When I was in college, I was taught about AC circuits, Bode plots, Laplace transforms, and pole-zero plots on the s-plane — all to help me analyze those AC circuits.
Sadly, only the Bode plots analysis really stuck. Every now and then, I take out one of my college texts and read up on the things I should know but don't quite. Mostly, this means I try to understand pole-zero plots.
My brother, who is a mechanical engineer and therefore not as well developed as I am from an engineering perspective, sent me a document that was published by MIT. It explains the pole-zero plots and ties the plots into real-world systems. It also shows system responses to step-function stimuli. With this, I started to really understand why some systems were not stable. And I developed a real appreciation of that joke about poles on the right side of the plane.
Unfortunately, I don't use this knowledge very often, so that understanding that I had seems to seep away. Much like a foreign language that you learned back in high school, if you don't use it, you lose it.
The MIT document to which I referred can be found here. One figure that helped a lot is shown below:
Just this one figure helped me a ton. I intuitively understood the transient waveforms shown and the sort of circuitry that will produce those waveforms. Now I understood the associated s-plane graphs, too.
I am not doing as much circuit analysis now as I was 20 years ago, so again, this knowledge is slipping away. I'll need to reread the document cited above about once every six months to stay sharp.
Let me know in your comments what you wish you could understand better. And let me know what resources you've found that help explain things or help you stay sharp.