**Up**
# E. Alec Johnson: Notes on Math, Physics, and Numerical methods

### Pedagogy: introductions, examples, and review

- Linear algebra
- Matrix algebra: block determinants
[pdf]

- Pre-calculus
- Calculus
- Rudimentary physics and numerics

### Summaries

- Basic numerics
- Fundamental Theorem of Numerical Analysis (Lax equivalence theorem):
ftna.pdf ,
ftna.tex
- LeVeque finite-volume shock-capturing wave-propagation
[.pdf]
- Discontinuous Galerkin framework
[.pdf]
- Consistency of discontinuous Galerkin method
[.pdf],
quadrature rules

- Basic physics
- Derivation of the fundamental laws of physics
- (part A) Classical physics
[.pdf]
- (part B) Relativity
- (part 1) Axiomatic deduction of the relativistic metric
[.pdf]
- (part 2) Special relativity derived from classical electrodynamics
[.pdf]
- (part 3) The relativistic Vlasov equation [incomplete]
[.pdf]

- Units
- Translation between H-L, cgs, and mks units for Maxwell's equations
[.pdf]
- Nondimensionalization of classical electrodynamics
[.pdf]

- Basic gas-dynamics
- Equilibrium thermodynamics for an ideal gas
[.pdf]
- A terse derivation of Navier-Stokes and Euler gas dynamics
[.pdf]
- Mathematical entropy and symmetric hyperbolic form
[.pdf]
- Convexity of mathematical entropy for gas-dynamics and two-fluid plasma
[.pdf]
- The Legendre transform
[.txt]

- Handwritten summaries (applied calculus and basic physics)
- Handwritten analysis summaries

### Coursework-related summaries

- Summaries for geophysical fluid dynamics