Course Unit Specification: MATH44041/MATH64041
Lecturer: Dr. Yanghong Huang
(yanghong.huang@manchester.ac.uk)
Office: Alan Turing 1.108
Office Hour: Thursday 11:00am-12:00pm or appointment or drop by the office
(check weekly grid).
Lectures times and locations:
Important Dates: (For a few of you, the Teaching and Learning Office make special arrangements for you to sit your test in a separate location. If this is the case please ignore this general information and go to the location given to you by the Teaching and Learning office.)
Meiss's Book | Outline | Lecture Notes | Tutorial exercies and solutions | Scanned notes |
---|---|---|---|---|
Chap 1 | ♠ Introduction | Part 1 | 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 | Part 2 | 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) | ||
Sec 5.3, 5.4 | ⚬ Nonlinear systems and stable manifold | Exercise Sheet 5 (Solution) | ||
Sec 1.3 | ⚬ Maps: fixed points and periodic orbits | Exercise Sheet 6 (Solution) | ||
Chap 2, 5, 6 | ♠ Periodic Orbits | Part 3 | Exercise Sheet 7 (Solution) | |
Sec 5.5 | ⚬ Poincare-Bendixson theorem for periodic orbtis | |||
Sec 2.8 | ⚬ Floquet theory for periodic coefficients | |||
Chapter 8 | ♠ Bifurcation and Centre Manifold | Part 4 | Exercise Sheet 8 (Solution) | |
Sec 5.6 | ⚬ Centre manifold and its approximation | |||
Sec 8.1 | ⚬ Extended centre manifold | Exercise Sheet 9 (Solution) | ||
Sec 8.1, 8.4, 8.6, 8.8 | ⚬ Bifurcations | |||
Chap 1, 21 | ♠ Maps and their bifurcation | Part 5 | Exercise Sheet 10 (Solution) | |
Sec 1.3 | ⚬ Stability of fixed points and periodic orbits | |||
Sec 21.1, 21.2, 21.3 | ⚬ Bifurcation of maps | |||
Sec 1.3 | ⚬ Logistic map and two-dimensional maps |
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).