or with others, must be acknowledged.
Copying from the works of another person (including Internet
sources) constitutes plagiarism, which is an offence within the
University’s regulations. Brief quotations from the published or
unpublished works of another person, suitably attributed, are
acceptable. You must always use your own words except when
using properly referenced quotations.
You are advised when taking notes from books or other sources
to make notes in your own words, in a selective and critical
way.
General Criteria
In grading your work we will be assessing the extent to which it
matches the criteria attached. The criteria are not of equal
importance, but it is not possible to ascribe an exact weighting
to each. What follows is intended as a general guide to the
standards.
1. Severe weakness in understanding the
issues/arguments/theory is likely to result in a mark of less than
40%.
2. Thorough coverage of the relevant material, with statements
supported by data, evidence, literature or examples, is necessary
to gain 52% or above.

9. 3. Work which is disorganised with points randomly ordered is
unlikely to gain more than 48%.
4. A logical, well-explained argument, combined with other
good characteristics is usually necessary to obtain 75%.
5. Fluent grammatical expression is important for expressing
ideas clearly. Errors in this area are likely to lead to a reduction
in marks.
4
Grade
Relevance
Knowledge
Analysis
Argument & Structure
Originality
Presentation
20%
20%
15%
20%
15%
10%
70 – 100%
Directly relevant to title. Able to address the implications,
assumptions and nuances of the title.
Relevance to practice is thoroughly and explicitly addressed.
Makes effective use of a comprehensive range of theory and
practice knowledge.

10. Demonstrates ability in the manipulation and transfer of subject
material to demonstrate a solid understanding of the issues in
both theory and practice.
A comprehensive analysis of the material resulting in clear and
illuminating conclusions.
Coherent and logically structured, making creative use of an
appropriate mode of argument and/or theoretical model.
Distinctive work showing independent thought and critical
engagement with alternative views.
A very well written answer with standard spelling and syntax.
Style is lucid and resourceful with an appropriate
bibliographical apparatus.
60-69%
Directly relevant to title.
Is able to demonstrate effective practice relevance.
Makes effective use of good theory and practice knowledge.
Manipulates and transfers some material to demonstrate a clear
grasp of the themes, questions and issues in theory and practice.
Good analysis of the material resulting in clear and logical
conclusions.
Generally coherent and logically constructed.
Uses an appropriate mode of argument or theoretical model.
Contains some distinctive or independent thinking.
Beginning to formulate an independent position
Well written with standard spelling and syntax.
Style is lucid utilising an appropriate format and bibliographical
apparatus.
50-59%
Generally addresses the title, sometimes addresses irrelevant

11. issues.
Relevance to practice effectively addressed, may be implicit in
places.
Adequate knowledge of a fair range of relevant theoretical and
practice related material with evidence of an appreciation of its
significance.
Adequate analytical treatment, with occasional descriptive or
narrative passages which lack clear analytical purpose.
Conclusions are clear.
Adequate attempt to construct a coherent argument, but may
suffer loss of focus and consistency.
Issues at stake may lack clarity or theoretical models couched in
simplistic terms.
Sound work which expresses a personal position, often in broad
terms and tends towards uncritical conformity to one or more
standard views of the topic.
Competently written with only minor lapses from standard
spelling and syntax.
Style is readable with acceptable format and bibliographical
status.
41-49%
Some degree of irrelevance to the title.
Superficial consideration of the issues.
Relevance to practice tends towards superficiality and is largely
implicit.
Adequate knowledge of a limited range of relevant theoretical
and practice related material with intermittent evidence of an
appreciation of its significance.
Evidence of analytical ability.

12. Intermittent passages of descriptive or narrative material which
lack clear analytical purpose.
Conclusions are not always clear and logical.
Some attempt to construct an argument is evident but it lacks
sufficient clarity and coherence.
Issues at stake are only vaguely stated.Largely derivative.
Attempts to present a personal view, but only in broad terms.
Is largely uncritical and conforms to one or more standard
views.
Generally competent writing although intermittent lapses from
standard syntax and spelling and pose occasional obstacles for
the reader.
Format and bibliography is generally error free and acceptable.
40%
Some degree of irrelevance to the title is common.
Only the most obvious issues are addressed at a superficial level
and in unchallenging terms.
Relevance to practice is superficially addressed and rarely made
explicit
Basic understanding of a limited range of relevant theoretical
and practice related material.
Largely descriptive or narrative in style with limited evidence
of analytical capability.
Conclusions are not always clear or logical
A basic argument is evident but tends to be supported by
assertion and lacks proper development.

13. Coherence and clarity are evident only intermittently
Largely derivative.
No personal view is adequately formulated
Wholly uncritical and conforming to one or more standard
views.
Style of presentation makes reading difficult.
Deficiencies in spelling, syntax, format or bibliographical
apparatus impact significantly upon clarity.
0-39%
Relevance to the title is intermittent or missing.
The topic is reduced to its vaguest and least challenging terms.
Relevance to practice is barely considered or not at all.
A limited understanding of a narrow range of relevant
theoretical and practice related material or a lack of basic
knowledge in either or both theory and practice necessary for an
understanding of the topic
Heavy dependence on description and/or narrative.
Paraphrase is common.
Evidence of analysis is lacking.
Clear and logical conclusions are sparse
Little evidence of coherent argument.
There is a lack of development and the work may be repetitive
and/or thin.
Almost wholly derivative.

14. The writer’s contribution rarely goes beyond simplifying
paraphrase.
No evidence of personal thought.
Poorly written with numerous deficiencies in syntax, spelling,
expression and presentation.
The writer may achieve clarity (if at all) only by using
simplistic or repetitious style.
(
)
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0.5
0.6
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0.8
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Acceptible
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Genius
0.5
0.6
0.1
0.1
0.5
0.8
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Fail
Acceptible
Standard
Genius
0.50.60.1
0.1
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AcceptibleStandard
Genius
0.1
0.4
0.1
A

16. B
C
0.3
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0.4
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A
B
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