1.             To provide an understanding of the techniques used in constructing, analysing, evaluating and interpreting mathematical models.

2.             To do this in the context of two non-physical applications, namely microeconomics and population dynamics.

3.             To use and develop mathematical skills introduced in Year 1 - particularly the calculus of functions of several variables and elementary differential equations.

After completing the module students should be able to:

-               Use techniques from several variable calculus in tackling problems in microeconomics.

-               Use techniques from elementary differential equations in tackling problems in population dynamics.

-               Apply mathematical modelling methodology in these subject areas.

All learning outcomes are assessed by both examination and course work.

Microeconomics: 

Functions of several variables.   Constrained maxima and minima.

Utility and its maximisation subject to budget constraint.   Demand. Wages and leisure.

Production.   Profit.  Associated optimisation.   Supply.

Markets and prices.   Ideal competition.   The effect of taxation.    Monopoly and duopoly.

Population dynamics:

Single species growth.   Exponential and logistic models.   Equilibrium.

‘Fishing’models.

Two interacting species.   Competition, predation, symbiosis.   Phase plane.

Equilibrium and linear stability theory.   Limit cycles.