MA209      Half Unit
Differential Equations

This information is for the 2025/26 session.

Course Convenor

Dr Pavel Gapeev

Availability

This course is available on the BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics, BSc in Mathematics, Statistics and Business, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.

Requisites

Pre-requisites:

Before taking this course, students must have completed: MA100 and (MA102 or MA103)

Additional 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.

Teaching

20 hours of lectures and 10 hours of classes in the Winter Term.

Formative assessment

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.

Assessment

Exam (100%), duration: 120 Minutes in the Spring exam period


Key facts

Department: Mathematics

Course Study Period: Winter Term

Unit value: Half unit

FHEQ Level: Level 5

CEFR Level: Null

Total students 2024/25: 129

Average class size 2024/25: 16

Capped 2024/25: No
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Personal development skills

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