Physics
Mechanics
Classical Mechanics
Fictitious forces, ballistic pendulum, Poisson’s equation, Kepler’s problem, inertia tensor — 60 pages: Classical_mechanics.pdf
Analytical Mechanics
The principle of virtual work is based on the study of pulley systems. Lagrangian mechanics is an application of generalised coordinates to the principle of virtual work extended to dynamics — 307 pages: Mecanique_analytique.pdf
Thermodynamics
Entropy
By studying the Carnot cycle and the associated thermodynamic temperature scale, Clausius discovers a new state function he calls entropy — 36 pages: Thermodynamics.pdf
Statistical Thermodynamics
Derivation of thermodynamic probabilities in classical Maxwell–Boltzmann statistics and in the quantum statistics of Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac — 54 pages: Statistical_thermodynamics.pdf
Quantum Mechanics
Schrödinger Equation
The Schrödinger equation is the quantum counterpart of the fundamental relation of dynamics. It can be derived from the conservation of mechanical energy and the Planck–Einstein relations — 14 pages: Schrodinger_equation.pdf
Celestial Mechanics
Equation of time
Explanation of the origin of the variation of the true solar day — 11 pages: Equation_of_time.pdf
Length of Day and Night
Calculation of the length of day and night depending on the date and latitude — 4 pages: Length_of_day_and_night.pdf
Relativity
Special Relativity
The Lorentz–Poincaré transformations — 39 pages: Lorentz_transformations.pdf
Special and General Relativity
Special and general relativity — 622 pages: Relativité_restreinte_et_generale.pdf