In this appendix we’ll “open the hood,” looking more closely at how some of the tools we have used work: specifically, run_solve_ivp, root_scalar, and maximize_scalar. Most of the time you can use these methods without knowing much about how they work. But there are a few reasons you might want to know.

One reason is pure curiosity. If you use these methods, and especially if you come to rely on them, you might find it unsatisfying to treat them as black boxes. In that case, you might enjoy opening the hood.

Another is that these methods are not infallible; sometimes things go wrong. If you know how they work, at least in ...

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