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 2020-21 | 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. |
|
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): |
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 |
| Final Assessment, open book and remote (50%) One hour time on task | One hour time on tas | 50 | ||||
| CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
| Homework 1 (10%) Equivalent to 2-5 sides of A4 | Equivalent to 2-5 si | 10 | ||||
| Homework 2 (10%) Equivalent to 2-5 sides of A4 | Equivalent to 2-5 si | 10 | ||||
| Homework 3 (10%) Equivalent to 2-5 sides of A4 | Equivalent to 2-5 si | 10 | ||||
| Homework 4 (10%) Equivalent to 2-5 sides of A4 | Equivalent to 2-5 si | 10 | ||||