I remember the first time we jumped into the complex domain in an electronics course to calculate something that we couldn’t reach with the equations we had so far.
… and then popping out the other side with a simple (and experimentally verified) scalar, after performing some calculation in the complex domain, using, bafflingly, real world inputs.
I suddenly felt like someone from the future barged into my Plato’s cave and proceeded to perform some ritual.
Like I know what’s happening, I’ve done these calculations before, but seeing them used as an intermediate step in something real in the real world was pretty cool!
Did not prepare me for all the Laplace et al shenanigans later. Did I test well in those courses? No. Did I have the most fun building the circuits regardless? You bet.
Oh to be a student again. Why are real world jobs so boring.
All of our trains in Lebanon have been ripped out in the 60s and 70s so we can siphon our money more efficiently to the patron class by buying cars and gas through their companies. Granted cars make sense for the topography but trains should have stayed in operation, especially for freight.
Not sure how recent some of these data points are, unless it just describes the law for some of these if less data is available