Unit 2
sec 1.7 the modelling cycle
15
October 2015
23:02
We
collected some data and made assumptions. These assumptions made the problem
simpler and easier to solve.
We were then able to describe the
method of solution mathematically and carry out calculations to find an answer.
We considered whether this answer was
realistic, and rounded the answer appropriately so that it is made sense within
the context of the problem. Changing the assumption to see how sensitive the
journey times were to variation in average speed.
If the conclusions do not make seem
reasonable, then more extensive changes to the model may be needed.
The types of steps used in many problems,
and the list of these steps is called modelling cycle. These steps can be applied to more complicated problems.
The
modelling cycle
1) Describe
the problem concisely so that you are clear about what you are trying to do. In
real life, and particularly if you are working within a team, this may involve
discussing the problem with others.
2) Make
assumptions to simplify the problem, so that you retain the essential features
but will be able to describe it mathematically. At this stage, it is also
useful to sort out what you already know about the problem, by collecting data
and other information.
3) Describe
the problem mathematically using numbers, formulas or graphs, and see these to
obtain new results.
4) Consider
what these new results mean practically, and check that the predictions seem
reasonable. If the predictions do not match reality, then you may need to
refine the assumptions, collect further information and go round the cycle
again. Your conclusions are only as good as the data you have used and the
assumptions you have made.
This modelling cycle can be used as a
framework for solving many practical problems involving both basic and advanced
mathematical skills.
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