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2010/1 Module Catalogue
Module Provider: Mathematics Short Name: MS213
Level: HE2 Module Co-ordinator: ROULSTONE I Prof (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability



Assessment Pattern

Unit(s) of Assessment


Weighting Towards Module Mark( %)










Qualifying Condition(s) 


An overall aggregate mark of 40% for the module is required to pass the module.



Module Overview

This module builds on the differential equation aspects of the level 1 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.   


MAT1015 Calculus (MS114)


MAT1016 Linear Algebra (MS124)


MAT1017 Proof, Probability and Experiment (MS125): Experiment submodule     
Module Aims
The aim of this module is to study both qualitative and quantitative aspects of Ordinary Differential Equations.
Learning Outcomes

By the end of the module a student should be able to:


·   find exact solutions to certain types of differential equations;


·   plot and interpret phase portraits on the line or in the plane; determine the stability of equilibria    and periodic solutions.
Module Content
  • Scalar first-order differential equations; review of separable and linear equations.


  • Phase portraits on the line; equilibria and their stability.


  • Theorems on existence, uniqueness, continuous dependence on initial conditions.


  • Linear, autonomous systems of differential equations: relation between stability and eigenvalues; classification of planar phase portraits. 


  •  Nonlinear systems: equilibria and their classification, linear stability analysis, Lyapunov functions, phase portrait near an equilibrium.


If time allows: Periodic solutions and their stability: Poincare maps; introduction to Floquet theory.


Methods of Teaching/Learning

Teaching is by lectures, tutorials and example classes. Learning takes place through lectures, exercises (example sheets), preparation for tests and background reading.




There will be 3 contact hours for 10 weeks consisting of lectures, tutorials and example classes.          
Selected Texts/Journals
  • D.K. Arrowsmith and
    C.M. Place


  • Dynamical Systems: differential equations, maps and chaotic behaviour; Chapman & Hall (1992)


  • D.W. Jordan and P. Smith.
    Nonlinear Differential Equations.
    Oxford University Press (1987).


  • M. Braun.
    Differential Equations and their Applications.
    Springer-Verlag (1993)


  • R.K. Nagle and E.B. Saff
    Fundamental of Differential Equations and Boundary Value Problems.
    Addison-Wesley (1993).


Last Updated
September 10