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

Notes on multivariable calculus

Linear algebra
- Matrix algebra: block determinants [pdf]
Pre-calculus
- Factoring polynomials [pdf] [tex]
Calculus
- Taylor Series
- Lagrange Multipliers
- Unit ball: surface area and volume [pdf] [tex]
Rudimentary physics and numerics
- Introduction to numerical methods via traffic flow

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

Summaries for geophysical fluid dynamics
- Boussinesq, Rotation, and Vorticity [.dvi] , [.pdf] , [.ps] , on one sheet [.ps] , on one sheet [.pdf]