## Notes

This is a collection of notes on various mathematical or physical (and esoteric) topics. I do not claim these to be accurate, finished, or adherent to any standards. Any additions, comments, corrections, and suggestions are welcome.

## Math reference

- Complex symmetric matrices - Spectral properties and orthogonality relations for complex symmetric matrices.
- Delta comb representation - Representation of a delta function by delta combs; essentially a derivation of the Poisson summation formula.
- FFT on non-orthogonal grids - A clarification to myself on how to apply FFTs when the basis vectors are not orthogonal.
- Trig identities - A collection of trigonometric identities.

## Physics notation

- Einstein and index notation - Some identities and reference formulas.
- Units - Unit conversions between SI and Gaussian units, as well as listing symbolic conversion factors and derived units.

## Math expositions

- Arc spline reference - A collection of representation and implementation notes on arc splines.
- Fourier transforms of polyhedra - Gives general explicit formulas for the Fourier transform of a polygon or a polyhedron given in boundary representation.
- Scattering and transfer matrices (alternative convention) - Explicit conversion formulas.
- Properties of the Redheffer star product - Explicit conversion formulas.
- Slab waveguide - A work in progress on completeness of slab waveguide modes.

## Physical expositions

- Dielectric slab - A collection of formulas for optical properties of a single dielectric slab.
- Maxwell equations - A work in progress book of electromagnetics.
- On the proper formulation of Maxwell's equations for waveguide modes - Gives a linear formulation of the waveguide eigenvalue problem which largely eliminates spurious modes.
- van Hove singularities - Derivation of the singularities for various forms of band extrema.