Course Unit Specification: MATH44041/MATH64041
Lecturer: Dr. Yanghong Huang
(yanghong.huang@manchester.ac.uk)
Office: Alan Turing 1.108
Learning outcomes. On successful completion of this course unit students will:
Meiss's Book | Outline | Tutorial exercies and solutions | Scanned notes |
---|---|---|---|
Chap 1 | ♠ Introduction | Exercise Sheet 1 (Solution) | |
Chap 1 | ♠ Notation and Basic Concepts | Sep 29 | |
Sec 1.2, 4.1, 4.2 | ⚬ ODEs: trajectories, phase portrait and flow | Oct 02 | |
Sec 4.1 | ⚬ Fixed points, perioidic orbits, invariant sets | Exercise Sheet 2 (Solution) | Oct 06 |
Sec 3.3 | ⚬ Existence and uniqueness | ||
Chap 2,4,5,6 | ♠ Linearisation and Equilibria | Exercise Sheet 3 (Solution) | Oct 13 |
Sec 2.1, 2.3, 2.5 | ⚬ Linear systems | Oct 20 | |
Sec 6.1, 6.2 | ⚬ Planar ODEs | ||
Sec 4.5, 4.6 | ⚬ Stability and Lyapunov functions | Exercise Sheet 4 (Solution) | Oct 27 |
Sec 5.3, 5.4 | ⚬ Nonlinear systems and stable manifold | Exercise Sheet 5 (Solution) | Nov 06 |
Sec 1.3 | ⚬ Maps: fixed points and periodic orbits | Exercise Sheet 6 (Solution) | Nov 10 |
Chap 2, 5, 6 | ♠ Periodic Orbits | Exercise Sheet 7 (Solution) | |
Sec 5.5 | ⚬ Poincare-Bendixson theorem for periodic orbtis | Nov 13 | |
Sec 2.8 | ⚬ Floquet theory for periodic coefficients | Nov 17 | |
Chapter 8 | ♠ Bifurcation and Centre Manifold | Exercise Sheet 8 (Solution) | Nov 20 |
Sec 5.6 | ⚬ Centre manifold and its approximation | Nov 24 | |
Sec 8.1 | ⚬ Extended centre manifold | Exercise Sheet 9 (Solution) | Nov 27 |
Sec 8.1, 8.4, 8.6, 8.8 | ⚬ Bifurcations | Dec 01 | |
Chap 1, 21 | ♠ Maps and their bifurcation | Exercise Sheet 10 (Solution) | Dec 04 |
Sec 1.3 | ⚬ Stability of fixed points and periodic orbits | Dec 08 | |
Sec 21.1, 21.2, 21.3 | ⚬ Bifurcation of maps | ||
Sec 1.3 | ⚬ Logistic map and two-dimensional maps | Dec 11 |
pplane
to
get the behaviours of trajectories of ODES on the phase plane. Download the java version (Java
Runtime Environment required),
as the matlab version does not work for current matlab distribution (MATLAB 2015).