Work update [RELEASE] (15/04/2026):

Defined what kind of physical quantities can be called conserved and introduced the concepts of state space. Derived the transport equation as a consequence, and studied what it means using these definitions for the momentum, the angular momentum and the energy to be conserved. Notes are available in the classical mechanics section.

After a short section on harmonic oscillator and periodic motions, I plan to move to analytical mechanics, Euler-Lagrange and Hamilton equations. In parallel, I plan to start an appendix dedicated on dynamical systems, phase space and Liouville theorem.

Work update (30/03/2026):

Properly formalized the definition of a frame in a physics from a mathematical point of view, using the language of differential geometry and manifolds. Introduced Newton law and work as a way to define kinetic energy. Started to question what "conservation" really means and derived a mathematical definition based on chain rule for function defined over phase space. Distinguished the advection equation from the conservation equation depending on whether the considered physical quantity is intensive or extensive.

Work update (15/03/2026):

Restructured the notes on electromagnetism. The electrostatics paragraph is now created (not online yet). I have started a new section devoted to the derivation and interpretation of the energy of the electromagnetic field and the wave equation. The plan is to temporarily pause this development and first introduce the Euler–Lagrange and Hamilton equations in the Analytical Mechanics section. I will also derive the general properties of wave equations there, before returning to electromagnetism with all the necessary ingredients in place.