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.

## General

### The mathematics of aircraft navigation

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

Supporting company: Thales

### Underground storage tanks

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

Supporting company: Rolls-Royce

### The study of engineering data

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

Supporting company: ECUK

### Study of the motion of knee and ankle during cycling

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

### Mathematics behind the water network in rural mountain areas

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

### Handling hazardous liquids during chemical processing

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

Supporting company: MW Kellogg Ltd

### Formula one race strategy

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

## Mechanical

### Steam pipe insulation

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

Supporting company: Rolls-Royce

### The mathematics of escalators on the London Underground

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

Supporting company: Transport for London

### Calculating power of JCB Dieselmax engines

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

Supporting company: JCB Power Systems Limited

### Study of vibrations in JCB Dieselmax engines

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

Supporting company: JCB Power Systems Limited

### The study of root mean square value

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

### Study of suspension in JCB construction machinery

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 dynamic systems in JCB construction machinery

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

### The mathematics of simple beam deflection

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 beam deflection

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

Supporting company: CITB - Construction Skills

### The mathematics of pumping water

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

### Understanding the motion of the wheels

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

Supporting company: Bloodhound Engineering Project

### Monitoring vibration levels in steam turbines

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

Supporting company: NPower

### Forces on large steam turbine blades

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

Supporting company: NPower

### Wind turbine power calculations

Mathematical and/or science area: calculating energy and power

Supporting company: NPower

### Dropped load assessment nuclear industry

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

Supporting company: British Energy

### Understanding the rocket performance in Bloodhound SSC

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

### The mathematics of material quality control

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

Supporting company: CITB - Construction Skills

## Civil

### Study of suspension in JCB construction machinery

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 dynamic systems in JCB construction machinery

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

### The mathematics of simple beam deflection

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 beam deflection

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

Supporting company: CITB - Construction Skills

### The mathematics of pumping water

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 earthwork calculations

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

Supporting company: CITB - Construction Skills

### The mathematics of framed bridge structures

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 highway design

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

Supporting company: CITB - Construction Skills

### The mathematics of construction shapes

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

Supporting company: CITB - Construction Skills

### The mathematics of material quality control

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

Supporting company: CITB - Construction Skills

### The mathematics of water flow in channels

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

Supporting company:  CITB - Construction Skills

### The mathematics of engineering surveying (1)

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

Supporting company: CITB - Construction Skills

### The mathematics of engineering surveying (2)

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

Supporting company: CITB - Construction Skills

### The mathematics of engineering surveying (3) – PDF

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

Supporting company: CITB - Construction Skills

## Electrical and electronics

### The study of root mean square value

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

### Wind turbine power calculations

Mathematical and/or science area: calculating energy and power

Supporting company: NPower