Mathematics is the foundation of engineering sciences and has become increasingly relevant to disciplines, which are driving technological developments in this digital age. In this module, we will build on the concepts taught in Year 1 to cover more advanced topics in mathematics that are relevant to both electrical and information engineering. The topics to be covered additional topics in Linear Algebra, Differential Equations, Numerical Solutions of Differential Equations, Probability and Statistics.

Upon successful completion of this module, you will be able to:

1. Use MATLAB to solve nonlinear two-dimensional differential equations based on numerical techniques.
2. Utilise concepts in linear algebra to solve problems in signal processing, systems and control.
3. Explain the concepts and techniques of probability and statistics and compute properties of random systems.
4. Use basic Bayesian estimator and calculate the method of moment and the maximum likelihood estimator.
5. Formulate the ways in which these mathematical techniques are applied to technical problems in your engineering modules.

Probability and statistics, random variables and random processes, probability density function, cumulative distribution function, expectation and variance of a single discrete or continuous random variable Bayesian estimator and maximum likelihood estimator. Linear transformations, matrix decomposition and computation with matrices. Singular Value Decomposition. Euler’s, Heun’s and 4th-order Runge-Kutta Methods for first-order and higher-order ODEs; finite-difference methods for ODEs and PDEs. The Practical Applications of Mathematics will cover numerical implementation of differential equations.