I first learned calculus in AP Physics with a similar approach, it was great! I did take a more "traditionally" taught sequence of calculus courses my first year of college. My college physics professors often prefaced math explanations with an apology to math majors in the room.
“If this equation’s abuse of numbers offends you, the Math Department is over there and his happy to help you with your change of major paperwork.” I know two people who did just that after the crimes against math we did Mathematical Methods of Physics A & B.
My professors were far more polite, but perhaps that was because the department had a shortage of physics majors.
Mathematical Methods of Physics is, by percentage, the second most failed class in universities after O-Chem. It is a stripped down and jury rigged jumble of a math degree that's "good enough" to get a physics major through to grad school. It is otherwise offensive to math.
The problem with physics is that its models, when properly grounded, are dependent on grad level concepts in differential geometry, which is far too complex and specialized to give to undergrads, so instead there's a bunch of dubiously reliable implicit heuristics used to achieve the same results.
It was one of my firm Bs in undergrad that confirmed I was right to be looking at a major hop for my master's degree, lol. Weirdly my best grades were in Classical Mechanics and StatMech, where I was top of the class in my year. But quantum, classical electromagnetism, and mathematical methods? Bs.
(on Canadian uni grade scales, not US)
I got Bs for Math Methods and was very proud. It left me with some enduring grudges toward some mathematical concepts, like the B-word Function. My most solid As we’re fluid dynamics and quantum mechanics, I just didn’t like QM. I can’t tell you how I passed E&M but I did.
I had to take an engineering course for Fluid Mech and I don't know how I got an A in that course but I somehow did. It was... not well orgnaised. I basically retaught myself it later. E&M I got a B+ in and I think it was the proudest I've ever been of a B+. But it was a *struggle*.
What engineering discipline has fluid mechanics courses for undergrads? As far as I can tell, physics departments usually don't even bother trying to teach fluid mechanics to undergrads?
Environmental engineering. It was mostly like, channelised flows and constricted pipe stuff. It was very high level, generalisable stuff. Civ Eng usually has the same sort of material for calculating basic flood tolerances etc.
Organic chemistry and any kind of statistics at all are the classes I most often regret not taking in college.
👀 Neither of the colleges I went to had that class, they did a combination of teaching relevant math in physics courses and requiring math courses as pre-reqs for physics courses, which is how I ended up with a minor in math.
I did really wish there was a physics-specific differential equations course, something I'm pretty sure the math professors also wished for (along with major-specific courses for other majors that required diff eq and not taught by math faculty).
Differential Equations I: the single worst passing grade I have ever received in a course in my life. Differential Equations II, where they actually taught applications and use cases rather than Pure Theory: I got an A-. Physics departments should not outsource this to math departments.
I barely passed calculus I by rote memorization. Then the next semester I took physics I (calc was a prerequisite) and within the first two weeks I retroactively understood everything I hadn't gotten from calc.
Yes. I got yelled at for using physics rather than math in ODE. Look, if you give me a projectile motion problem I know how to do that in three lines.
We had differential equations as a prerequisite for an engineering class they called System Dynamics. We walk in and sit down the first day, "Hey so you know that whole course you all took last semester? Yeah nobody actually does that. Let me tell you about the Laplace transform."
The problem is that physics majors aren't the only people who have to take differential equations, you also have chemistry majors, potentially some econ and biology majors, and various engineering majors if you're somewhere with engineering programs.
this was a small regional undergrad uni and the class was 30% physics, 60% engineers, 10% math majors. it was tailored only to the last. phys and eng probably would have gotten along fine with a course tailored to either.
I took it twice in order to pass it. The second time I had a professor who tried to include applications but was unfamiliar with common conventions in physics including what units are used, so it was confusing and frustrating for everyone. I think the chemistry majors would have said the same.
a huge part of it was just that the textbook they used for DE II was better and explained things without bogging down in abstract theory. at the end of the course the entire cohort went "you should use this book for both classes" and the prof implemented it because the class GPA was *28% higher*.