WaveLab: Explore, Derive and Simulate Waves and Optics
An interactive computational textbook and virtual laboratory for university-level waves, oscillations and optics — built to take you from zero to exam-ready, at the depth of a good book, with everything a computer adds: live simulations, laboratories, quizzes, exams and demonstration videos.
Everything in this course revolves around one idea:
A vibrating string, a resonant cavity, a diffraction pattern and a quantum wavefunction are one mathematical structure wearing four costumes. Learn to think in waves once, and you have learned them all.
How to study here¶
Every module follows the same climb:
Opening — a physical puzzle you can feel, and a prediction you commit to before any equation.
Core — an interactive laboratory, the precise derivation, and a computational check. This is the exam-relevant spine.
Consolidation — transfer to new contexts, worked examples, quizzes and exam-style problems.
Advanced — clearly marked deeper material. Skip it freely on a first pass; nothing later depends on it.
The course map¶
The full course runs from oscillations through waves to optics and photonics: mathematical foundations, oscillations, coupled oscillators and normal modes, the wave equation, Fourier methods and dispersion, electromagnetic waves, interfaces, polarization, interference, diffraction, geometrical optics, Fourier optics, and Gaussian beams, lasers and waveguides.
Currently available:
Phasors: the language of waves — why adding two sounds can produce silence, and the one complex-number idea the whole course runs on. Start here.
The simple harmonic oscillator — the single curve that clocks, molecules and circuits all follow, and why its period ignores its amplitude.
Damping, resonance, and the quality factor — why one sustained note shatters a glass and its neighbours do nothing, and where the response really peaks (not where almost every textbook says).
Fourier series — where a 100 Hz square wave keeps its 300 Hz, why a violin and a flute playing one note sound nothing alike, and the 9% overshoot that no number of terms removes.
The Fourier transform and convolution — what frequency a hand-clap is, why nothing can be both brief and pure, and the two ways sampled data lies to you.
One reference page sits outside the sequence and is meant to be returned to: conventions.