> Financial models, physics models, biology models commonly use them.
In what specific everyday situations would most people find these useful? It's not like it's common for people run into situations where they say "if only I could calculate the predator prey systems" or "if only I could calculate radioactive decay." I've studied these, and I don't think I've ever run into some everyday situation where I've said "Man, I'm really glad I can apply my differential equations/vector calculus/etc. here." Even in the rare situation where I want to calculate compound interest I opt to just use a interest calculator since it's quicker and less error prone than doing it by hand.
Can you give an example? I can't think of any everyday situation that most people would run into where calculus comes in handy. It's definitely necessary for certain specific applications, but not ones I'd call everyday situations.
Someone who's studying these as a hobby is likely going to run into more uses for Mandarin in their day to day life than, say, Calculus. You're more likely going to run into a situation where you're saying "I wish I could talk to that person" or "I wish I knew what that said" than you are going to run into a situation where you go "I wish I could calculate the second derivative of that formula." And though I doubt self-studying either of those is going to boost your career much, self-studying Mandarin is probably going to be more beneficial (it makes sense to stick "I speak Mandarin" on more resumes than "I know calculus").
In the end, though, you're best off either studying something to reach a specific goal (learning the math that engineers need in order to become an engineer) or studying something that interests you.
In what specific everyday situations would most people find these useful? It's not like it's common for people run into situations where they say "if only I could calculate the predator prey systems" or "if only I could calculate radioactive decay." I've studied these, and I don't think I've ever run into some everyday situation where I've said "Man, I'm really glad I can apply my differential equations/vector calculus/etc. here." Even in the rare situation where I want to calculate compound interest I opt to just use a interest calculator since it's quicker and less error prone than doing it by hand.