MA209      Half Unit
Differential Equations

This information is for the 2020/21 session.

Teacher responsible

Dr Arne Lokka


This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.


Mathematical Methods (MA100) and Introduction to Abstract Mathematics (MA103) (or MA102) are pre-requisites. Real Analysis (MA203) and/or Further Mathematical Methods (MA212) are highly desirable, and students who have done neither MA203 nor MA212 should contact the lecturer.

Course content

The course concentrates on the theory and qualitative analysis of (ordinary) differential equations, although some solution techniques will be considered as well. Special attention will be paid to geometric concepts and the role of differential equations in the theory of dynamical systems. Specific topics covered are: First examples; illustrations of use of the computer package Maple. Existence and uniqueness of solutions. Autonomous 1 and 2 dimensional systems. Linear equations and systems: phase portraits; classification of systems in the plane; higher dimensional systems and higher order equations. Nonlinear systems in the plane: local and global behaviour; linearisation and stability at equilibrium points; Lyapunov functions; limit cycles. Control theory; linear systems; controllability.


This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Lent Term. This year, some or all of this teaching will be delivered through a combination of virtual classes and lectures delivered as online videos. 

Formative coursework

Written answers to set problems will be expected on a weekly basis.

Indicative reading

Full notes will be handed out throughout the course. A good additional text book is D K Arrowsmith & C M Place, Dynamical Systems - Differential Equations, Maps and Chaotic Behaviour. Other books closely related to R Grimshaw, Nonlinear Ordinary Differential Equations and W A Brock & A G Malliaris, Differential Equations, Stability and Chaos in Dynamic Economics.


Exam (100%, duration: 2 hours) in the summer exam period.

Important information in response to COVID-19

Please note that during 2020/21 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the situation of students in attendance on campus and those studying online during the early part of the academic year. For assessment, this may involve changes to mode of delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2019/20: 89

Average class size 2019/20: 15

Capped 2019/20: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

  • Self-management
  • Problem solving
  • Application of information skills
  • Communication
  • Application of numeracy skills
  • Specialist skills