Give me a good slide rule and a manual of practical mathematics, eh?

As for scavenged parts, you're going to need a warehouse of manuals and datasheets, eh?

Depending on the details of your post-apocalyptic scenario planning, simple automation driven by relays or clockwork logic will be more likely than e.g. scavenged microcontrollers.

I applaud the spirit of the project though: I don't want to live on Gilligan's Island making everything out of coconuts and vines.