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IB Maths AI AHL 5.16 - Numerical Solutions of Differential Equations Notes

IB Maths AI AHL 5.16 - Numerical Solutions of Differential Equations Notes

Subject: Mathematics

Age range: 16+

Resource type: Worksheet/Activity

Last updated

15 April 2026

pdf, 1.26 MB
pdf, 1.26 MB
pdf, 1.27 MB
pdf, 1.27 MB

This IB Maths AI HL AHL 5.16 – Numerical Solutions of Differential Equations notes resource builds clear, structured understanding of Euler’s method and numerical modelling.

Students learn how to apply Euler’s recurrence formula ( x_{n+1}=x_n+h ) and ( y_{n+1}=y_n+h f(x_n,y_n) ) to approximate solutions of first-order differential equations, understand the impact of step size on accuracy, and complete structured solution tables. The notes extend this approach to coupled systems, guiding learners through simultaneous updates for multiple variables and interpreting results in real-world contexts .

Through applications such as predator–prey (Lotka–Volterra) models and marine ecosystem scenarios, this resource strengthens modelling fluency, numerical reasoning, and exam-ready method presentation — essential Higher Level skills for differential equations and applied calculus in the IB curriculum.

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