A Little Calculus

Re:A Little Calculus by mikebenfield on Thursday May 04, 2023 @10:22PM (#35824578)

Yes, it is possible to treat d as a differential operator, and then dy and dx are the differentials of functions, and it makes sense to take their ratio. You can learn about this by reading about differential forms:

https://en.wikipedia.org/wiki/Differential_form

Unfortunately I don't know a treatment of this subject that explains how to apply this concept to basic calculus without introducing some other more difficult concepts.

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Re:A Little Calculus by JBits on Thursday May 04, 2023 @10:36PM (#35824639)

Differential forms looks really cool and I really want to learn more about them at some point!

That said, isn't calculus, mainly the chain rule, enough to tell you what operations are allowed?

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Re:A Little Calculus by mikebenfield on Thursday May 04, 2023 @11:09PM (#35824782)

I definitely didn't understand how to use differentials just by learning calculus, but maybe it is possible.

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Re:A Little Calculus by lupire on Thursday May 04, 2023 @11:11PM (#35824804)

For single variable calculus (y=f(x)), yes.

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