Mathematical models (Chapter 1)

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1.1 What is a Mathematical model?

A Mathematical model is a simplification of a real world situation. It can be used to make predictions about a real world problem, and by analysing the model you can obtain an improved understanding of the situation.

Advantages

Quick and easy to produce

Simplification of a complex situation

Disadvantages

Simplification means it does not include all aspects of the problem

May only work in certain situations

1.2 The process of designing a Mathematical model

1. A real world problem is observed

2. A mathematical model is devised

3. The mathematical model is used to make predictions about the expected behaviour of the real world problem

4. Experimental data is collected from the real world

5. Predicted and observed outcomes are compared

6. Statistical tests are used to assess how well the model describes the real world

7. The mathematical model is refined, to improved the match of predicted outcomes with observed data