A mathematical model can be very simple or very complex. The goal is to represent a system or process using precise definitions and mathematical relationships. One way to create a model is to simply start building it, acknowledging it won't be perfect, but trying to improve the model along the way. Eventually you should arrive at a basic (fairly simple) model, which you can then make more complex (and perhaps more accurate) by elaborating in areas that previously were glossed over.
For instance, if I want to represent amount of daylight in a single day, one of the simplest models might be:
- For any given day D, some percentage of that day occurs in which there is measurable daylight L.
However, I can improve this model and make it more complicated by:
- Measuring daylight L as hours, minutes, seconds, milliseconds (or similarly as some percentage up to a particular decimal point e.g. 49.255%) of some day.
- Adding new variables, such as a geolocation--G1 longitude and G2 latitude, since daylight is a function of where on the earth measurement is taken. Or, allowing daylight to be more than a percentage, represented by an additional variable for luminosity U (imagine clouds reducing the impact of daylight).
However, perhaps some of the complications are not relevant given the context, so one may want to simplify the model to simply be:
- Daylight L for any given day D is a function of location only (G1 longitude and G2 latitude). Now, if we construct a look-up table for daylight at any given geolocation, we'd be able to find L(G1, G2) = some # of seconds per day D.