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The way calculus was discovered was via highly geometric methods that are beyond the comprehension of people today. So the historical development of calculus ne
by bmitc 4y ago
The way calculus was discovered was via highly geometric methods that are beyond the comprehension of people today. So the historical development of calculus needs to be modernized into modern notation and concepts, which at that point basically becomes examples.
While calculus is actually easy to develop and motivate, the way we "discover" it today is nowhere close to how it was originally discovered.
In my opinion, calculus is most easily motivated via physical examples. Here is a curve, it represents some information, and what are some things we'd like to know about this curve and thus the information it represents? What are some things we can do with that information? Such motivation can be more abstract and not rely on physical examples, but I think the physical examples help tie it to the so-called real world and somewhat mirrors, in spirit, how and why calculus was originally developed.