What is Mathematical Modelling?
Mathematical Model: A mathematical equation or function used to represent and describe a real-world phenomenon or situation.
Mathematical modelling is one of the most powerful tools in applied mathematics. Rather than studying the world directly, we translate a real situation into mathematics, analyse it, and then interpret our findings back in the real-world context.
In SL 2.6, you will develop the skills to:
- Choose an appropriate model for a given situation
- Fit the model to data by finding its parameters
- Test whether the model is reasonable
- Use the model to make predictions and interpret results
Think of a mathematical model like a map. A map is not the actual territory , it simplifies and abstracts reality , but it is still incredibly useful for navigation. Similarly, a mathematical model simplifies a real-world situation but gives us powerful tools to understand and predict it.
The Modelling Process
Mathematical modelling is not a single step , it is a cycle of interconnected stages. Understanding this process will help you structure your work clearly, especially in assessments.
The key stages are:
- Identify the problem , What exactly are you trying to model or predict?
- Make assumptions and define variables , Simplify the real situation; decide what to include and what to ignore. Define your variables clearly with units.
- Formulate the model , Choose an appropriate function type and write the equation.
- Solve the mathematical problem , Find parameters, evaluate, calculate.
- Interpret the solution , Translate your mathematical answer back into the real-world context.
- Validate the model , Check whether the model produces sensible, accurate results against known data.
- Refine the model (if necessary) , If the model doesn't fit well, adjust your assumptions or try a different function type.
Modelling is an iterative process. Your first model may not be perfect , that is completely normal. Refinement is a natural and expected part of the process, not a sign of failure.