NUMERICAL & EXPERIMENTAL METHODS - 2022/3

Module code: ENG2093

Module Overview

Engineers frequently have to carry out testing and experimental procedures on products. They also often have to solve engineering problems which are mathematically intractable by approximate numerical methods, normally using software involving some degree of programming.

The laboratory part of this module is designed both to support learning in other parts of the FHEQ level 5 curriculum through practical experiments and also to further develop generic and transferable skills (building on the HEFQ level 4 module Experimental and Transferable Skills), including practical laboratory skills, data handling, understanding experimental uncertainty and scientific writing.

The numerical methods covered in this module introduce the use of mathematical methods to solve complex engineering problems with appropriate IT tools such as Matlab.

Where appropriate the experiments include the application of Matlab and numerical methods.

Module provider

Mechanical Engineering Sciences

MARXEN Olaf (Mech Eng Sci)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 5

JACs code: G140

Module cap (Maximum number of students): N/A

Independent Learning Hours: 96

Lecture Hours: 10

Tutorial Hours: 10

Laboratory Hours: 16

Captured Content: 18

Module Availability

Semester 2

Module content

Indicative content includes:

1. Numerical Methods :

The lectures and tutorials cover the following areas:

• Computer representation of numbers, rounding errors. Taylor series expansion and truncation errors.

• Roots of nonlinear equations: interval searching, bisection method, false position, simple iteration, Newton-Raphson method.

• Solution of single ordinary differential equations by Euler, Heun and 4th order Runge-Kutta methods- derivation, errors, applications. Systems of ODEs and higher-order equations.

• Numerical Integration: Trapezoidal rule and Simpson's rule, errors and applications

• Solution of systems of linear equations:  Gauss elimination with inclusion of partial pivoting; LU-decomposition; Gauss-Seidel iteration.

• Application of simple programming to solve numerical methods problems using Matlab

2. Laboratory Experiments

9 laboratory experiments will be conducted in small groups. These experiments are complementary to the wider FHEQ level 5 curriculum.

Five of the experiments are common and relate to areas of solid mechanics, dynamics, control and electronics covered by all programmes including this module. Four of the experiments are specific to the four discipline areas, for example: diesel engine performance (Automotive), aircraft dynamic stability (Aerospace), refrigeration (Mechanical) and gait analysis (Medical).

Measurement techniques appropriate to the measurement and use of displacement, curvature, velocity, acceleration, frequency, force, pressure, temperature, thermodynamic properties, energy transfer, power, flow rate, voltage, current, etc. are covered.

General laboratory methods pertaining to preparation and experimental design, organisation, procedural optimisation, data recording, data analysis, error measurement, error propagation are developed over the series of experiments. Health and safety issues are included in preparatory briefings.

Assessment pattern

Assessment type Unit of assessment Weighting
Coursework LABORATORY REPORT 1 15
Practical based assessment LABORATORY SESSIONS (ONLINE AND IN-PERSON) 20
Coursework LABORATORY REPORT 2 15
Examination ONLINE (OPEN BOOK) EXAM WITHIN 24HR WINDOW 50

Alternative Assessment

Laboratory participation element to be replaced by i) written answers requiring background research for two different experiments and (ii) a report on the performance of one laboratory accounting for the nature and minimisation of experimental error.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to

• choose and implement suitable numerical methods for engineering problem solutions and know the limitations and possible sources of error

• write programs (in Matlab) to implement such methods in efficient ways

• relate taught material form other modules to the laboratory experiments and research further

• carry out laboratory experiments and analyse and discuss results, including experimental uncertainty

• produce written technical reports to an industry and professional standard

Thus, the summative assessment for this module consists of:

• Examination on numerical  methods, testing knowledge and concepts  and with short ‘by-hand’ demonstrations of ability to implement methods

Learning outcome 1             1 hr                            25%

• Numerical methods coursework consisting of a series of weekly online quizzes and/or programming exercises covering analysis, application of suitably chosen numerical methods to problems, use of Matlab ,discussion of results

Learning outcome 1,2, 5                                25%

• Preparation and participation / review of laboratory session (approximately weekly)

Learning outcomes 3,4,5                                 20%

• Production of two lab reports, for which the respective marking schemes may differ in order to put emphasis on certain aspects of report writing

Learning outcomes 3,4,5                               30% total (15% each)

Formative assessment and feedback

Formative feedback is given throughout the semester in numerical methods IT-Lab based tutorials by staff and PG assistants, and through example solutions and programmes posted on the VLE.

In every laboratory session, students have face-to face discussions with the experiment supervisor

Written feedback on the first lab report will enable feed-forward to the writing of the next report, and is formative as well as summative.

Likewise written feedback on the numerical methods coursework is formative, towards the examination.

Module aims

• Knowledge and experience of using standard numerical methods in order to solve complex engineering problems.
• Knowledge and experience of using Matlab and programming as a tool to solve engineering problems.
• Laboratory experience which reinforces and illustrates wider aspects of the FHEQ level 5 engineering curriculum.
• Thorough training in experimental approaches, including the handling of data and dealing with experimental uncertainty by error propagation theory.
• Further development of report writing skills.

Learning outcomes

Attributes Developed
001 UK-SPEC Learning Outcome codes: SM1b, SM2b, SM2m, EA1b, EA3b, EA3m, D6, EL1, EL6, P1, P2, P3, P8, P11, G1 On successful completion of this module, students will be able to: Use a range of standard numerical methods to solve complex engineering problems;; (K,C,P) KCP
002 Use Matlab and programming as a tool in solving engineering problems; KCPT
003 Demonstrate an ability to prepare, perform and effectively report experimental investigations commensurate with FHEQ level 5; KCPT
004 Demonstrate an ability to identify and address experimental uncertainty; CP
005 Demonstrate progress towards ongoing independent development of applying experimental and numerical methods to real engineering situations. CPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to

• introduce students to a range of numerical methods with their derivations and limitations,

• consolidate students’ programming skills with Matlab through implementation of numerical methods taught

• reinforce engineering science concepts taught in other modules though practical experimentation and demonstration

• give students  good grounding in experimental procedure and scientific/technical report writing

The learning and teaching methods include:

• Lectures (for numerical methods) 17 hrs total, 2/wk for 6 weeks, 1/wk for 5 weeks

• IT-lab based tutorials using Matlab programming to implement numerical methods (1 hr/wk)

• Introductory briefing lectures on lab work ( 2 hrs total, wks 1 /2)

• 9 x 1-2 hrs/wk laboratory sessions in small groups; in addition to electronic or supervisor-led introduction to experiment and apparatus, and group work on experiment itself to obtain results and conclusions, lab sessions may feature supervisor-led discussions of preparatory work and session results.

• Production of 2 laboratory reports, following written and oral guidance given on report production

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: ENG2093

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Aerospace Engineering BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Automotive Engineering MEng 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Automotive Engineering BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Automotive Engineering (Dual degree with HIT) BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mechanical Engineering BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mechanical Engineering MEng 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Aerospace Engineering MEng 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Biomedical Engineering BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Biomedical Engineering MEng 2 Compulsory A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2022/3 academic year.