Ordinary Differential Equations (G5142)

15 credits, Level 5

Autumn teaching

You will study ordinary differential equations (ODEs), which are differential equations for functions of one independent variable.

Differential equations are equations involving an unknown function and its derivatives. They are an important tool used in areas such as physics, economics, ecology, epidemiology, engineering and many, many more to describe the rates of change of real-world phenomena.

You will look at a range of methods that can be used to explicitly solve first-order ODEs, where the highest derivative involved is a first-order derivative.

You will also look at the theory that underpins this topic by proving important theorems that tell us when solutions to ODEs exist and when they are unique. We will prove and apply Grönwall’s inequality - a tool that lets us construct a bound on a solution to an ODE, even in cases where we are not able to find the solution explicitly. This will be built upon in future modules where differential equations are solved numerically.

You will also study systems of first-order ODEs, applying and building on knowledge gained studying Linear Algebra 2, specifically eigenvalues and eigenvectors. Finally we learn how to solve a certain class of higher-order ODEs.


100%: Lecture


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

Contact hours and workload

This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 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: