Work update (30/04/2026):
Finished the harmonic oscillator section and added it to the corresponding pdf in classical mechanics on the website. Derived
the wave equation from the chain of springs in the continuum limit (will be available in the continuum mechanics pdf soon). Started
to introduce Euler Lagrange equation. Changed the note global structure: appendices are now only for long derivation in the notes. Started
new "mathematical tools" and "examples" sections.
After a writing down the principle of least action and Hamilton equation, I'm planning to work on phase space, Liouville theorem, chaos theory and
Fourier transforms in mathematical tools. Then write illustrative examples for those concepts.
Welcome
Physics Compiled is a long-term personal project: a structured attempt to understand how mathematical structures emerge from — and constrain — experimental reality.
These notes are neither popular science nor a conventional textbook. They aim to pedagogically present complex physics through equations. The three general rules I follow when writing them down is:
- Pedagogy — explain concepts with clarity, especially by connecting them to facts
- Mathematical meaning — presenting the equation, without getting too far in pure mathematics (or in appendices)
- Independency — each section must be readable on its own, but can reference others.
The guiding questions are simple:
- Why was a model introduced?
- What experiments forced this structure upon us?
- Could we have made different assumptions?
The objective is ambitious: to cover most major domains of physics — from classical mechanics to quantum fields — in a unified narrative written in my own words. It comes from my desire of understanding mathematically every phenomenon that I'm looking at. In physics, equations are a language.
This is a living document. Criticism, discussion, and collaboration are warmly welcome. Feel free to create issues the github repository or directly contact me at
A dynamical system. Taken from this article
