Notes

Physics and mathematics from my coursework, written out in full. I have left in the steps that took me longest, which are usually the ones a textbook skips. Corrections are welcome.

Statistical Mechanics

Where the sharp numbers of thermodynamics come from, given that nobody can measure a single microstate.

Probability Distributions Ensembles and the Meaning of Temperature The Ising Model and Phase Transitions The Partition Function Bosons and Fermions

Thermodynamics

The four laws, worked from the classical side. Nothing in here assumes atoms exist.

The Four Laws Entropy, Properly Phase Equilibrium The Thermodynamic Potentials Stability and Response Functions

Electromagnetism

Maxwell's equations, plus the boundary value problems you spend most of a course actually solving.

Electrostatics and the Laplace Equation Magnetostatics in Media Electromagnetic Waves The Multipole Expansion Potentials and Gauge Freedom

Differential Equations

Separation, Green's functions, Sturm-Liouville theory. Mostly about what the boundary conditions are quietly doing.

Separation of Variables Green's Functions Sturm–Liouville Theory Fourier Series and the Transform Series Solutions and Special Functions

Linear Algebra

Inner products, decompositions, spectral theory. This is the background the other notes assume you have.

Vector Spaces and Inner Products Eigenvalues and the Spectral Theorem Singular Value Decomposition Quadratic Forms and Definiteness The Matrix Exponential