In this video you learn how you will work with the modelling cycle in this course.
And at last, you will see what these fish are about.
So, in this course we keep your eyes on the ball, and follow the whole modelling cycle:
P for problem, M for mathematical model, C for calculations and V for validation.
As an example for mathematical modelling we will use rainbowfish.
We pretend that we grow rainbowfish to sell in pet shops.
The question is, how fast does the population grow?
As a first mathematical model, we use a differential equation describing the growing population.
Then in the first modelling cycle, we will calculate the analytical solution of the differential equation
with a hand calculation.
This first result will turn out to be okay for the short term,
but after a longer time the results are nonsense.
So we will specify the problem further:
how will our fish population change, not only in a few days, but also seen over longer periods?
The model has to be adapted,
and with another calculation method, the long term behaviour is estimated,
and the results are validated again.
The results will still not be satisfactory, so the cycle has to be completed a few times more.
In one of these cycles, we will switch from analytical calculations, to numerical calculations.
The results will be approximated with Euler's method.
And you will practice writing a computer program.
In the meantime, you are also starting your project:
you form a team of two, choose your own subject and your own problem,
and start cycling through the modelling cycle with your own model and computer programs.
The last module of the course is about scientific writing:
about the do's and don't of writing a report.
You will also learn to use LaTeX.
The end goal for your team is to write a scientific report about your own research project.
The report is not in a linear form, like you would do for a scientific paper,
and which has to be very short.
No, the report follows the modelling cycle, and describes each of the modelling steps you took.
In that way you tell the story of your research project and you can convince the reader
that each of the choices you made is okay.
So, in this course, we practice together with the rainbowfish problem,
but in the end, each team produces a report on a different and new research problem.
Do not be afraid: the aim of this course is educational.
The aim is that you learn the basics of mathematical modelling,
so your project will be primarily to practice all those new skills.
Please use your creativity and experiment.
The results do not have to qualify for a peer reviewed scientific journal.
So, the aim is to learn, but who knows.
You will all be on new grounds, and you might actually solve a important real-life problem!