Course Unit Specification: MATH44041/MATH64041
Lecturer: Dr. Yanghong Huang
(yanghong.huang@manchester.ac.uk)
Office: Alan Turing 1.108
Lectures location:
Meiss's Book | Outline | Tutorial exercies and solutions | Scanned notes |
---|---|---|---|
Chap 1 | ♠ Introduction | ||
Chap 1 | ♠ Notation and Basic Concepts | ||
Sec 1.2, 4.1, 4.2 | ⚬ ODEs: trajectories, phase portrait and flow | ||
Sec 4.1 | ⚬ Fixed points, periodic orbits, invariant sets | ||
Sec 3.3 | ⚬ Existence and uniqueness | ||
Chap 2,4,5,6 | ♠ Linearisation and Equilibria | ||
Sec 2.1, 2.3, 2.5 | ⚬ Linear systems | ||
Sec 6.1, 6.2 | ⚬ Planar ODEs | ||
Sec 4.5, 4.6 | ⚬ Stability and Lyapunov functions | ||
Sec 5.3, 5.4 | ⚬ Nonlinear systems and stable manifold | ||
Sec 1.3 | ⚬ Maps: fixed points and periodic orbits | ||
Chap 2, 5, 6 | ♠ Periodic Orbits | ||
Sec 5.5 | ⚬ Poincare-Bendixson theorem for periodic orbtis | ||
Sec 2.8 | ⚬ Floquet theory for periodic coefficients | ||
Chapter 8 | ♠ Bifurcation and Centre Manifold | ||
Sec 5.6 | ⚬ Centre manifold and its approximation | ||
Sec 8.1 | ⚬ Extended centre manifold | ||
Sec 8.1, 8.4, 8.6, 8.8 | ⚬ Bifurcations | ||
Chap 1, 21 | ♠ Maps and their bifurcation | ||
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).