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

• Engineering Professors Council (EPC)

• The Higher Education Academy: Engineering Subject Centre

• The Royal Academy of Engineering

• Institute of Mathematics and its Application (IMA)

• Engineering Diploma Development Partnership (EDDP)

• Engineering Council UK (ECuk)

• Mathematics in Education and Industry (MEI)

• University of Cambridge

• National Centre for Excellence in the Teaching Mathematics (NCETM)

The Task Group has also benefited from the input of observers from

• Qualifications and Curriculum Authority (QCA)

• A number of Awarding Bodies licensed to award qualifications to school and college leavers.

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:

• ASL Maths Unit (131KB)

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

	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:

• Teachers Resources (131KB)

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The Engineering Diploma Mathematics for Engineering