# Calculus

- Calc I
- Derivatives
- Integrals
- Multivariate
- Partial Derivatives
- Vector Calc
- Exterior Calculus
- Calculus of Variations
- Analysis
- Limits
- Hyperreals

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

# Limits

# Hyperreals

Goldblatt

Compactness is important here? Huh.