Department of Mathematical Sciences, Unit Catalogue 2008/09 |
MA20202 Modelling the dynamics of life 2 |
| Credits: 6 |
| Level: Intermediate |
| Semester: 2 |
| Assessment: EX50CW50 |
| Requisites: |
| Before taking this unit you must take MA20201 |
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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. |