- Calc I
- Partial Derivatives
- Vector Calc
- Exterior Calculus
- Calculus of Variations
Is there anything to even say about calculus? Probably!
Calculus vs Analysis. Basically the same thing https://en.wikipedia.org/wiki/Calculus
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
Somewhat subtle actually. What does it mean to “fix” the other coordinates?
Grad Div Curl are best understood via their definition as
Stokes theorem https://en.wikipedia.org/wiki/Stokes%27_theorem
See also differential geometry
Calculus of Variations
Functional Derivative Path Integral
Some book reccomendations:
Abbott understanding analysis Spivak Calculus Tao I and II Rudin Jay Cummings
Completeness of Reals
open-closed induction. Very interesting.
https://en.wikipedia.org/wiki/Apartness_relation apartness relatiobn
Compactness is important here? Huh.