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Mathematics for Engineering: An ASL Qualification for The Advanced Diploma in Engineering
Introduction
Mathematics is an integral part of the study of engineering
regardless of which branch of engineering is chosen. Many in the engineering
community believe that additional mathematics material should be available
for those students studying the Advanced Diploma in Engineering to prepare
them for progression onto engineering degree courses at university. Many
also appreciate that teachers in schools and colleges need more real engineering
examples to underpin the essential mathematics and also to excite interest in
engineering. In response to these challenges, the engineering and maths communities
joined together in May 2007 to form a Maths Task Group.
Maths Task Group
The group contains
representatives from well established organisation
like
The Task Group has also
benefited from the input of observers from
This group has developed an Additional and Specialist
Learning (ASL) Mathematics qualification that will be available for any Level 3
learner wishing to develop his or her mathematical skills and knowledge
in a real life context, especially in engineering. A consensus is emerging
that students thinking of studying engineering at university should
take this qualification as an ASL Qualification along with the Advanced Diploma
in Engineering at Level 3. However, learners enrolled on other diplomas
might also choose to study this qualification.
Mathematics for Engineering
The ASL qualification is based on a foundation
year course taught at Loughborough University over many years. This course
is designed for students without A level Mathematics who wish to go on to
study engineering to degree level. It has been designed to contain all
the necessary topics from A level Mathematics to facilitate such study.
The unit is designed for 90 guided learning hours calculated as actual
class contact hours, lectures or tutorials etc. Very good results have
been achieved by students following this course in their subsequent engineering
studies at Loughborough.
Clearly, this ASL qualification would provide an appropriately
rigorous maths programme within the Engineering Diploma, tailored to the
needs of engineering students. To provide powerful motivation to students,
teachers/lecturers will be expected to highlight engineering applications of
the mathematics in the course. Support will be available to the
teachers to teach this qualification. Engineering Mathematics Exemplars are currently
under development and will be uploaded on this website as they are completed.
We are confident, based on the Loughborough experience,
that success in this demanding programme can prepare students on the Engineering
Diploma for subsequent university studies in Engineering, and possibly other
science or technology subjects as well.
For more information, please
see the following document:
This qualification is now
available in the National Database Accredited
Qualification catalogue and the details can be seen
on the following link:
http://www.accreditedqualifications.org.uk/qualification/50041368.seo.aspx
Engineering Mathematics Exemplars
The exemplars are intended to:
-
motivate mathematics
teaching and learning
-
provide support for
teachers teaching contextualised mathematics for
the first time
-
help students gain fluency
in the use of mathematics for practical problem
solving
-
illustrate the
applicability of the mathematics in the ASL unit
-
exemplify valuable
activities undertaken by engineers
Proposed Distribution of 50 exemplars over different engineering streams
 |
Engineering Stream |
 |
% & No. of Exemplars |
 |
Examples |
|
 |
|
 |
 |
Mechanical |
 |
20%
10 |
 |
Design, analysis and manufacture of
motor vehicles, aircraft, heating & cooling systems, watercraft, manufacturing plants,
industrial equipment and machinery, medical devices, Wind Turbines, Gas Holders,
machine tools, precision tools, engines, etc. |
|
 |
 |
Civil |
 |
20%
10 |
 |
Structural Engineering, Geotechnical
Engineering, Water Engineering, Transportation,
Highways, Construction, Engineering Surveying,
Material Technology
|
|
 |
 |
Electrical/Electronics |
 |
20%
10 |
 |
Design and construction of electronic circuits
to solve practical problems
Circuit Theory, Electronic Components (Resistors, Capacitors, Inductors, Diodes,
Transistors), Power Transmission, Motor Control, Domestic Appliances,
Telecommunications (Mobile phones, Landline, Internet), Computers and
integrated circuits, Battery Charger, Television, Radar and radio location
|
|
 |
 |
Chemical & Process Industries |
 |
20%
10 |
 |
Petroleum extraction, treatment, pipeline
transport and refining, petrochemical, chemical and pharmaceutical industries, pulp and
paper manufacturing, mining, food, beverages, ceramics, base metals, coal, plastics, rubber,
textiles, tobacco, wood and wood products, paper and paper products, etc.
|
|
 |
 |
Automotive & Aerospace |
 |
10%
5 |
 |
Design, construction and science behind Cars, Trucks,
Buses, Motorcycles, Trains, Aircrafts, Spacecrafts, Rockets, etc.
