MAT530: March 2012 – July 2012

Introduction to Mathematical Modelling

Projects

  1. Project Proposal (20%)
  2. Group Project (20%)

Class Schedule

CSB5Aq, CSB5Bq

  • Monday – 1100-1150 – F140
  • Thursday – 1600-1750 – A218
  • Friday – 0800-0850 – LAB02

Contents

  1. The Mathematical Modelling Process
    • Definition of a model
    • Classification of models
    • Construction of models
      • Identify the problems
      • Make assumptions
      • Interpret the model
      • Verify the model
      • Implement the model
      • Maintain the model
      • Illustrative examples
  2. Static Models
    • Model fitting
    • Least squares method
    • Choosing a best model
    • Illustrative examples
  3. Discrete Dynamical Systems
    • Population growth models
    • Qualitative behaviour of solution
    • Analyse using Excel Spreadsheet
    • Illustrative examples
  4. Continuous Dynamical Systems
    • Population growth models
    • Qualitative behaviour of solution
    • Analyse using Mathematical software
    • Illustrative examples
  5. First-Order Systems of Differential Equations
    • Two-species interaction
    • Qualitative behaviour of solution
    • Analyse using Mathematical software
    • Illustrative examples
  6. Research Proposal
    • Literature survey
    • Proposal planning
    • Preliminary investigation
    • Report writing

Textbook

Giordano, F.R., Weir, M.D. and Fox, W.P (2003), A First Course in Mathematical Modeling. 3rd Ed., Pacific Groves, CA: Thomson Brooks/Cole.
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