Mathematical Modelling and Applications

What this page covers

This unit sits in the Applied Mathematics and Context strand of Mathematics. Most of the resources are mind maps, with a small set of flashcard decks and a few notes and a flowchart. Together they follow one idea: turning a real situation into mathematics, then using the result to make predictions.

Where to start

Begin with the basics of what a model is. The notes Mathematical models (Chapter 1) explain that a mathematical model is a simplification of a real world situation, used to make predictions. The mind map What is Math Modeling? and the flowchart what is math modeling then lay out the steps: defining the problem, making assumptions, defining variables and so on.

1. Read Mathematical models (Chapter 1) for the definition.
2. Open What is Math Modeling? to see the steps as a map.
3. Check the flowchart for the same process in another layout.
4. Try the flashcard deck on the stages of a model, with its advantages and disadvantages.

Moving to worked examples

Once the process is clear, look at models in use. The Exponential Model note builds a population equation from birth and death rates and arrives at dN/dt = aN. Other mind maps apply modelling to an infectious disease, a volleyball service and optic testing in ophthalmology. Mathematics in the Workplace - Post Visit shows how ordering, measuring and quoting use numbers on the job.

For university study

The deck Engineering Maths flashcards asks about Taylor series, in single and multi-variable form. The deck B5.5 covers Fick's Law of Diffusion and a one-dimensional tumour model. The Differential Equations mind map is a useful companion to both.

Using maps and flashcards together

This page lists no quizzes, so make your own check. Read a mind map, hide it, then write out the steps from memory. Turn gaps into flashcard questions and test yourself again a day later. Teachers can use the maps as ready-made starting points for a class discussion. Choose one map today and see what you can recall.