tl; dr: The system is unstable as it has positive feedback loops. You can "first day of class" think of it as the implied series 1/(s-p) -- p the pole, s the Laplace variable -- exists and converges.
And in particular you want that series to converge on the imaginary axis which means it does not diverge in the frequency domain (Fourier transform). Essentially, that means that you have regions of frequencies where your system diverges/amplifies them excessively and thus breaks down: is unstable. Filters do the opposite.
P.S. The other note is that for real linear time invariant systems the region of convergence of the series/Laplace transform of the system must be positive for the system to be causal -- and thus real and implementable. So the joke could also have been modified to get a magical and unstable plane.
> You can "first day of class" think of it as the implied series 1/(s-p) -- p the pole, s the Laplace variable -- exists and converges. And in particular you want that series to converge on the imaginary axis which means it does not diverge in the frequency domain (Fourier transform)
If this was the first day of any class I took, I would have dropped it before the second day.
That makes me think of calculus in freshman's year. The first week the prof explained all maths we had learned in highschool, and then seemingly continued that same pace every week, it was rough. Especially for some of the smart kids who had never experienced learning material coming at them faster than they could take it in. The types who opened their textbook the night before the exam and would ace it in highschool got a real test of character.
That's why letting kids cruise in high school is a terrible mistake. So many school systems are uninterested in making sure everyone is challenged, especially in maths.
University is good because you'll meet lots of people who are smarter than you are.
I don't even know how kids cruised in high school and still got their diplomas.
I flunked out of high school despite getting A's and B's on all my tests because I never did my homework which was always at least 50% of our grade.
Trigonometry was so interesting to me as a 15 year old that I decided to make it my internet alias. 95+% on every test (even trig identities!), still got a C in the class, with the teacher taking me aside 1-on-1 to tell me "I'm breaking the rules to give you this C when I'm supposed to be giving you an F because you only did 2 of the 30 homework assignments."
In my highschool maths grades were always 100% based on tests.
I get the idea of motivating students to do their homework failing them when they test perfect doesn't make sense.
I like it when the homework allows the students to skip questions on the test. That way you reward the work but still let's the students catch up if they didn't do the homework.
I like what my Calculus teacher in college did. Homework was only 3% of your grade, but if you did at least 80% of the homework, then you could redo any questions you got wrong on the tests and midterm.
That's why I feel it's good to learn a bit about Laplace transform for anybody doing anything technical. It has so many applications you can hardly get away from it.
P.S. The other note is that for real linear time invariant systems the region of convergence of the series/Laplace transform of the system must be positive for the system to be causal -- and thus real and implementable. So the joke could also have been modified to get a magical and unstable plane.