Differential Equations › Section B · First order differential equations › Topic B.7
Modeling with first order equations
Tanks, populations, falling bodies and circuits all obey first-order equations once the physical rules are written down carefully. Setting up the equation is usually the hard part; this topic shows how to do it, solve it and check that the answer makes sense.
In this topic
- Three stages of a model
- Rate in minus rate out
- Worked example: a tank that fills
- Worked example: growth with removal
- Falling bodies and sign conventions
- Worked example: a skydiver
- Circuits, decay and cooling
- Checking a model
- Common mistakes to avoid
- Key takeaways
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