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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. They 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,
members of 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
Observers from the
Qualifications and Curriculum Development Agency and
a number of awarding organisations have also
contributed to the work of the Task Group.
The group has developed an
Additional and Specialist Learning (ASL) Mathematics
qualification that is available for any Level 3
learner wishing to develop their 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. For more information please
download the flyer below:
OCR Level 3 Certificate in Mathematics for Engineering (H860)
This qualification is offered
by OCR and all the necessary details with full
specification and sample assessment material are
available on the OCR’s website on the following
link:
http://www.ocr.org.uk/qualifications/type/ogq/maths/eng_l3_cert/index.html
This 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. Very good results in their
subsequent engineering studies have been achieved by
students at Loughborough who followed this course.
This ASL qualification
provides 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 practical engineering
applications of the mathematics in the course. 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 all branches of Engineering,
and possibly other science or technology subjects as
well.
This qualification is also
available in The Register of Regulated
Qualifications and the details can be seen
on the following link:
http://register.ofqual.gov.uk/Qualification/Details/500_4136_8
OCR Level 3 Certificate in Mathematical Techniques and Applications for Engineers (H865)
If you wish to study
OCR Level
3 Certificate in Mathematics for Engineering (H860)
with any level 3 diploma other than Engineering
Diploma, like the Manufacturing Diploma or the
Construction and Built Environment Diploma, then you
will find
OCR Level 3 Certificate in Mathematical
Techniques and Applications for Engineers (H865)
significantly helpful to cope with the in-depth used
in H860. In other words, H865 serves as a
prerequisite for H860.
Engineering Mathematics Exemplars
To support the teachers of
this qualification, a number of Engineering
Mathematics Exemplars have been developed during the
last two years and they are available to download
from this webpage; please see below.
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 |
|
|
|
|
|
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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. |
|
|
|
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Civil |
|
20%
10 |
|
Structural Engineering, Geotechnical
Engineering, Water Engineering, Transportation,
Highways, Construction, Engineering Surveying,
Material Technology
|
|
|
|
|
Electrical/Electronics |
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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
|
|
Sr.No. |
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Exemplar Detail |
|
Engineering Stream |
|
Maths Used |
|
Supporting Company |
|
Status |
|
|
|
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1 |
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The Mathematics of Aircraft Navigation (1746KB) |
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Automotive & Aerospace |
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Trigonometry, Formula transposition, graphical methods, Vectors |
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Thales |
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C |
|
|
|
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2 |
|
Steam Pipe Insulation (249KB) |
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Mechanical, Electrical, Built Environment, Process Industries, Automotive & Aerospace |
|
Geometry, Heat Transfer, Functions,
Graphs |
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Rolls-Royce |
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C |
|
|
|
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3 |
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Underground Storage Tanks (283KB) |
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Chemical Industries |
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Integration by substitution, 2D Geometry of Ellipse, Use of trigonometric functions |
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Rolls-Royce |
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C |
|
|
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4 |
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The Mathematics of Escalators on the London Underground (342KB) |
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Mechanical |
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Functions, Simple Calculations, Differentiation, Percentages,
Graphs |
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Transport for London |
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C |
|
|
|
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5 |
|
Calculating Power of JCB Diesalmax Engines (316KB) |
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Mechanical |
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Functions, Equation of Straight Line, Graphs, Differentiation |
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JCB Power Systems Limited |
|
C |
|
|
|
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6 |
|
Study of Vibrations in JCB Diesalmax Engines (346KB) |
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Mechanical |
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Quadratic Equation, Differentiation, Matrix Method to solve Simultaneous Equation |
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JCB Power Systems Limited |
|
C |
|
|
|
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7 |
|
The Study of Engineering Data 1 (579KB) |
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Health and Well Being |
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Mean, Median, Bar Chart, Pie Chart, Line Graph |
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ECUK |
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C |
|
|
|
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8 |
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The Study of Root Mean Square Value (245KB) |
|
Mechanical, Electrical, Electronics |
|
RMS value is
Trigonometrical identities
Integration
Plotting graphs of any function using ICT
|
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The Diploma in Engineering |
|
C |
|
|
|
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9 |
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Study of the
Motion of Knee and Ankle during Cycling (249KB) |
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Public Health Engineering |
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Inertial Forces, Newton’s Law of Motion, Differentiation, Components of Vector Quantities |
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The Diploma in Engineering |
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C |
|
|
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|
10 |
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Study of Suspension System in JCB Construction Machinery (291KB) |
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Mechanical and Civil Engineering |
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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 |
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JCB Excavators Limited |
|
C |
|
|
|
|
11 |
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Study of Dynamic Systems in JCB Construction
Machinery (417KB) |
|
Mechanical and Civil Engineering |
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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 |
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JCB Excavators Limited |
|
C |
|
|
|
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12 |
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Mathematics behind the Water Network in Rural Mountain Areas (340KB) |
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Public Health Engineering |
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Differential Equation, Optimisation, Graphs, Matrices |
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The Diploma in Engineering |
