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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 materials should be made available to students studying what was originally the Advanced Diploma in Engineering to prepare them for progression onto engineering degree courses at university. The resources are also useful for current Level 3 programmes that have further mathematics elements.

Teachers in schools and colleges need access to more real engineering examples to underpin the mathematics as well as to excite an 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.

The following sets of resources are the outcome of the work carried out and present mathematics being used by engineers. They are laid out in sector order, so each resource may appear in more than one sector. Underneath each resource title is a description of the mathematical and/or science area it covers along with the supporting company behind the resource.

Mathematical and/or science areas are trigonometry; formula transposition; graphical methods and vectors

Supporting company: Thales

The mathematics of aircraft navigation (1.72 MB)

Mathematical and/or science area: integration by substitution; 2D geometry of ellipse and use of trigonometric functions

Supporting company: Rolls-Royce

Underground storage tanks (283.83 KB)

Mathematical and/or science area: mean; median; bar chart; pie chart and line graph

Supporting company: ECUK

The study of engineering data (579.39 KB)

Mathematical and/or science area: inertial forces; Newton’s law of motion; differentiation; trigonometry and components of vector quantities

Study of the motion of the knee and ankle during cycling (249.85 KB)

Mathematical and/or science area: differential equation; optimisation; graphs and matrices

Mathematics behind the water network in rural mountain areas (340.71 KB)

Mathematical and/or science area: Bernoulli’s conservation of energy equation; Integration and differentiation

Supporting company: MW Kellogg Ltd

Handling hazardous liquids during chemical processing (270.92 KB)

Mathematical and/or science area: Use of empirical formulae; tabular data and graphs; using derivatives to find the optimum point; integration; area under the curve

Supporting company: McLaren Racing Limited

Formula one race strategy (498.59 KB)

Mathematical and/or science area: geometry; heat transfer; functions and graphs

Supporting company: Rolls-Royce

Steam pipe insulation (250.13 KB)

Mathematical and/or science area: functions; simple calculations; differentiation; percentages and graphs

Supporting company: Transport for London

The mathematics of escalators on the London Underground (342.66 KB)

Mathematical and/or science area: functions; equation of straight line; graphs and differentiation

Supporting company: JCB Power Systems Limited

Calculating power of JCB Dieselmax engines (317.40 KB)

Mathematical and/or science area: quadratic equation; differentiation and matrix method to solve simultaneous equations

Supporting company: JCB Power Systems Limited

Study of vibrations in JCB Dieselmax engines (347.68 KB)

Mathematical and/or science area: RMS value is trigonometrical identities; integration and plotting graphs of any function using ICT

The study of root mean square value (244.86 KB)

Mathematical and/or science area: 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

Supporting company: JCB Excavators Limited

Study of suspension in JCB construction machinery (291.76 KB)

Mathematical and/or science area: Newton’s Laws of motion; Hooke’s Law of stiffness; principle of conservation of momentum; product rule of differentiation; finding maximum values using first derivatives and plotting graphs using Excel or similar software

Supporting company: JCB Excavators Limited

Study of dynamic systems in JCB construction machinery (417.23 KB)

Mathematical and/or science area: some terminology relating to structural design and construction; Young’s modules Algebraic processes

Supporting company: Laing O’Rourke

The mathematics of simple beam deflection (174.08 KB)

Mathematics and/or science area: curvature; bending moments; calculus; geometry of triangle and centroid

Supporting company: CITB - Construction Skills

The mathematics of beam deflection (130.23 KB)

Mathematical and/or science area: introduction to the terminology used in pumping water; conversion of units; solving problem with back-substitution method and plotting graphs using Excel sheets

Supporting company: AECOM Design Build

The mathematics of pumping water (600.22 KB)

Mathematical and/or science area: frames of reference; parametric equations of circle and cycloid; calculation of velocity and acceleration

