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Analysing skid marks
This unit is the second in the series of five units on mathematical modelling. In this...
This unit is the second in the series of five units on mathematical modelling. In this unit you are asked to relate the stages of the mathematical modelling process to a previously formulated mathematical model. This example, that of skid mark produced by vehicle tyres, is typical of accounts of modelling that you may see in books, or produced in the workplace. The aim of this unit is to help you to draw out and to clarify mathematical modelling ideas by considering the example. It assumes that you have studied the unit 'Modelling pollution in the Great Lakes'.
After studying this unit you should be able to:
- create simple models, given a clear statement of the problem;
- write down the simplifying assumptions that underpin a model;
- identify the key variables and the parameters of a model;
- apply the input–output principle to obtain a mathematical model, where appropriate;
- obtain mathematical relationships between variables, based on or linking back to the simplifying assumptions;
- interpret the mathematical solution to a modelling problem in terms of the original statement of the problem;
- understand the processes involved in evaluating a model, both qualitatively and quantitatively.
Analysing skid marks
In the first unit of this series you saw how some of the stages of a mathematical modelling process can be applied in the context of modelling pollution in the Great Lakes. In this second unit you are asked to relate the stages of the mathematical modelling process to another practical example, this time modelling the skid marks caused by vehicle tyres. By considering the example you should be able to draw out and clarify your ideas of mathematical modelling.
This unit, the second in a series of five, builds on the ideas introduced in
This unit is an adapted extract from the course MSXR209 Mathematical modelling.