MA6020  Mathematical Modelling (2024/25)
Module specification  Module approved to run in 2024/25  
Module title  Mathematical Modelling  
Module level  Honours (06)  
Credit rating for module  30  
School  School of Computing and Digital Media  
Total study hours  300  


Assessment components 


Running in 2024/25 (Please note that module timeslots are subject to change) 

Module summary
This module develops a rigorous approach to the whole process of solving problems arising from real life scenarios and the module consists of providing solutions to a number of such problems. For each given problem, the process of dealing with it includes an initial analysis, identification of the main factors involved, establishment of a differential or difference equation as a mathematical model of the problem, analytical and/or numerical analysis to solutions of the equation, making predictions and drawing conclusions to the model, and feedback to solving the problem.
The module aims to
1. Introduce the process of model building from a nonmathematical description of a physical or industrial process or in a business application.
2. Introduce the idea of mathematical modelling as a means of solving real problems.
3. Present powerful tools of differential/difference equations to analyse the models in order to make appropriate predictions.
4. Develop the student's ability to work effectively ingroups.
5. Improve the student's communication skills through report writing and presentation.
Prerequisite knowledge: MA5011 Further Calculus and MA5052 Differential Equations (studied or Corequisite)
Syllabus
Basic concepts of mathematical modelling.
Problems (single species population, drug concentration, rocket motion, heat conduction, mechanical systems, electrical circuit, etc.) modelled by a first and second order ordinary differential equation.
Problems (interactive species populations, heat conduction, mechanical systems, electrical circuit, etc) modelled by a system of first order differential equations.
Problems (nonsteady state heat process, mass/energy conservation, evolutionary processes, etc) modelled by partial differential equations. LO1,LO2,LO3,LO4
Balance of independent study and scheduled teaching activity
The module will be delivered through a weekly 3hour block consisting of a mixture of a lecture and a tutorial or workshop (in a computer lab). While the theory and methods will be covered during the lectures, the practice exercises and studentled group discussions will be carried out in tutorial and workshop sessions. The tutorled sessions are intended to teach students the problem solving skills, whereas the studentled sessions are designed to train students the ability of independence as well as collaboration. Materials for learning are provided through main text books supplemented by online sources and an integrated learning environment (currently WebLearn). In addition to the timetabled classes, students are required to spend about 7 hours each week working individually and in their groups. Then the tutorial sessions and workshops will provide an ideal setting for students to meet up with their group members on regular basis and carry out their discussions and investigations.
Learning outcomes
On successful completion of the module, students should be able to
LO1 Understand the concept of mathematical modelling and develop a mathematical
model from a nonmathematical description of physical, industrial or business
process.
LO2 Solve and analyse problems modelled by first and second order differential
equations (mainly ODEs) and first order twodimensional ordinary differential
systems.
LO3 Interpret the results arising from mathematical models in practical terms and
critically evaluate the implications and analyse the effect of various changes to
the input parameters of the model, relating these effects to the solution obtained.
LO4 Demonstrate effective collaboration when working in a group and communicate
effectively through report writing and presentation.
Bibliography
Core Text:
Belinda Barnes and Glenn Robert Fulford (2011), Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple and MATLAB, Second Edition illustrated, revised, CRC Press, ISBN 2011 1420083503, 9781420083507
Recommended Reading:
Frank R. Giordano, William P. Fox, Maurice D. Weir, Steven B. Horton (2008), A First Course in Mathematical Modelling (Fourth Edition), Publisher: Cengage Learning.
William E. Boyce, Richard C. DiPrima (2005), Elementary Differential Equations and Boundary Value Problems, with ODE Architect CD, 8th Edition.
D Dennis, G. Zill and Michael R. Cullen (2008), Differential Equations with BoundaryValue Problems (Hardcover) by Publisher: Brooks Cole; 7 edition.
Richard Haberman Publisher (2003), Applied Partial Differential Equations (4th Edition) by: Prentice Hall; 4 edition).