*SQM Classification* - **Systems**: Mathematical models express knowledge, intuition, and assumptions about a real world phenomenon or process in a mathematical language. This involves identifying suitable [[Variable|variables]] that quantify aspects deemed of importance and of relevance. Scientists often talk about a ***state of a system*** that is characterised by the values of at least some of the these variables. - [[Physical System]] v [[Conceptual Systems]] - Deterministic v stochastic systems - [[Continuous Systems]] v [[Discrete Systems]] - Finally systems are also distinguished by their application area - **Questions**: There are three broad types of mathematical problems - [[Forward Problems]]; - [[Inverse Problems]]; and - [[Control Problems]]. - **Mathematical Statements (Maths)**: In mathematical modelling, the variables characterising a system are related to each other by means of mathematical statements. In this module, we will mostly use [[Differential Equation|differential equations]], to some extent also [[Linear Recurrence Relation with Constant Coefficients|difference equations]] for this purpose.