# 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.

### Teaching 61%: Lecture 19%: Practical (Workshop) 20%: Seminar

### Assessment 30%: Coursework (Portfolio, Problem set) 70%: Examination (Unseen examination)