# MEng Mechanical Engineering with Management

Year of entry: 2023

## Course unit details:Numerical Methods & Computing (Mechanical

Unit code MECH20042 10 Level 2 Semester 2 No

### Overview

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  Please see Blackboard / course unit related emails for any further updates

Modern engineers are faced with the design, analysis and manufacture of highly complex physical systems which can be understood through the application of engineering science.  The description of highly complex systems can require the solution of discrete, differential or integral equations which can be achieved through the application of numerical techniques.  Many of the analysis tools used by modern engineers are founded on numerical methods and it is essential that engineers are aware of the limitation of said tools and methods.  This unit provides an introduction and the foundations underpinning a selection of some of the numerical techniques used in engineering.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Mathematics 1M1 MATH19661 Pre-Requisite Compulsory
Mathematics 1M2 MATH19662 Pre-Requisite Compulsory
Tools for Engineers (Aerospace) AERO12101 Pre-Requisite Compulsory
Tools for Engineers (Mechanical) MECH12301 Pre-Requisite Compulsory

Matlab programming required from Tools units

### Aims

To introduce students to numerical approximation techniques and further develop Matlab programming skills.

### Syllabus

(1) Algebraic systems:
(i) Matrix systems
(ii) Linear problems
(iii)  Determinates of 3X3 matrices and greater
(iv) Eigenvalues and eigenvectors
(2) Iterative methods:
(i)  Interval methods
(ii) Updated input methods including Newton-Raphson
(3) Solvers for linear system of equations:
(i) Gauss-Seidel method
(ii)  Jacobi method
(4) Data fitting:
(i) Fourier Series and Transforms
(ii)  Fourier Series
(iii) Fourier Transforms
(iv) resolution and Window functions
(v) Aliasing
(5) Polynomial fitting:
(i) Lagrange interpolation method
(ii) Finite Difference techniques
(iii) Divided Difference method
(iv) Splines
(6) Numerical differentiation and integration

### Assessment methods

Method Weight
Other 5%
Written exam 80%
Report 15%

Other - assessed tutorial work

### Feedback methods

Exam via script viewing

### Study hours

Scheduled activity hours
eAssessment 3
Lectures 24
Project supervision 6
Tutorials 7
Independent study hours
Independent study 60

### Teaching staff

Staff member Role
Milan Mihajlovic Unit coordinator