Chapter 8: Modelling a changing world
Difference and differential equations as models of change — growth, decay, recurrence and feedback.
The chapter problem
Will the lake ever clear?. A pollutant enters a lake and is washed out at a rate proportional to how much is there. You will model it, solve the model, and say how long the lake takes to reach a safe level — and what the model assumes that might not hold.
Where it is used: Population, disease, pollution, cooling, radioactive decay and finance.
Your turn to connect it: What changes in your life or your area at a rate set by how much of it there already is?
Sections
- 8.1 Rates of change and differential equations — tier O · refs S4
- 8.2 Exponential growth and decay — tier O · refs S4
- 8.3 Recurrence relations as discrete models — tier O · refs S4
- 8.4 First-order difference equations — tier O · refs S4
- 8.5 Feedback and limited growth — tier O · refs S4
- 8.6 The logistic model — tier H · refs S4
- 8.7 Solving separable differential equations — tier H · refs S4
- 8.8 Comparing a discrete and a continuous model — tier H · refs S4