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A comment on What are Differential Equations and how do they work?. Parent comment

Re:What are Differential Equations and how do they work? by ianhorn on Sunday October 04, 2020 @05:01PM (#24682221)
One of the last classes I ever took was nonlinear dynamical systems. It should have been one of the first after basic calc/vector calc!

The typical progression is to start with systems you can solve by hand and then move to ones you can’t usually solve, but can still usefully describe, teaching how to analyze them.

It should be the other way around! Start with generally useful tools that apply broadly and then teach the special cases you happen to be able to solve analytically. General tools like basins of attraction and nondimensionalization, should be considered more rudimentary than perfect closed form solutions.

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Re:What are Differential Equations and how do they work? by AareyBaba on Sunday October 04, 2020 @05:39PM (#24682469)
I agree. The biggest eye-opener was learning that the output of some dynamical systems described by deterministic diff equations cannot be predicted because infinitesimal changes in initial conditions lead to exponential changes in the output (popularly known as chaos). This was profound just like Godel's Theorem - we cannot know everything.
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