That's a great list. The only thing that's missing would be a linear algebra course. The OP mentions it in passing, but a good understanding of LA goes a long way. I did UGRAD in engineering, and when I switched to physics everything was over my head, but my knowledge of LA still managed to keep me afloat. Also, matrix quantum mechanics is essentially straight up linear algebra (vectors, unitaries, projections, etc.)
Now switching to a shameless plug mode, I'll mention my math+mech+calc book, which would be a good addition to the section 1. Introduction to Mechanics. Chapter2 of the book (on topic) is part of the preview: https://minireference.com/static/excerpts/noBSguide_v5_previ...
Thanks for plugging your book. Math has always been a struggle for me and considering I got my ass kicked through undergrad barely passing my math courses, I constantly I'd enjoy math as a programmer if I had just had the proper schooling in highschool.
I was always amazed that more physics curricula do not require linear algebra. You don't even need to get to quantum for LA to be amazingly helpful. Our classical mechanics text from undergrad was swarming with LA...
I was amazed that my EE degree didn't required it. We had a rushed treatment as part of a required ODEs course, but I didn't really get it until I took a theory heavy course dedicated to the subject. It and probability both made my life a lot easier and are essential parts of my daily work.
I'll second that Lay was the textbook I used throughout my Engineering Degree. It is sitting on my shelf at work right between "The C++ Programming Language" and "Numerical Recipes"
Now switching to a shameless plug mode, I'll mention my math+mech+calc book, which would be a good addition to the section 1. Introduction to Mechanics. Chapter2 of the book (on topic) is part of the preview: https://minireference.com/static/excerpts/noBSguide_v5_previ...