| Contents* | Lecture
Notes (password protected!) |
|
| Week 1 | Introduction, Difference Equations
and applications, Review on Matrix theory |
Lecture Notes for Week 1 to 3 (ps pdf) or full set in book format (ps pdf) |
| Week 2 | Fibonacci Sequences, Leslie Matrices
and Stability
in Difference Equations. Non-Linear Models. |
|
| Week 3 | Non-Linear Models (contd.), the
Discrete Logistic Growth Equation for different growth rates. Population Genetics using Difference Equations. |
|
| Week 4 | Continuous Models, Malthus' Law and
the Continous Logistic Growth Model (+ added culling) |
Exercise Sheet 1(ps), pdf Lecture Notes for Week 4 to 7 (ps pdf) |
| Week 5 | Equilibrium and Stability,
Derivation of the
Chemostat Model Equations, Dimensional Analysis |
|
| Week 6 | Bank Holiday |
|
| Week 7 | Stability at Steady States for the
Chemostat: The Jacobian Matrix and different forms of stability |
|
| Week 8 | Linear Interaction Models, Diabetes Detection. Non-Linear Models, Phase Plane Analysis. Mutual Destruction, the Guerrilla Combat model Phase plane analysis & Stability |
Exercise Sheet 2(ps),
pdf Lecture Notes for Week 8 to 10 (ps pdf) |
| Week 9 | Phase plane analysis & Stability of Predator-Prey Models & SymbioticModels |
|
| Week 10 | Infectious Diseases (SIR & SIRS model): Phase plane analysis & Stability. The Chemostat Model revisited |
Exercise Sheet 3(ps),
pdf Sample Exam Paper (pdf) |
| Week 11 | Spare | |
| Week 12 | Course Review |
*This is not a hard-wired timetable; contents of lectures can change as term progresses