Faculty of Science

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6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences


Professor Paul Cally and Dr Simon Clarke



  • Second semester 2017 (Day)


This unit examines two particular classes of ordinary differential equations: dynamical systems and boundary-value problems. The investigation of boundary-value problems considers Sturm-Liouville eigenvalues problems and orthogonal polynomials, shooting and direct matrix methods for the numerical investigation of boundary-value problems and iterative matrix methods. The second topic of dynamical systems considers analytical and numerical methods for planar autonomous systems, classification of critical points using eigenvalues and eigenvectors and perturbation methods for periodic and nearly periodic motion. Programming skills are developed in the context of the analytic and numerical investigation of advanced ordinary differential equations using MATLAB.


On completion of this unit students will be able to:

  1. Understand the importance of differential equations in modelling;

  1. Understand and solve Sturm-Liouville eigenvalue problems and use orthogonal polynomials to find exact solutions of boundary-value problems;

  1. Solve linear ordinary differential equations using series methods and Green's functions;

  1. Apply both analytical and numerical methods for the solution of planar autonomous systems;

  1. Classify critical points using eigenvalues and eigenvectors;

  1. Use perturbation methods for periodic and nearly periodic motion.


Examination (3 hours): 70%
Assignments and tests: 30%

Workload requirements

Three 1-hour lectures and one 2-hour combined tutorial and computer laboratory class per week

See also Unit timetable information

Chief examiner(s)

This unit applies to the following area(s) of study