# Year 3: numerical analysis

This module provides a foundational overview of numerical methods commonly employed in engineering for analysis and design tasks.

Covered topics comprise:

• Root finding and optimisation
• Solving systems of linear algebraic equations
• Curve fitting techniques
• Numerical integration and differentiation methods
• Numerical approaches to solving elementary ordinary and partial differential equations

The course places a strong focus on ensuring numerical precision, stability in computations, and optimising processing speed. Practical applications will be demonstrated through case studies drawn from Electrical and Electronic Engineering, Electronic Engineering, and Mechatronic Engineering disciplines. Practical examples include:

• Analysing electrical circuits
• Optimising power flow
• Processing digital signals
• Charting voltage/current (V/I) characteristics
• Identifying poles of transfer functions
• Implementing transfer function responses

Pre-requisites to this module include Signals and Systems for year 2, and completion of year 2 Mathematics course.

#### Module aims

The course unit seeks to bolster students’ self-assurance in utilising Matlab and other pertinent software platforms for numerical analysis. It aims to provide a comprehensive overview of numerical methods that are regularly employed by professionals in the fields of electrical, electronic, and mechatronic engineering. Furthermore, the course will demonstrate the practical application of these methods through examples that students may encounter across various stages of their first, second, and third-year units.

#### Module outcomes

Upon completion of the module, students will have demonstrated and developed the following skills:

• Computing numerical solutions for integration challenges and the temporal progression of basic dynamical systems.
• Programming fundamental algorithms to perform root finding, LU decomposition, and least squares estimation.
• Solving elementary problems in line fitting and optimization.
• Understanding the application of randomisation in tackling non-convex optimisation problems.
• Assessing numerical accuracy concerning floating-point arithmetic and setting appropriate stopping points for numerical operations.
• Factorising matrices and interpreting the significance of their rank, condition number, and singular values in connection with linear algebraic equations used in physical models.
• Developing code for the numerically efficient execution of matrix computations.

#### Teaching and assessment methods

The module will be delivered primarily through lectures and laboratory work with heavy emphasis on numerical examples and applications.

The bulk of the assessment, 80%, will be completed via a written exam, the remaining 20% will be coursework based.