|
C |
|
|
|
|
13 |
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Handling Hazardous Liquids during Chemical Processing (270KB) |
|
Chemical |
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Bernoulli’s conservation of energy equation; Integration and differentiation |
|
MW
Kellogg Ltd |
|
C |
|
|
|
|
14 |
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Formula One Race Strategy (500KB) |
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Sports Technology |
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Use of empirical formulae, tabular data and graphs; using derivatives to find the optimum point; integration; area under the curve |
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Mclaren Racing Limited |
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C |
|
|
|
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15 |
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The Mathematics of Simple Beam Deflection (189KB) |
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Civil |
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Some terminology relating to structural design and construction, Algebraic processes |
|
Laing O’Rourke |
|
C |
|
|
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|
16 |
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The Mathematics of Pumping Water (151KB) UPDATED |
|
Civil and Mechanical |
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Introduction to the terminology used in pumping water; Conversion of units; Solving problem with Back-substitution method; Plotting graphs using Excel sheets |
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AECOM Design Build |
|
C |
|
|
|
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17 |
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Understanding the motion of the wheels (322KB) |
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Mechanical |
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Frames of reference; Parametric equations of circle and cycloid; Calculation of velocity and acceleration |
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Bloodhound Engineering Project |
|
C |
|
|
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|
18 |
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Monitoring Vibration Levels in Steam Turbine (794KB) |
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Mechanical, Electrical, Power Industry |
|
Testing the effects of vibration, statistics |
|
NPower |
|
C |
|
|
|
|
19 |
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Forces on large steam turbine blades (728KB) |
|
Mechanical, Electrical and Power Industry |
|
Centripetal Forces and stress calculation |
|
NPower |
|
C |
|
|
|
|
20 |
|
Wind Turbine Power Calculations (98KB) |
|
Mechanical, Electrical, Power Industry, Renewable Energy |
|
Calculating energy and power |
|
NPower |
|
C |
|
|
|
|
21 |
|
Dropped Load Assessment in Nuclear Industry (296KB) UPDATED |
|
Electrical, Mechanical |
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Risk assessment; Inertia Forces; Calculating stress, strain, energy, etc. |
|
British Energy |
|
C |
|
|
|
|
22 |
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Understanding the Rocket Performance in BLOODHOUND SSC (85KB) |
|
Mechanical |
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Terms used in Aerodynamics; Simple calculations
and manipulating algebraic expression; Some
terminology from Chemistry and Physics |
|
Bloodhound Engineering Project |
|
C |
Exemplars: Advanced Diploma in Construction and Built Environment
(These exemplars are being developed in association with Institution of Civil Engineers.)
|
|
Sr.No. |
|
Exemplar Detail |
|
Engineering Stream |
|
Maths Used |
|
Supporting Company |
|
Status |
|
|
|
|
|
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1 |
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The Mathematics of Beam Deflection (147KB) |
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Civil |
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Curvature, Bending Moments, Differential Equation and Integration Techniques, Geometry of Triangle, Centroid |
|
CITB - Construction Skills |
|
C |
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2 |
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The Mathematics of Earthwork Calculations (133KB) |
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Civil |
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Maps and contours,
Geometry, Trigonometry,
Numerical Integration
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CITB - Construction Skills |
|
C |
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3 |
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The Mathematics of Framed Bridge Structures (171KB) |
|
Civil |
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Structural design and construction, Vector components of force, Solution of simultaneous equations using matrix techniques |
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CITB - Construction Skills |
|
C |
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4 |
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The Mathematics of Highway Design (198KB) |
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Civil |
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Highway construction, Geometry and properties of the circle |
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CITB - Construction Skills |
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C |
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5 |
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The Mathematics of Construction Shapes (505KB) |
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Civil |
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Construction technology, Geometry, Integration techniques |
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CITB - Construction Skills |
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C |
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6 |
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The Mathematics of Material Quality Control (109KB) |
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Civil |
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Concrete testing technology, Statistical Methods |
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CITB - Construction Skills |
|
C |
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7 |
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The Mathematics of Water Flow in Channels (87KB) |
|
Civil |
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Principles of hydraulics and construction methods, Geometry |
|
CITB - Construction Skills |
|
C |
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8 |
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The Mathematics of Engineering Surveying (1) (160KB) |
|
Civil |
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Engineering surveying, Geometry, Trigonometry
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CITB - Construction Skills |
|
C |
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9 |
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The Mathematics of Engineering Surveying (2) (118KB) |
|
Civil |
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Engineering surveying, Geometry, Trigonometry |
|
CITB - Construction Skills |
|
C |
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10 |
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The Mathematics of Engineering Surveying (3) (137KB) |
|
Civil |
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Engineering surveying, Geometry, Trigonometry |
|
CITB - Construction Skills |
|
C |
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
Project Officer (Engineering) - National HE STEM
Programme
The Royal Academy of Engineering
3 Carlton House Terrace
London
SW1Y 5DG
Email: Sapna Somani
Other Teaching Resources
A summary of useful websites for teachers:
Videos on Mathematics and
Engineering Careers
The Royal Academy of
Engineering, in collaboration with the Institute of
Mathematics and its Applications (IMA), has produced
some exciting career videos filming young and
diverse engineers working in industries, showing how
mathematics is a vital part of engineering in their
day to day life.
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