Guide to Mathematical Modelling

WHAT IS MODELLING? Introduction. Models and Modelling. The Learning Process for Mathematics Modelling. Summary. GETTING STARTED. Introduction. Examples. Conclusion. Further Examples. Further Comments on the Examples in Section 2.2. MODELLING METHODOLOGY. Introduction. Definition and Terminology. Methodology and Modelling Flow Chart. The Methodology in Practice. Summary. UNITS and DIMENSIONS. Introduction. Units. Dimensions. Dimensional Analysis. Summary. MODELLING SKILLS. Introduction. Listing Factors. Making Assumptions. Types of Behaviour. Translating into Mathematics. Choosing Mathematical Functions. Relative Sizes of Terms. Reducing the Number of Parameters. Summary. USING DATA. Introduction. Data Collection. Empirical Models. Estimating Parameters. Errors and Accuracy. Testing Models. Summary. USING RANDOM NUMBERS. Introduction. Modelling Random Variables. Generating Random Numbers. Simulations. Using Simulation Models. Packages and Simulation Languages. Summary. USING DIFFERENTIAL EQUATIONS. Introduction. First Order, One Variable. Second Order, One Variable. Second Order, Two Variables (Uncoupled). Simultaneous Coupled Differential Equations. Summary. REPORT WRITING and PRESENTATIONS. Introduction. Report Writing. A Specimen Report. Presentation. EXAMPLE MODELS. Introduction. Doing the Dishes. Shopping Trips. Disk Pressing. Gutter. Turf. Parachute Jump, On the Buses. Further Battles. Snooker. Further Models. BIBLIOGRAPHY. SOLUTION to EXERCISES. INDEX.