(October 7, 2022 at 8:40 pm)Fireball Wrote: A linear algebra class offered by the math department seems to be one of those classes few physics majors take. Not sure why. It's a great intro to proofs. My alma mater also offered a class that used Dennis Sentilles' book for a class that focused primarily on how to "do" proofs. I got a tiny bit of series solutions and Fourier Transforms at the very end of my DE class. I went to work in electromagnetic propagation topics right out of uni. I didn't get enough of what I needed at uni. Antenna radiation propagation and scattering is full of it. I got out of the antenna business 22 years ago, and don't remember much. I remember even less about quantum mechanics, which I never used.
Math classes don't emphasize Fourier series and transforms nearly enough. The difficulty is that the main results are not so easy to prove and there are a LOT of subtleties quite close to even undergraduate courses.
For example, take a continuous periodic function and look at its Fourier series. Does that series actually converge to the original function?
The answer is complicated. In general, the series does NOT have to converge everywhere, let alone converge to the function. But it *does* converge 'almost everywhere' to the function. But this is very difficult to prove and is usually not even done in graduate classes unless it is specifically for those going into harmonic analysis.
Even the partial results mentioned in undergraduate classes are usually not proved in those classes. The proofs are MUCH deeper than can be done effectively at the undergraduate level.
Even a good treatment of the dirac delta 'function' usually waits until graduate level measure theory.
