Is there anything to even say about calculus? Probably!

Calculus vs Analysis. Basically the same thing https://en.wikipedia.org/wiki/Calculus

Calc I

Stewart Book

Derivatives

Tangents and Secants

When do derivatives exists Continuity Moduli of continuity https://en.wikipedia.org/wiki/Lipschitz_continuity

Product Rule Chain Rule

Sequences Series Convergence Tests

Mean Value Theorem

Taylor Series

Infinitesimals

Integrals

Multivariate

Partial Derivatives

Somewhat subtle actually. What does it mean to “fix” the other coordinates?

Vector Calc

Grad Div Curl are best understood via their definition as

Line integrals

Stokes theorem https://en.wikipedia.org/wiki/Stokes%27_theorem

Exterior Calculus

See also differential geometry

Calculus of Variations

Functional Derivative Path Integral

Analysis

Some book reccomendations:

Abbott understanding analysis Spivak Calculus Tao I and II Rudin Jay Cummings

Completeness of Reals

Bolzano Weierstrauss

open-closed induction. Very interesting.

Constructive Analysis

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

https://en.wikipedia.org/wiki/Apartness_relation apartness relatiobn

Bishop

Marshal

Computable Analysis

Limits

Hyperreals

Goldblatt

Compactness is important here? Huh.