|
|
 |
 |
Health and Well Being |
 |
10%
5 |
 |
Recycling, Environmental Safety Issues, Water Purification,
etc.
|
Exemplars: Advanced Diploma
in Engineering
Keywords:
NS = Not Started
IP = In Progress
C = Complete
TBA = To Be Assigned
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Sr.No. |
 |
Exemplar Detail |
 |
Engineering Stream |
 |
Maths Used |
 |
Supporting Company |
 |
Status |
|
 |
|
 |
 |
1 |
 |
The Mathematics of Aircraft Navigation (1746KB) |
 |
Automotive & Aerospace |
 |
Trigonometry, Formula transposition, graphical methods, Vectors |
 |
Thales |
 |
C |
|
 |
 |
2 |
 |
Steam Pipe Insulation (249KB) |
 |
Mechanical, Electrical, Built Environment, Process Industries, Automotive & Aerospace |
 |
Geometry, Heat Transfer, Functions,
Graphs |
 |
Rolls-Royce |
 |
C |
|
 |
 |
3 |
 |
Underground Storage Tanks (283KB) |
 |
Chemical Industries |
 |
Integration by substitution, 2D Geometry of Ellipse, Use of trigonometric functions |
 |
Rolls-Royce |
 |
C |
|
 |
 |
4 |
 |
The Mathematics of Escalators on the London Underground (342KB) |
 |
Mechanical |
 |
Functions, Simple Calculations, Differentiation, Percentages,
Graphs |
 |
Transport for London |
 |
C |
|
 |
 |
5 |
 |
Calculating Power of JCB Diesalmax Engines (316KB) |
 |
Mechanical |
 |
Functions, Equation of Straight Line, Graphs, Differentiation |
 |
JCB Power Systems Limited |
 |
C |
|
 |
 |
6 |
 |
Study of Vibrations in JCB Diesalmax Engines (346KB) |
 |
Mechanical |
 |
Quadratic Equation, Differentiation, Matrix Method to solve Simultaneous Equation |
 |
JCB Power Systems Limited |
 |
C |
|
 |
 |
7 |
 |
The Study of Engineering Data 1 (579KB) |
 |
Health and Well Being |
 |
Mean, Median, Bar Chart, Pie Chart, Line Graph |
 |
ECUK |
 |
C |
|
 |
 |
8 |
 |
The Study of Root Mean Square Value (245KB) |
 |
Mechanical, Electrical, Electronics |
 |
RMS value is
Trigonometrical identities
Integration
Plotting graphs of any function using ICT
|
 |
The Diploma in Engineering |
 |
C |
|
 |
 |
9 |
 |
Study of the
Motion of Knee and Ankle during Cycling (249KB) |
 |
Public Health Engineering |
 |
Inertial Forces, Newton’s Law of Motion, Differentiation, Components of Vector Quantities |
 |
The Diploma in Engineering |
 |
C |
|
 |
 |
10 |
 |
Study of Suspension System in JCB Construction Machinery (291KB) |
 |
Mechanical and Civil Engineering |
 |
Newton’s laws of motion; Hooke’s law of
elasticity; Solving simultaneous equations using
the matrix method followed by the substitution
method that involves first and second
derivatives; Expanding a determinant and finding
inverse of a matrix |
 |
JCB Excavators Limited |
 |
C |
|
 |
 |
11 |
 |
Study of Dynamic Systems in JCB Construction
Machinery (417KB) |
 |
Mechanical and Civil Engineering |
 |
Newton’s Laws of motion and Hooke’s Law of
stiffness, Principle of Conservation of
Momentum, Product rule of differentiation,
Finding maximum values using first derivatives,
Plotting graphs using Excel or similar software |
 |
JCB Excavators Limited |
 |
C |
|
 |
 |
12 |
 |
Mathematics behind the Water Network in Rural Mountain Areas (340KB) |
 |
Public Health Engineering |
 |
Differential Equation, Optimisation, Graphs, Matrices |
 |
The Diploma in Engineering |
 |
C |
|
 |
 |
13 |
 |
Handling Hazardous Liquids during Chemical Processing (270KB) |
 |
Chemical |
 |
Bernoulli’s conservation of energy equation; Integration and differentiation |
 |
MW
Kellogg Ltd |
 |
C |
|
 |
 |
14 |
 |
Formula One Race Strategy (500KB) |
 |
Sports Technology |
 |
