Mathematical Modelling Process

Key idea

Define, simplify, solve, validate and refine a model.

In depth

Steps: define the question, make assumptions, build the model, solve, validate against data, interpret, and refine. A model is a simplified description, not reality. Sensitivity analysis shows which assumptions matter.

Worked example

Modelling a falling object: first ignore air resistance, then add drag if the data disagree.

Real-world uses

• Turning a real problem, such as traffic or disease spread, into a model that can be tested and improved

Common mistake

Trusting model results outside the range where the assumptions hold.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related advanced topics in Differential Equations, Abstract Algebra & Applied Math

• What Is a Differential Equation? – An equation relating a function and its derivatives.
• Order and Linearity of ODEs – Classify equations by highest derivative and linearity.
• Direction Fields – Slope fields show solution curves visually.
• Separable Equations – Separate variables and integrate both sides.
• First-Order Linear Equations – Use an integrating factor.
• Exponential Growth and Decay Models – dy/dt = ky gives y = y₀eᵏᵗ.