Lecture Timeline · PHY621
Mathematical Methods in Physics I, in teaching order (semester 1, one 3-hour lecture per week). Lecture 0 marks the vector-calculus review inherited from the older PC604 version of the course.
| Lecture | Topics | Wiki pages |
|---|---|---|
| Lec 0 (review) | Coordinate systems, vector algebra, div/grad/curl, integral theorems | Coordinate systems · Vector operations · Triple products · Grad, div, curl · Divergence theorem · Stokes' theorem · Vector operators (eq.) |
| Lec 1 | Vector spaces, matrices, determinants, orthogonal transformations | Matrices & determinants · Orthogonal transformations |
| Lec 2 | Eigenspaces: eigenvalues, diagonalization, Hermitian matrices | Eigenvalues & eigenvectors · Diagonalization · Hermitian matrices · Characteristic equation (eq.) |
| Lec 3 | Integral transforms I: Fourier series and Fourier transform | Fourier series · Fourier transform · Fourier integral (eq.) · Fourier series builder |
| Lec 4 | Integral transforms II: Laplace transform, convolution | Laplace transform · Convolution · Laplace integral (eq.) |
| Lec 5 | Ordinary differential equations, special functions | ODEs · Special functions |
| Lec 6 | Partial differential equations: separation of variables | PDEs |
| Lec 7 | Green's functions | Green's functions · Green's function for ODEs (eq.) |
The spine of the course
Everything converges on solving physics PDEs: linear algebra supplies the eigenmode language, transforms diagonalize derivatives, and Green's functions assemble the general solution from point sources. PHY622 continues with calculus of variations, complex analysis and group theory.