Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title MATHEMATICAL MODELS: MICROECONOMICS AND POPULATION DYNAMICS
Code MATH227
Coordinator Dr DM Lewis
Mathematical Sciences
D.M.Lewis@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 Level 5 FHEQ First Semester 15

Aims

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

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

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

Learning Outcomes

(LO1) 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.

Syllabus
 

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.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
MATH102 CALCULUS II; MATH101 Calculus I; MATH103 Introduction to Linear Algebra 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Assessment 2 Assessment Schedule (When) :First semester  2.5    50       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Assessment 1 Assessment Schedule (When) :First semester  0    10       
No assessment details provided  0    10       
No assessment details provided  0    10       
No assessment details provided  0    10       
No assessment details provided  0    10