Edexcel A Level Maths: Pure:复习笔记8.3.4 Modelling with Differential Equations
Modelling with Differential Equations
What can be modelled with differential equations?
- Derivative terms like
are “rates of change” - There are many situations that involve “change”
-
- Temperature
- Radioactivity
- Medication
- Sales
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:
- Important phrases here are …
- … “rate of change” ... reference to a derivative term like
- … directly/inversely proportional to ...
- … 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)
- … “rate of change” ... reference to a derivative term like
- Some differential equations may involve Connected Rates of Change
Exam 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
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