MAU23205 Ordinary differential equations
| Module Code | MAU23205 |
|---|---|
| Module Title | Ordinary differential equations |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. John Stalker |
| Module Prerequisites |
MAU11102 Linear algebra II and
MAU11204 Analysis on the real line |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 20% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures per week.
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, first-order linear, linear with constant coefficients).
- Give examples of differential equations for which either existence or uniqueness of solutions fails.
- Compute the exponential of a square matrix.
- Use either linearization or the Lyapunov theorems to check the stability of critical points for a given autonomous system.
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 square matrix.
- Reduction of order, undetermined coefficients, variation of parameters.
- Autonomous systems, stability theory, Lyapunov functions.
Recommended Reading
- The qualitative theory of ordinary differential equations by Brauer and Nohel.