Mathematics

Ordinary Differential Equations

Module code: G5142
Level 5
15 credits in autumn semester
Teaching method: Seminar, Lecture, Workshop, Class
Assessment modes: Unseen examination, Coursework

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.

Module learning outcomes

• Select and employ appropriate methods to solve ordinary differential equations;
• Appreciate and understand existence and uniqueness theorems for ordinary differential equations;
• Comprehend and use the structure of solutions for linear ordinary differential equations;
• Have gathered sufficient knowledge of different career paths for mathematics graduates that they can draw up their own plan to achieve employment success after graduation