Introduction to Models and Change Equations: The Bathtub

Summary

• four critical pieces of structure: state space is in black, trajectories are in red.

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• what tells the trajectory which way to go? The answer is: a model

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• standard form of a model: state variable, say, \(X\) on the left with a little prime symbol \(X'\)

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• \(X'\) is the change of \(X\) in a unit time. Then we write an equals sign and put on the right hand side what makes \(X\) go up and what makes \(X\) go down? This is called a change equation

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• Bathtub with a faucet flowing in

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• Bathtub with an inflow and an outflow