Department of Mathematical Sciences, Unit Catalogue 2009/10 |
MA20202: Modelling the dynamics of life 2 |
 Credits:
| 6 |
| Level:
| Intermediate |
| Period: | Semester 2 |
| Assessment:
| CW 50%, EX 50% |
| Supplementary Assessment: | Like-for-like reassessment (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take MA20201 |
| Description: | Aims: To develop students' mathematical techniques so that they can model a range of biological systems and interpret the outcomes of the modelling. Learning Outcomes: At the end of this unit, students should be able to: * write down and analyse a range of classical mathematical models used to describe biological processes; * carry out a range of techniques in matrix algebra and understand its role in analysing biological models; * work competently with complex numbers. Skills: Calculus and matrix algebra (T, A); modelling (T, F, A). Content: First-order non-linear difference equations: cobweb diagrams, steady states, stability; biological applications, e.g. density-dependent population growth, selection in a bacterial population. Matrices and determinants: eigenvalues and eigenvectors, complex numbers; Leslie matrices, age-structured populations, host-parasitoid systems. Second-order linear ordinary differential equations. Second-order non-linear ordinary differential equations: steady states, Jacobian, phase plane analysis; prey-predator systems, competition systems. |