Preliminaries (simultaneous linear equations, quadratic equations, completing the square, partial fractions, Heaviside functions).
Complex numbers.
Matrices and solving linear equations.
Calculus (differentiation, integration and partial differentiation).
First and second order differential equations (general definitions, simple examples, numerical solution).
Laplace transforms (partial fractions and use of tables, solving first and second-order differential equations, Dirac and Heaviside functions).
One optional topic (from z-transforms, Fourier transforms, Fourier series, Eigenvalue analysis or Statistics & Probability).

Four 1hr online tests weighted at 25% each assessing learning outcomes 1-4 respectively (to be invigilated remotely via e.g.: Blackboard Collaborate).

The module will run over 12 weeks.
You will be provided with material through the Blackboard VLE platform. Material will be presented via a mixture of printable handouts, presentations and videos that will include both theory and worked examples. You will be required to keep up-to-date with the schedule and work through the tutorial questions to consolidate understanding. Support will be provided via a discussion group on Blackboard and contact with Module Tutors via telephone and/or video call (e.g.: Blackboard Collaborate).
It is expected that you allocate a minimum of 12 hours to engage and interact with your Module Tutors and peers on the module (including 4 hours of online tests) and 138 hours on independent learning activities.

Full Text Online:
Bird, J. (2010) Engineering Mathematics, 6th Edition, Elsevier.
James, G. (2015) Modern Engineering Mathematics, 5th Edition, Pearson Education.
Bird, J. (2010) Higher Engineering Mathematics, 6th Edition, Elsevier.
James, G. (2016) Advanced Modern Engineering Mathematics, 4th Edition, Prentice Hall.

Available in the Library:
Stroud, K.A. & Booth D.J. (2013) Engineering Mathematics, 7th Edition, Palgrave Macmillan
Stroud, K.A. & Booth, D.J., (2011) Advanced Engineering Mathematics, 5th Edition, Palgrave Macmillan.
Singh, K., (2011) Engineering Mathematics through Applications, 2nd Edition, Palgrave Macmillan.
Kreyszig, E. (2011) Advanced Engineering Mathematics, 10th Edition, John Wiley and Sons.

Blackboard VLE platform and Blackboard Collaborate
Internet and a computer of appropriate specification with camera.

A Level Mathematics or equivalent, a STEM-based degree-level qualification and employment in an engineering environment.

1. Understand a range of mathematical techniques including Calculus.
(KNOWLEDGE & UNDERSTANDING, LEARNING ANALYSIS)

2. Solve differential equation models of engineering systems using Calculus methods, and interpret the solution found.
(APPLICATION, ANALYSIS, PROBLEM SOLVING, REFLECTION, COMMUNICATION)

3. Solve differential equation models of engineering systems using Laplace transform methods, and interpret the solution found.
(APPLICATION, ANALYSIS, PROBLEM SOLVING, REFLECTION, COMMUNICATION)

4. Apply one of Z-transforms, Fourier Series, Fourier Transforms, Eigenvalues or Statistics & Probability to analyse engineering systems, with appropriate interpretation.
(APPLICATION, ANALYSIS, PROBLEM SOLVING, REFLECTION, COMMUNCATION)