I use the book by McQuarrie
as basic reference, and plenty
of additional material as discussed in the videos.
SW = the more basic ones are in Swedish only, happy to add closed captioning if
needed (started in video 4b due to request).
0. General intro (SW)
1. Little intro to ODEs (SW)
2. Series ansatz for ODEs, Frobenius method (SW)
3a. From physics to PDEs to ODEs (SW). (Example: Laplace equation)
3b. Orthogonal polynomials part 1: Legendre (SW)
4a. Special functions part 1, e.g. Bessel (SW)
4b. Classification of PDEs (SW)
5. Fourier series and transforms (SW).
6. Sample solutions for wave, heat and quantum (SW).
7a. Ortogonal polynomials part 2: Sturm-Liouville-theory
7b. Green's functions and integral equations
8. Special functions part 2: hypergeometric ("Geometry and ODEs")
9. Qualitative discussion of differential equations
("Dynamical systems").
10. Differential forms and cohomology.
11. Riemann surfaces.