UNIT 7: CALCULUS TO SOLVE ENGINEERING PROBLEMS
Unit 7: Calculus to Solve Engineering Problems
Level: 3
Unit type: Internal
Guided learning hours: 60
Unit in brief
Learners use differential (rates of change) and integral (summing) calculus to solve engineering
problems and develop a mathematical model of a local and relevant system.
Unit introduction
Many of the products, components and systems that we use have been subject to a rigorous design
process that will have involved the use of calculations including mathematical calculus. During the
design stage, it is important to be able to predict how a product will perform in service, for example
the handling characteristics of a car or the power output from an electrical power supply. Also,
investing time and resources in setting up manufacturing machinery and supply chains is very
expensive – working with formulae and numbers on paper or using a computer involves a lot less
cost and allows engineers to determine optimal (or near-optimal) solutions.
In this unit, you will investigate how to apply differential and integral calculus methods to solve
engineering problems. You will learn about the rules and procedures of calculus mathematics to
obtain solutions to a variety of engineering problems. You will solve a complex problem from your
specialist area of study and perhaps from a local organisation by breaking it down into a series
of linked manageable steps. Each step will be solved using calculus methods learned through
investigation and practice. These mathematical skills are transferable and will be used to support
your study of other topics in the BTEC Nationals engineering programme, for example in mechanical
principles and electrical systems.
As an engineer you need to understand and develop the skills required to solve problems using
calculus and other mathematical procedures. This unit will prepare you well for progressing to
higher education to study for an engineering degree or a Higher National Diploma (HND). It will
also help prepare you for an apprenticeship or for employment in a range of engineering disciplines
as a technician, and will help you work with professional engineers as part of a team working on
cutting-edge products and systems.
Learning aims
In this unit you will:
A Examine how differential calculus can be used to solve engineering problems
B Examine how integral calculus can be used to solve engineering problems
C Investigate the application of calculus to solve a defined specialist engineering
problem.
Pearson BTEC Level 3 National Extended Diplomas in Engineering – 111
Specification – Issue 8 – May 2021 © Pearson Education Limited 2021
, UNIT 7: CALCULUS TO SOLVE ENGINEERING PROBLEMS
Summary of unit
Learning aim Key content areas Recommended
assessment approach
A Examine how differential A1 Functions, rate of change,
calculus can be used to gradient
A report containing the results
solve engineering problems A2 Methods of differentiation
of learners’ analysis and
A3 Numerical value of a calculation, carried out under
derivative controlled conditions.
A4 Second derivative and
turning points
B Examine how integral B1 Integration as the
calculus can be used to reverse/inverse of
A report containing the results
solve engineering problems differentiation
of learners’ analysis and
B2 Integration as a calculation, carried out under
summating tool controlled conditions.
B3 Numerical integration
C Investigate the application C1 Thinking methods
A report containing the results
of calculus to solve a C2 Mathematical modelling of
of learners’ analysis, planning
defined specialist engineering problems
and calculation, carried out
engineering problem C3 Problem specification and under controlled conditions.
proposed solution
C4 Solution implementation
112 Pearson BTEC Level 3 National Extended Diplomas in Engineering –
Specification – Issue 8 – May 2021 © Pearson Education Limited 2021
Unit 7: Calculus to Solve Engineering Problems
Level: 3
Unit type: Internal
Guided learning hours: 60
Unit in brief
Learners use differential (rates of change) and integral (summing) calculus to solve engineering
problems and develop a mathematical model of a local and relevant system.
Unit introduction
Many of the products, components and systems that we use have been subject to a rigorous design
process that will have involved the use of calculations including mathematical calculus. During the
design stage, it is important to be able to predict how a product will perform in service, for example
the handling characteristics of a car or the power output from an electrical power supply. Also,
investing time and resources in setting up manufacturing machinery and supply chains is very
expensive – working with formulae and numbers on paper or using a computer involves a lot less
cost and allows engineers to determine optimal (or near-optimal) solutions.
In this unit, you will investigate how to apply differential and integral calculus methods to solve
engineering problems. You will learn about the rules and procedures of calculus mathematics to
obtain solutions to a variety of engineering problems. You will solve a complex problem from your
specialist area of study and perhaps from a local organisation by breaking it down into a series
of linked manageable steps. Each step will be solved using calculus methods learned through
investigation and practice. These mathematical skills are transferable and will be used to support
your study of other topics in the BTEC Nationals engineering programme, for example in mechanical
principles and electrical systems.
As an engineer you need to understand and develop the skills required to solve problems using
calculus and other mathematical procedures. This unit will prepare you well for progressing to
higher education to study for an engineering degree or a Higher National Diploma (HND). It will
also help prepare you for an apprenticeship or for employment in a range of engineering disciplines
as a technician, and will help you work with professional engineers as part of a team working on
cutting-edge products and systems.
Learning aims
In this unit you will:
A Examine how differential calculus can be used to solve engineering problems
B Examine how integral calculus can be used to solve engineering problems
C Investigate the application of calculus to solve a defined specialist engineering
problem.
Pearson BTEC Level 3 National Extended Diplomas in Engineering – 111
Specification – Issue 8 – May 2021 © Pearson Education Limited 2021
, UNIT 7: CALCULUS TO SOLVE ENGINEERING PROBLEMS
Summary of unit
Learning aim Key content areas Recommended
assessment approach
A Examine how differential A1 Functions, rate of change,
calculus can be used to gradient
A report containing the results
solve engineering problems A2 Methods of differentiation
of learners’ analysis and
A3 Numerical value of a calculation, carried out under
derivative controlled conditions.
A4 Second derivative and
turning points
B Examine how integral B1 Integration as the
calculus can be used to reverse/inverse of
A report containing the results
solve engineering problems differentiation
of learners’ analysis and
B2 Integration as a calculation, carried out under
summating tool controlled conditions.
B3 Numerical integration
C Investigate the application C1 Thinking methods
A report containing the results
of calculus to solve a C2 Mathematical modelling of
of learners’ analysis, planning
defined specialist engineering problems
and calculation, carried out
engineering problem C3 Problem specification and under controlled conditions.
proposed solution
C4 Solution implementation
112 Pearson BTEC Level 3 National Extended Diplomas in Engineering –
Specification – Issue 8 – May 2021 © Pearson Education Limited 2021
