Circuit theory becomes much more elegant if you start to use complex numbers (conceptually, the Laplace transform [1]). But for an introductory lesson, this page seems nice, though perhaps a bit long.
But only if you use linear components (meaning L,C,R). Introduce just one diode and the system of diff equations needs to be solved numerically. In which case you have switch to simulations like spice anyways. Therefore there is no reason to even bother with Laplace transforms nowadays. For hobbyists (and the vast majority of professionals) I would consider it completely useless knowledge.
> Introduce just one diode and the system of diff equations needs to be solved numerically
Not really. Maybe that's why nobody invented anything with a diode in the signal path before computers were commonplace right? Like radio and guitar distortion pedals
> Therefore there is no reason to even bother with Laplace transforms nowadays
Sure, let's forget the math and make engineers totally dependent on numerical simulation without knowing the basics, I'm sure that'll work just fine
> For hobbyists (and the vast majority of professionals) I would consider it completely useless knowledge.
LOL
Sure, in the same way that sorting algorithms don't are useless for computer science students, right? Just call .sort() and you're done!
Also don't forget Digital Signal Processing, that also relies on that "useless knowledge"
> Not really. Maybe that's why nobody invented anything with a diode in the signal path before computers were commonplace right? Like radio and guitar distortion pedals
No, those problems were solved via ultra simplified models. E.g. The current through a diode is described as I = I_0 \Theta(U - 0.7 V). And the rest was done via try and error.
> Sure, let's forget the math and make engineers totally dependent on numerical simulation without knowing the basics, I'm sure that'll work just fine
How about, lets learn how to solve every differential equation you will ever come across in electronics using e.g. Runge-Kutta.
> Just call .sort() and you're done!
If you want to get shit done you do exactly that. This is a great problem of many fresh CS graduates. Instead of doing the actual work they would rather first implement their own sort function. In 99.9% of the cases it is a complete waste of time.
> Also don't forget Digital Signal Processing, that also relies on that "useless knowledge"
In Digital Signal Processing you mainly need to Fourier transform and know the properties of the sin(x)/x function, Nyquist, Shannon etc... Learning how to solve a very special case of systems of differential equations using the Laplace transform won't help you there at all.
>Instead of doing the actual work they would rather first implement their own sort function.
Strawman much. On the otherhand I regularly come across people who call library functions without understanding their runtime consequences, well those are the good ones, the bad ones 'get shit done" by calling sort just to find the maximum. Yeah they do get exactly that done, that is, shit.
[1] https://en.wikibooks.org/wiki/Circuit_Theory/Laplace_Transfo...
(If you grasp this reference, then you understand, I'd say, about 25% of what electrical engineering is about)