Use of empirical formulae, tabular data and graphs; using derivatives to find the optimum point; integration; area under the curve |
 |
Mclaren Racing Limited |
 |
C |
|
 |
 |
15 |
 |
The Mathematics of Simple Beam Deflection (189KB) |
 |
Civil |
 |
Some terminology relating to structural design and construction, Algebraic processes |
 |
Laing O’Rourke |
 |
C |
|
 |
 |
16 |
 |
The Mathematics behind the Deflection in Cantilever |
 |
Civil |
 |
Some terminology relating to structural design and construction, Algebraic processes, differential equation |
 |
Laing O’Rourke |
 |
IP |
|
 |
 |
17 |
 |
The Mathematics of Pumping Water |
 |
Civil and Mechanical |
 |
Introduction to the terminology used in pumping water; Conversion of units; Solving problem with Back-substitution method; Plotting graphs using Excel sheets |
 |
AECOM Design Build |
 |
IP |
|
 |
 |
18 |
 |
Calculating Forces around the Wings of Bloodhound SSC |
 |
Mechanical |
 |
Bernoulli’s Equation . |
 |
Bloodhound Engineering Project |
 |
IP |
|
 |
 |
19 |
 |
Understanding the Rocket Performance in BLOODHOUND SSC |
 |
Mechanical |
 |
Terms used in Aerodynamics; Simple cakculations and manipulating algebraic expression; Some terminology from Chemistry and Physics |
 |
Bloodhound Engineering Project |
 |
IP |
|
 |
 |
20 |
 |
Understanding the motion of the wheels |
 |
Mechanical |
 |
Frames of reference; Parametric equations of circle and cycloid; Calculation of velocity and acceleration |
 |
Bloodhound Engineering Project |
 |
IP |
|
 |
 |
21 |
 |
Vibrations in Gas Turbine |
 |
Mechanical |
 |
Testing the effects of vibration, statistics |
 |
NPower |
 |
IP |
|
 |
 |
22 |
 |
Forces on large steam turbine blades |
 |
Mechanical, Electrical and Power Industry |
 |
Centripetal Forces and stress calculation |
 |
NPower |
 |
IP |
|
 |
 |
23 |
 |
Wind Turbine Power Calculations |
 |
Mechanical, Electrical, Power Industry |
 |
Calculating energy and power |
 |
NPower |
 |
IP |
|
 |
 |
24 |
 |
Dropped Load Assessment in Nuclear Industry |
 |
Electrical, Mechanical |
 |
Risk assessment; Inertia Forces; Calculating stress, strain, energy, etc. |
 |
British Energy |
 |
IP |
|
 |
 |
25 |
 |
Optimising the Cost of Tipping |
 |
Civil |
 |
Pythagoras Theorem, Cost and Time analysis |
 |
Transport for London |
 |
IP |
|
 |
 |
26 |
 |
Addressing growing demands on London Overground |
 |
Mechanical, Health and Well Being |
 |
Simple Calculations, Graphs, |
 |
London Rail |
 |
IP |
|
 |
 |
27 |
 |
The Cutting Tool Industry |
 |
Manufacturing, Process Industry |
 |
Functions, Log graph, Cost Optimisation using Differentiation |
 |
Boxford |
 |
IP |
|
 |
 |
28 |
 |
Calculating Work done, Temperature and Thrust for a Water Rocket |
 |
Mechanical |
 |
Work done; Temperature; Thrust |
 |
National Physical Laboratory |
 |
IP |
|
 |
 |
29 |
 |
Engineering behind London Eye |
 |
Civil, Mechanical, Electrical |
 |
2D Geometry, Circles, Forces, Trigonometry |
 |
TBC |
 |
IP |
We are committed to produce as many exemplars as possible
in any of the above Engineering Stream. Further support in exemplar development will
be highly appreciated. If you have any further question, wish to add your
suggestions, need more information or want to support this development with an
engineering case study, please contact:
Dr Sapna Somani
Maths Coordinator
14-19: Diploma in Engineering
The Royal Academy of Engineering
3 Carlton House Terrace
London
SW1Y 5DG
Mobile: 07878 633 730
Email: Sapna Somani
Other Teaching Resources
A summary of useful websites for teachers:
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