### "Calculus-based physics"

I dislike this whole “non-calculus physics”/”calculus physics” distinction created in schools, because it degrades mathematics to some kind of a weird tool used in physics.

Physics is just the study of the mathematical stuff we do observe — every physical system is a mathematical system on a fundamental level, which for pedagogical purposes and stuff, we often approximate with other mathematical systems (e.g. modelling stuff as rigid bodies, not considering the motion of every single particle within an extended body, neglecting gravity in particle physics, etc.). So of course you will find math being “used” in physics, because physics is mathematics!

Physics uses math in the same way that mathematics uses math — like how you “use” differentiability in defining lie groups, or how you “use” calculus and linear algebra in differential geometry, or how you “use” matrices in describing linear transformations, or whatever. Neither the physics, nor the mathematics should be classified or segregated by what mathematical methods, or “math” is used in describing or defining it.

You shouldn’t divide physics as “calculus-based” and “non-calculus” for the same reason you don’t divide it into “partial fractions-based” and “non-partial fractions”, or “elementary algebraic” and “non-elementary algebra”, or at a little higher level, “differential geometry-based” and “non-differential geometry-based”.

Use whatever tools you have to use! The point of physics is to describe what we observe — aka the universe — as efficiently and conveniently as possible, not to do elementary calculus.

There are other, more sensible ways to divide physics — experimental, theoretical and phenomenology — “mathematical physics”, which is basically physics done with as much rigor as you find in the mathematics literature, so you ensure everything you know about physics is consistent and stuff (the physics exists), you know what your underlying assumptions/axioms/postulates (that you must verify empirically) are, etc. — you could define it as “symmetry-based physics” and “non-symmetry based physics”, where the good physics is symmetry-based and the bad physics isn’t, but since Einstein, all physics is symmetry-based, so this is irrelevant today.