Intuition
The most fundamental science: Physics describes the rules of the universe, from the smallest particles to the largest structures. It is the science of “why things work” at the deepest level, and it provides the foundation for all other sciences and engineering.
Why it matters: Physics underpins all technology, understanding mechanics lets you build bridges, understanding electromagnetism lets you build computers, and understanding quantum mechanics lets you build lasers and semiconductors.
The key insight: Physics progresses by finding unifications, the more phenomena a single theory explains, the deeper our understanding. This drive for unification is what makes physics the most elegant of the sciences.
Why This Matters
Physics is the most fundamental natural science, it seeks to explain the behaviour of matter and energy through mathematical laws. These notes provide rigorous, derivation-based coverage of undergraduate physics, building from classical mechanics through quantum theory. Understanding these concepts is essential for careers in physics, engineering, and related fields. Physics trains you to think precisely about the natural world, to model complex systems with mathematical equations, and to test theories against experimental evidence.
What You Will Find
- Classical Mechanics: Newton’s laws, Lagrangian and Hamiltonian mechanics, oscillations, and central forces. Classical mechanics describes all macroscopic motion through energy and momentum conservation. It is the foundation for engineering, astrophysics, and biomechanics.
- Electromagnetism: Electrostatics, magnetostatics, Maxwell’s equations, and electromagnetic radiation. Electromagnetism unifies electricity, magnetism, and light into a single force. It is the foundation for electronics, telecommunications, and optics.
- Quantum Mechanics: Wave functions, operators, angular momentum, perturbation theory, and entanglement. Quantum mechanics governs physics at atomic and subatomic scales. It explains the periodic table, chemical bonding, and semiconductor behaviour.
- Thermal Physics: Thermodynamics, statistical mechanics, and kinetic theory. Thermal physics connects microscopic particle behaviour to macroscopic observables like temperature and pressure. It explains phase transitions, heat engines, and the behaviour of gases.
- Optics: Wave optics, interference, diffraction, and polarisation. Optics describes how light propagates and interacts with matter. Applications include lasers, holography, optical fibres, and imaging systems.
Tracks and prerequisites
The tracks are ordered by dependency, not by interest. Classical mechanics needs calculus; electromagnetism needs vector calculus; thermal physics needs the first law and linear algebra; quantum mechanics needs all of the above.
| Track | Needs first | Start here |
|---|---|---|
| Classical Mechanics | Calculus, vectors | Newtonian Mechanics Review |
| Electromagnetism | Vector calculus | Electromagnetism |
| Optics and Waves | Oscillations, some EM | Optics and Waves |
| Thermal Physics | Mechanics, linear algebra | Thermodynamics and Statistical Mechanics |
| Quantum Mechanics | Mechanics, EM, linear algebra | Postulates of Quantum Mechanics |
| Solid State Physics | Quantum mechanics, EM | Solid State Physics |
| Particle Physics and Cosmology | Quantum mechanics, relativity | Particle Physics and Cosmology |
Beyond the degree. Symplectic Structure and KAM Theory is the research tier: it assumes the Lagrangian and Hamiltonian material and continues into integrable systems, the KAM theorem, Arnold diffusion and the open question of whether the solar system is actually stable. The wider research tier lives on the mathematics site: spectral theory, stochastic calculus and SPDEs, representation theory, Ricci flow, and posterior asymptotics.
Cross-References
- Introduction: Start here for an overview of the notes and how to navigate them.
- Study Hub: The full table of contents, prerequisite map and the rigour ladder.
- Classical Mechanics: Newtonian mechanics and conservation laws form the foundation of physics.
- Quantum Mechanics: Wave functions and operators describe physics at atomic scales.
- How to Use These Notes: The method these pages are built on.
Common Mistakes
Confusing units across physical domains: Mixing CGS and SI units (e.g., Gauss vs Tesla for magnetic fields) gives wrong numerical answers. Always convert to a consistent unit system.
Forgetting that physics equations are only valid in certain regimes: Newtonian mechanics fails at relativistic speeds; classical electromagnetism fails at quantum scales. Check assumptions before applying formulas.
Neglecting dimensional analysis: Every valid physics equation must be dimensionally consistent. If units don’t balance, the equation is wrong or misapplied.
How to Study Physics
Physics is not read, it is practised. The order that works:
- Read the derivation, not the result. Every page here derives what it states. If you skip to the formula you are learning the formula’s history rather than its reason, and you will not be able to rederive it when the problem is unfamiliar.
- Check units before you check answers. Dimensional analysis catches most errors in seconds and costs nothing. If the units do not balance, stop.
- Do the worked examples with the solution covered. The point is to find where you stall, not to confirm that you can follow along.
- Use the recall prompts. Each flagship page opens with questions to answer from memory before reading. Retrieval practice is stronger than re-reading, and the failure to recall is the signal that you should read that section rather than skim it.
- Come back at increasing intervals. Spacing is what converts reading into knowledge.
The mistakes section above is drawn from what students actually get wrong, and is worth reading once before starting a track.