A LevelMaths: Pure 3CIERevision Notes5. Integration5.2 Differential Equations5.2.4 Modelling with Differential Equations

Modelling with Differential Equations (CIE A Level Maths: Pure 3)

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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 Tip

  • 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

    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 – one of the many reasons he is excited to be a member of the SME team.