I graduated with my bachelors in Electrical & Computer Engineering not too long ago but took a bunch of physics courses up to senior level Electromagnetism and y'all have my respect. My head still hurts thinking about it, but yeah -- physics is cool even though I can only handle so much physics as an engineer before I start going off like the ICP in Miracles. But hey, physicists, we can be friends!
I got to Fourier transforms in my physics education before I NOPED out of it
True story, I almost didn't make it to graduation because of a hardcore Linear System and Signals professor who gave us the craziest Fourier transform problems during exams. One of the most stressful periods of my life before one of my most miraculously clutch moments of scoring just enough to finish my degree!
To answer some of your last two questions: we had mad physics labs, but they were not as report-crazy as the engineering ones I had to do. Engineering labs get really crazy with data collection and analysis. Also, I still don't regret being an engineer, as much as I continue to respect my physicist contemporaries out in the world. ;_;7