I believe the place of calc (just like trig) is overinflated in pre-real- analysis education. As far as I am concerned, sin is just a function defined a certain

I believe the place of calc (just like trig) is overinflated in pre-real- analysis education. As far as I am concerned, sin is just a function defined a certain way and I ain't worried about SOH-CAH-TOA or anything to that effect. I don't think one requires 1000 page book to learn a few core calc concepts either. Derivative is a slope. That's it. It's the same value along the length of a line. The only problem is non-linear functions where slope changes along every point. In which case we bring in the machinery of tangent/secant lines and take a limit for a very intuitive reason, but the underlying concept remains the same. This informs the definition of derivative. From this point on derivative is just a function defined a certain way and in this regard is no different from any other function like indicator function or whatever. The rest of the talk about derivatives is often just a padding and general interest. Have you ever seen a 500 page book written about the step function? When you take a bit more advanced class, the symbols for partial derivatives and integrals will be interspersed with other symbology and flash before your eyes like elements in a humongous matrix. You won't have time to think about stuff you learned from 1000+ page doorstop. You have to learn to think more nimbly and abstractly like a mathematician. To that end, check out "intro to math proofs" textbooks. If by calculus you meant modern math analysis, then simply disregard the stuff above.