Supporting company: Bloodhound Engineering Project

Understanding the motion of the wheels (72.05 KB)

Mathematical and/or science area: testing the effects of vibration and statistics

Supporting company: NPower

Monitoring vibration levels in steam turbines (793.42 KB)

Mathematical and/or science area: centripetal forces and stress calculation

Supporting company: NPower

Forces on large steam turbine blades (174.36 KB)

Mathematical and/or science area: calculating energy and power

Supporting company: NPower

Wind turbine power calculations (93.99 KB)

Mathematical and/or science area: risk assessment; inertia forces; calculating stress; strain and energy

Supporting company: British Energy

Dropped load assessment nuclear industry (168.76 KB)

Mathematical and/or science area: terms used in aerodynamics; simple calculations and manipulating algebraic expression; terminology from chemistry and physics

Supporting company: Bloodhound Engineering Project

Understanding the rocket performance in Bloodhound SSC (81.02 KB)

Mathematical and/or science area: concrete testing technology and statistical methods

Supporting company: CITB - Construction Skills

The mathematics of material quality control (88.66 KB)

Mathematical and/or science area: 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

Supporting company: JCB Excavators Limited

Study of suspension in JCB construction machinery (291.76 KB)

Mathematical and/or science area: Newton’s Laws of motion; Hooke’s Law of stiffness; Principle of conservation of momentum; product rule of differentiation; finding maximum values using first derivatives and plotting graphs using Excel or similar software

Supporting company: JCB Excavators Limited

Study of dynamic systems in JCB construction machinery (417.23 KB)

Mathematical and/or science area: some terminology relating to structural design and construction; Young’s modules algebraic processes

Supporting company: Laing O’Rourke

The mathematics of simple beam deflection (174.08 KB)

Mathematics and/or science area: curvature; bending moments; calculus; geometry of triangle and centroid

Supporting company: CITB - Construction Skills

The mathematics of beam deflection (130.23 KB)

Mathematical and/or science area: introduction to the terminology used in pumping water; conversion of units; solving problem with back-substitution method and plotting graphs using Excel sheets

Supporting company: AECOM Design Build

The mathematics of pumping water (600.22 KB)

Mathematical and/or science area: of maps and contours; geometry; trigonometry and numerical integration

Supporting company: CITB - Construction Skills

The mathematics of earthwork calculations (118.81 KB)

Mathematical and/or science area: structural design and construction; vector components of force; solution of simultaneous equations using matrix techniques

Supporting company: CITB - Construction Skills

The mathematics of framed bridge structures (153.82 KB)

Mathematical and/or science area: highway construction; geometry and properties of the circle

Supporting company: CITB - Construction Skills

The mathematics of highway design (179.46 KB)

Mathematical and/or science area: construction technology; geometry; integration techniques

Supporting company: CITB - Construction Skills

The mathematics of construction shapes (481.43 KB)

Mathematical and/or science area: concrete testing technology; statistical methods

Supporting company: CITB - Construction Skills

The mathematics of material quality control (88.66 KB)

Mathematical and/or science area: principles of hydraulics and construction methods; geometry

Supporting company: CITB - Construction Skills

The mathematics of water flow in channels (71.16 KB)

Mathematical and/or science area: engineering surveying; geometry; trigonometry

Supporting company: CITB - Construction Skills

The mathematics of engineering surveying (1) (137.35 KB)

Mathematical and/or science area: engineering surveying; geometry; trigonometry

Supporting company: CITB - Construction Skills

The mathematics of engineering surveying (2) (103.34 KB)

Mathematical and/or science area: engineering surveying; geometry and trigonometry

Supporting company: CITB - Construction Skills

The mathematics of engineering surveying (3) (120.74 KB)

Mathematical and/or science area: RMS value is trigonometrical identities; integration and plotting graphs of any function using ICT

The study of root mean square value (244.86 KB)

Mathematical and/or science area: calculating energy and power

Supporting company: NPower