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Module MAU23205: Ordinary Differential Equations

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2019-20
Contact Hours
11 weeks, 3 lectures including tutorials per week
Dr. Gurpreet Singh
Learning Outcomes
On successful completion of this module, students will be able to:
  • Apply various standard methods (separation of variables, integrating factors, reduction of order, undetermined coefficients) to solve certain types of differential equations (separable, 1st-order linear, linear with constant coefficients;
  • Give examples of differential equations for which either existence or uniqueness of solution fails;
  • Compute the exponential of a square matrix;
  • Apply standard methods (linearization, Lyapunov theorems) to check the stability of critical points for automous systems
Module Content
  • Terminology (order, scalar vs. system, linear vs. nonlinear, invariant);
  • Separable equations, first-order equations, Gronwall inequality;
  • Existence and uniqueness of solutions, blow up in finite time;
  • First-order linear systems, exponential of a matrix;
  • Reduction of order, undetermined coefficients, variation of parameters;
  • Autonomous systems, phase portraits, stability, Lyapunov functions.
Module Prerequisite
MAU11100, MAU11204
Assessment Detail
This module will be examined in a 2 hour examination in Michaelmas term. Continuous assessment will contribute 20% to the final grade with the exam counting for the remaining 80%. Supplementals if required will consist of 100% exam.