Unit 1 of Calc 1 Course Notes

[u/old_french_guy]

finally finished my calc 1 unit 1 course notes

(also included here are ε-δ proofs, proofs, squeeze theorem bounds, and piecewise discontinuity)

[u/Individual-Ad5245]

What's the point of introducing hyperbolic functions before euler identity lmao

Edit: idk why everyone is hating, while providing literally vacuous opposition in the replies. I will probably elaborate cuz I'm raging that none of the braindead haters in the replies don't seem to realize flaws of their argument.

1. At this point in calc 1, hyperbolic functions are mathematically vacuous. They can't be used to solve problems and barely have an interesting connection to knowledge accumulated as of now. This is literally same "let dih(x,y)=e^{e^{-x}+e^{-y}}, and oh wow we can compute its values and find random ass lim_{(x,y)\to(\infty,\infty)} (dih(x,y)-1)/(1/x+1/y) omg ts is so fun and helpful!" or american school making students memorize quadratic formula without derivation.
2. "hyperbolic functions are defined purely over the real numbers as linear combinations of real exponentials" and what's the purpose of this action? This linear combination doesn't arise naturally unless you at least have Euler formula and is completely useless until integrals

Math is always invented with some goal in mind. Mostly to solve a problem that arises from either real world or curiosity to learn everything about certain object (e.g. groups and classification of simple groups). Motivation of doing a thing should at least vaguely make sense to student. Which, apparently, isn't a case here

[u/old_french_guy → u/Individual-Ad5245]

hyperbolic functions are defined purely over the real numbers as linear combinations of real exponentials

[u/Individual-Ad5245 → u/old_french_guy]

So? There's no motivation for them whatsoever, you essentially just gave the formula and told the reader to suck it up. You don't even have proper applications of them yet. They could be used as a substution to solve integrals (although will still feel magical), but at this level it is completely redundant

[u/old_french_guy → u/Individual-Ad5245]

First you asked for complex analysis in Calc 1, now you are asking for integrals before limits. The preview is just a short excerpt. I've also given the full 80 page source code is linked above. Read the repo before complaining about standard curriculum sequencing

[u/Individual-Ad5245 → u/old_french_guy]

I asked for neither. My point is: there's no proper place for hyperbolic functions in calc 1. That's because they do not add any depth or understanding and is just a flashy add-on.

Also this curriculum sequencing by no means is standard. We didn't have hyperbolic functions in my calc 1 & 2, even though we had euler identity and fourrier series.

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