Mathematical Ecology and Biology

Synopsis

Mathematical ecology and biology introduces the applied mathematician to practical applications of the subject, particularly in situations where continuous models are appropriate, and where these may be modelled by differential equations, either ordinary or partial. Biology is ideally suited to do this at a reasonably introductory level, and apart from the variety of applications in ecology, biology, immunology, epidemiology and physiology, the course will bring out the way in which the common applied mathematical themes of stability, wave propagation, oscillations, extinction, hysteresis and excitability occur in all these subjects.

Discrete and continuous population models, predator-prey systems, harvesting. Enzyme reactions, glycolytic oscillations. Genetics; wave phenomena, signal propagation in nerve cells. Pattern formation; epidemiological and immunological models. The course assumes some knowledge of phase plane analysis.