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Here's how I see the relationship: Calculus helps define the underlying rules for the higher-level (simpler by appearance) math we use daily. "I know, I can solve this with calculus!" is unlikely to ever come up, but the vague idea that there's something there you can dig into when you need to can be helpful in rare edge cases, where other people might be lost. An example using programming languages: If all you've ever been exposed to was python, and no CS, you may never have considered why using "insert" on a list may be slow. Python presents it as a single function call, so you probably think of it as a single operation and don't go any further. That's the equivalent of the higher-level (simpler by appearance) math. But if you've been exposed to something lower-level, like C where you may well have implemented "insert" yourself on an array, or general CS concepts where you had to use big-O notation, you'll probably have in the back of your mind "yeah, that's not a single operation, it's doing more stuff in the background". Usually not something you need to think about, until you hit that edge case where it's suddenly running really slowly. Remember very early on in education when you had to memorize various equations like area of a circle? Those equations can be generated from basic calculus. One I could never remember was area of a sphere, until one day when I was bored at my part-time job, found a pencil and scrap of paper, and decided to see if I could use what I'd just learned in class to derive it. And it worked, and I've never forgotten that equation since, because instead of it just being a series of numbers and letters to memorize, each part now has meaning. |