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Modelling with Differential Equations (OCR A Level Maths A) : Revision Note

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OCR Maths A: PureCambridge (CIE) Maths: Pure 3AQA Maths: PureEdexcel Maths: Pure

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Modelling with Differential Equations

What can be modelled with differential equations?

  • Derivative terms like  fraction numerator d y over denominator d x end fraction are “rates of change”

  •   There are many situations that involve “change”

  • Temperature

  • Radioactivity

  • Medication

  • Sales

Notes de_scenes, AS & A Level Maths revision notes

How do I set up a model with differential equations?

  • The first task is to set up a differential equation from a description in words:

Notes de_setup, AS & A Level Maths revision notes

  • Important phrases here are …

    • … “rate of change” ... reference to a derivative term like fraction numerator d y over denominator d x end fraction

    • … directly/inversely proportional to ... y space equals space k x, y space equals k over x

    • … formulate ... means to write as an equation

      • you may need to choose and define letters for variables

      • V for volume, h for height (of a cylinder, say)

    8-3-4-notes-de-setup2

  • Some differential equations may involve Connected Rates of Change

 

Notes de_croc_setup, AS & A Level Maths revision notes

Examiner Tips and Tricks

  • Use a highlighter (or underline) to pick out important words/phrases

  • Read and re-read the question several times

  • Jot down bits and pieces as you go; do not expect to go straight from reading to writing down a differential equation.

Worked Example

Example soltn, AS & A Level Maths revision notes

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    Paul

    Author: Paul

    Expertise: Maths Content Creator (Previous)

    Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams.