Objectives

This subject is devoted to the studies of the basic principles of the mathematical modelling process. It is designed to equip the students with a more complete and extensive exposure to how mathematics can be applied to solving problems arising from various disciplines. In particular, the case study approval is adopted in which the modelling process is described by means of a series of examples arising from various areas. Where applicable, problems will be modelled in more than one way to illustrate the flexibility and diversity involved in mathematical modelling.

References

• R. Haberman, Mathematical Models, Prentice-Hall, 1977.
• P. McCullagh and J.A.Nelder, Generalized Linear Models, 2nd Edition, London: Chapman and Hall, Ch 1-6.
• J. O'Canoll, A.W. Bush, M. Cross, R.D. Gibson and T.S. Wilkinson, Modelling and Simulation in Practice 2, Emjor Press, 1979.
• Eds. D.J.G. James and J.J. McDonald, Case Studies in Mathematical Modelling, Stanley Thomes, England, 1981.
• Walter J. Meyer, Concepts of Mathematical Modelling, McCoracs Hill, 1985.
• Eds. J.S. Berry, D.N. Burgher, I.D. Huntley, D.J.G. James, A.O. Moscardini, Mathematical Modelling Methodology, Models and Micros, Ellis Horwood Limited, 1986.
• Michael Mesterton-Gibbons, A Concrete Approach to Mathematical Modelling, Addison-Wesley, 1989.

Assessment (subject to minor adjustment)

• Continuous assessment (50%)
  • Assignment 1 (10%)
  • Assignment 2 (10%)
  • Problem Solving (5%)
  • Mini-project Presentation (5%)
  • Mini-project Report (20%)
• Final Examination (50%)

Subject Contents in Outline

1. General Introduction to the Concept of Mathematical Modelling (12 hours)
   Including Steps in Building a Mathematical Model and Illustrations by Means of Examples such as
   1. Decay of Pollution
   2. Radioactive Decay
   3. Plant Growth

   Students will also be coached in mini-projects of modelling

2. Case Studies on Open-Ended Problems (30 hours)
   Topics would be Selected from Different Disciplines such as
   1. Traffic Dynamics and Traffic Flow
   2. Water Quality in Rivers
   3. Biological and Medical Problems
   4. Markov Chain Model

This year, the two topics selected for Part II are:

Traffic Flow using the PDE approach (14 hours)

1. Continuum Hypothesis of Macroscopic Model
2. Conservation Equation and Characteristics Method
3. Applications & Advanced Topics in Traffic Flow

Markov Chains & Modelling (12 hours)

1. Markov Chain Model
2. Discrete Markov Chain Model