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You can solve differential equations by integrating or by differentiating. Real-world integrators were easier to build back when DEs were solved with analog com
by dreamcompiler 3y ago
You can solve differential equations by integrating or by differentiating. Real-world integrators were easier to build back when DEs were solved with analog computers. Although "easier" is an understatement: Differentiators have a nasty habit of trying to blow up to infinity, which means you can't really build a good, general differentiator either with analog or digital electronics.
Integrators are much better behaved pets and they don't shit on the carpet. So everybody uses integrators. Integrators have lots of issues too but those can be sufficiently mitigated for many classes of problems. Differentiators are mostly hopeless, feral beasts.
- mnw21cam 3y agoAre you sure you got these the right way round? It seems logical that something that integrates over time should veer off towards infinity eventually, but something that differentiates should be stable.
- dreamcompiler 3y agoIntegrals are summers so they can increase without bound over time. But if the input function varies around y=0 -- as many do -- they can remain stable. Now let's talk about infinities that can happen instantly: What's the derivative at the upward edge of a square wave?