MATH10001 Mathematical Workshop. Mathematical Modelling and Problem Solving. Traditional view of maths?. Maths is useless The only jobs maths can be used for are accountancy and teaching Maths has no link with the real world. The truth is that mathematicians have changed the world,
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Mathematical Modelling and Problem Solving
Radio, digital revolution
eg. Finite element modelling to reduce vibration
Divide car into small
Treat it a bit like masses
and springs in a network.
Vibrations modelled using eigenvalues of matrices.
We start with 500 bacteria in a Petri dish. After one day we have 525 bacteria, after two days we have 551 bacteria.
We write down the relationship
Assuming a growth rate of 0.05 (from our observations) we get
6. Test the solution: we test our solution against observations.
We can see that the model works well at the start but after 6 days the model is not accurately predicting the population. This tells us that we need to modify our model.
could be due to a change in food available or room to grow. We chose to ignore those variables in the original model. As the growth rate is changing we could replace our constant rate by one which is a function of n.
Why do we need mathematical models? Why don’t we simply make lots of observations?