module specification

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 non-mathematical 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 in-groups.
5. Improve the student's communication skills through report writing and presentation.
Pre-requisite knowledge: MA5011 Further Calculus and MA5052 Differential Equations (studied or Co-requisite)

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 (non-steady state heat process, mass/energy conservation, evolutionary processes, etc) modelled by partial differential equations. LO1,LO2,LO3,LO4

The module will be delivered through a weekly 3-hour 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 student-led group discussions will be carried out in tutorial and workshop sessions. The tutor-led sessions are intended to teach students the problem solving skills, whereas the student-led 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.

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   non-mathematical 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 two-dimensional 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.

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 Boundary-Value Problems (Hardcover) by Publisher: Brooks Cole; 7 edition.
Richard Haberman Publisher (2003), Applied Partial Differential Equations (4th Edition) by: Prentice Hall; 4 edition).