- To provide a theoretical basis for the understanding of population ecology

- To explore the classical models of population dynamics

- To learn basic techniques of qualitative analysis of mathematical models

The ability to relate the predictions of the mathematical models to experimental results obtained in the field.

Single species systems: Fundamental balance equations. Malthus''s model. Intraspecific competition. Continuous time logistic model. Discrete time models: Hassell model and logistic map. Relationship between continuous and discrete time models. Equilibria, stability, cycles and a mention of period doubling and chaos in the discrete time models. Explicit time delays, stability triangle. Age structure, use of Leslie matrices for linear problems.

Multi-species systems: Coupled balance equations leading to m-species discrete and continuous time models. Linear stability analysis, community matrix for both continuous and discrete time.
Lotka-Volterra-Gause models for interspecific competition. Gause''s competitive exclusion principle. Lotka-Volterra and other predator-prey models, including a discussion of functional and numerical responses. Nicholson-Bayley host-parasitoid model as a predato r-prey system in discrete time. Kermack-McKendrick models of infectious diseases.
Methods of analysis: Linear stability analysis and phase plane analysis. Poincare-Andronov-Hopf theorem. Lyapunov stability theory. Poincare-Bendixson theory.