PHY621 · Mathematical Methods in Physics I

A knowledge wiki for PHY621 — Thammasat University graduate course, semester 1. The working mathematics of a physicist: linear algebra, transforms, and the differential equations they conquer.

The course in one paragraph

Physics problems keep asking the same mathematical questions. What are the natural modes? — eigenvalues and eigenvectors, with Hermitian operators guaranteeing real, measurable answers. How do I unravel derivatives? — Fourier and Laplace transforms, which turn calculus into algebra (and multiplication into convolution). How do I solve the equations of physics? — ODEs with their special functions, PDEs by separation, and the master key: Green's functions, which build any response from the response to a single kick.

Start here

• Lecture timeline — teaching order, review Lec 0 → Green's functions
• Concept graph — the dependency map
• Fourier series builder — watch harmonics assemble a square wave
• Normal modes lab — a real eigenvalue solver on coupled oscillators
• Worked examples — Green's functions and separation of variables, checked both ways
• Quizzes · Glossary

Where this mathematics gets used

The eigenmode language powers quantum mechanics; transforms power every signal and wave problem; Green's functions reappear in electrodynamics and field theory. In this wiki family: FDTD and Poisson solvers are these methods gone numerical, and PHY622 continues with variations, complex analysis and groups.