Module MA2326: Ordinary Differential Equations

Credit weighting (ECTS)

5 credits

Semester/term taught

Hilary term 2014-15

Contact Hours

11 weeks, 3 lectures including tutorials per week

Lecturer

Prof. John Stalker

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

Analysis on the Real Line II (MA1124)

Assessment Detail

This module will be examined in a 2 hour examination in Trinity term. Continuous assessment will contribute 20% to the final grade for the module at the annual examination session. Supplemental exams if required will consist of 100% exam.