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 Unit that will be available for any Level 3 learner wishing to develop his or her mathematical skills and knowledge in real life context, especially in engineering. A consensus is emerging that students thinking of studying engineering at university should take this unit 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 syllabus of this ASL Unit 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 180 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 unit 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. Adequate support will be available to the teachers to teach this unit. 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.
	Construction and Built Environment		20% 10		Structural Engineering, Water Provision, Transportation, Architecture City planning, Construction, Cultural landscape, Environmental Design, Interior architecture, Landscape architecture, Urbanism
	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

List of Proposed Exemplars

Status:
NS = Not Started
IP = In Progress

	Sr.No.		Exemplar Detail		Engineering Stream		Maths Used		Related Industry		Status
	1		The Mathematics of Aircraft Navigation		Automotive & Aerospace		Trigonometry, Formula transposition, graphical methods, Vectors		Thales		IP
	2		Steam Pipe Insulation		Mechanical, Electrical, Built Environment, Process Industries, Automotive & Aerospace		Geometry, Heat Transfer, Functions, Graphs		Rolls-Royce		IP
	3		Underground Storage Tanks		Chemical Industries		Integration by substitution, 2D Geometry of Ellipse, Use of trigonometric functions		Rolls-Royce		IP
	4		Operating Escalators on London Underground		Mechanical		Functions, Simple Calculations, Differentiation, Percentages		London Underground		IP
	5		Engineering behind London Eye		Civil, Mechanical, Electrical		2D Geometry, Circles, Forces, Trigonometry		London Eye Company Limited		IP
	6		JCB Diesalmax Power Engines		Mechanical		Functions, Equation of Straight Line, Graphs, Differentiation		JCB Power Systems Limited		IP
	7		Vibrations in Gas Turbine		Mechanical		Testing the effects of vibration, statistics		NPower		IP
	8		Engineering of Wind Turbines		Mechanical		Statistics, Using Empirical formulae, calculating velocity, time, etc.		E.ON		IP
	9		Water Sealed Gas Holder		Mechanical		Calculating temperature, pressure of gas, pump capacity, etc.		National Grid		IP
	10		The Deflection of Beam		Civil		Curvature, Bending Moments, Differential Equation and Integration Techniques, Geometry of Triangle, Centroid		TBC		IP
	11		The Mathematics of Earthwork Calculations		Civil		Maps and contours, Geometry, Trigonometry, Numerical Integration		The Environment Agency		IP
	12		The Mathematics of Engineering Surveying		Civil		Engineering surveying, Geometry, Trigonometry		TBC		IP
	13		The Analysis of Framed Bridge Structures		Civil		Structural design and construction, Vector components of force, Solution of simultaneous equations using matrix techniques		TBC		IP
	14		The Mathematics of Highway Design		Civil		Highway construction, Geometry and properties of the circle		TBC		IP
	15		Construction of Tunnels, Dams, Bridges		Civil		Engineering Material				NS
	16		Simple Harmonic Motion of a piston in a machine		Mechanical		Differential equation				NS
	17		Functioning of hot water kettle/coffee maker		Electrical /Electronics		Calculating temperature, pressure, optimum height, etc.				NS
	18		Glass Industry		Process Industries		Temperature, Pressure, Calculus				NS
	19		Functioning of water pumps		Mechanical, Electrical		Pressure, Calculus				NS
	20		Water Purifier / Filter		Mechanical, Electrical, Health and Well Being		Calculating pressure, optimum height, etc.				NS
	21		Engineering behind the hand dryer		Electrical, Electronics, Health and Well Being		Velocity, temperature, time, etc.				NS
	22		Television Transmitter		Electrical, Electronics		Circuit theory				NS
	23		Paper Manufacturing		Process Industries		Engineering material				NS
	24		Power Station		Electrical						NS
	25		Nuclear Reactor		Mechanical						NS
	26		Space, Rocket, Satellite		Aeronautical						NS
	27		Chemical Plant		Process Industries						NS
	28		Oil Refinery		Process Industries						NS
	29		Air Conditioning System		Electrical, Design Technology						NS
	30		Washing Machine		Electrical, Electronics, Health and Well Being						NS
	31		Electronics Gadgets like digital MP3 Player, Ipod, Mobile Phone, Laptop, Desktops, Fax Machines, Printers, etc.		Electrical, Electronics						NS
	32		Designing Furniture, Analysing new material for latest furniture technology		Process Industries, Design Technology						NS

We are committed to produce as many exemplars as possible in any of the above Engineering Stream. Any 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

Direct Tel.: 020 7766 0639
Mobile: 07878 633 730
Email: Sapna Somani

Other Teaching Resources

• Teachers Resources (131KB)

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The Engineering Diploma Mathematics for Engineering