As far as building your own analog computer, look at op amps. They're called that because they perform mathematical operations, such as summing, multiplying, and integration. Of course they do the inverse operations as well.
https://www.nutsvolts.com/magazine/article/the_perceptron_ci...
For those still tinkering with analog computers, could you recommend a setup for a beginner? Something that’d let me build real things that isn’t crazy expensive (and isn’t just a simulator). Is there something like a RPi for analog computing?
If you don't even want to hassle with all of that, then you can look into something like the Elenco electronic playground for $50 which has most of what you need mounted and then you just jumper, ala the old analog computers.
If you wanted to get really advanced, you would want to go to something like the guys at https://www.xmicrowave.com/ make, but that gets awfully spendy on a hobby budget.
The Cypress pSOC series is fairly similar (programmable analog blocks mated to a Cortex-M microcontroller core) and easier to find on sale. I'd argue that it's also more useful in modern mixed-signal designs.
