# NUMERICAL METHODS & APPLIED PROGRAMMING - 2023/4

Module code: ENG2124

## Module Overview

Engineers frequently have to solve engineering problems which are mathematically intractable by approximate numerical methods, normally using software involving some degree of programming. The module introduces the use of mathematical methods to solve complex engineering problems with appropriate IT tools, including Matlab. An introduction to the general, open programming language Python is also given and then applied to the solution of engineering problems.

### Module provider

Mechanical Engineering Sciences

MARXEN Olaf (Mech Eng Sci)

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

Independent Learning Hours: 100

Lecture Hours: 20

Tutorial Hours: 11

Guided Learning: 11

Captured Content: 8

Semester 2

## Prerequisites / Co-requisites

ENG1091Experimental and Professional Skills

## Module content

Indicative content includes:

Numerical Methods:

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

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

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

• Fitting and Interpolation.

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

• 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.

Applied Programming Skills

• Consolidation of Matlab and developing of Python skills including those for data handling, manipulation and presentation, as they are essential to solve engineering problems.

• Application of simple programming techniques to implement numerical methods using Matlab and Python

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test Programming Class Test - 45mins 30
Examination Exam (2 hours) 70

N/A

## 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 the solution of engineering problems and know the limitations and possible sources of error, and to write computer code in Matlab and Python to implement such methods in efficient ways.

The class test will test the students' ability to understand the key concepts and syntax of programming tools required to implement numerical methods for engineering problems. The examination tests the students' knowledge and command of numerical solution techniques and may include short, manually written demonstrations of ability to implement methods;

Thus, the summative assessment for this module consists of an Examination [Learning outcome 1] and a Class Test [Learning outcome 2].

Formative assessment and feedback:

Formative feedback is given throughout the semester in IT-Lab based tutorials by staff and/or PG assistants, and through example solutions and computer codes posted on the VLE. Likewise, feedback on the class test is formative, towards the examination.

## Module aims

• Knowledge and experience of selection, implementation and application of common numerical methods in order to solve standard engineering problems.
• Knowledge and experience of using Matlab and Python programming as a tool to solve standard engineering problems.

## Learning outcomes

 Attributes Developed 002 Ability to use computer programming in support of solutions to engineering problems; CPT 001 Ability to use a range of standard numerical methods to solve common engineering problems; KC

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 and extend these skills by introducing Python through the implementation of numerical methods taught.

The learning and teaching methods include:

• weekly synchronous lectures, including question and answer session;

• pre-recorded captured content;

• guided learning (such as electronic/online learning and multi-media resources);

• IT-lab based tutorials, were practical programming skills are developed through several formative exercises.

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: ENG2124

n/a

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Automotive Engineering (Dual degree with HIT) BEng (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Aerospace Engineering 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
Automotive Engineering BEng (Hons) 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
Automotive 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
Mechanical 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 2023/4 academic year.