Engineering Mathematics 2 (H1042)

15 credits, Level 5

Autumn teaching

The Engineering Mathematics 2 module is divided into two sections.

The first builds on the mathematics you studied in the first year as  you further study the solution of linear differential equations of various types – a topic of considerable importance in engineering analysis. You’ll also look at methods of transforming linear differential equations into the frequency domain using the Laplace transform, a method that is central to the analysis of modern engineering control systems. Additionally you’ll consider basic methods for numerically solving first order ordinary differential equations. You’ll also explore solution methods for some of the partial differential equations common in engineering analysis, such as the heat and wave equations.

The second section of the module introduces you to probability theory and statistical methods, illustrated with examples showing how these concepts can be used to gain estimates of the outcomes of the complex interactions that often occur in real engineering systems.

Topics include:

  • revision of first order and second order differential equation time domain solution methods
  • Laplace transform and associated theorems; convolution
  • solution of ODEs via the Laplace transform
  • numerical solution of first order ODEs
  • partial differential equations; separation of variables; outline of Fourier series solution; Laplace, Poisson, heat and wave equations
  • probability: random variables; Bayes’ theorem; continuous and discrete distribution and density functions; expectations; normal distribution; central limit theorem; estimation of parameters; moment and maximum likelihood methods; student’s t-test; confidence intervals; quality control; acceptance sampling; reliability; failure rates; the Weibull distribution.


77%: Lecture
23%: Practical (Workshop)


20%: Coursework (Problem set)
80%: Examination (Unseen examination)

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 43 hours of contact time and about 107 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2024/25. However, there may be changes to these modules in response to feedback, staff availability, student demand or updates to our curriculum. We’ll make sure to let you know of any material changes to modules at the earliest opportunity.


This module is offered on the following courses: