It varies throughout the country. But for me it was:

* Calculus I: limits, derivatives, integrals

* Calculus II: More integration techniques (substitution, by parts, table), infinite series and convergence, basic numerical methods

* Calculus III: multi-variable calculus (partial derivatives, multiple integrals), vector calculus (gradient, divergence, curl, surface and line integrals)

ODEs were a class you could take after Calc II.

Wait, is this high school or college? That looks like 3 different courses you're listing there - I've never heard of a high school offering more than a single year of calculus.

Some schools which allow students to take calculus 1 and 2 before senior year also offer multivariate calculus (3), differential equations, and linear algebra courses to round out the fourth year of math. This is especially prevalent when students can take geometry in 8th grade which leads to Algebra II, Pre-Cal, Calculus, Advanced Math Electives as the four year progression.

My public high school in TX had that track.

Is this uncommon in California schools?

(I think the idea that it's in any means required to be able to do STEM in college is ludicrous, but having the option is great.)

My public high school in WA also had this. "AP Calculus" covered Calc I and II, and once you had completed that there was a special elective called "Advanced Calculus" that covered Calc III (and prepared you for the AP Calc BC exam). In my graduating class about 30/430 ended up in this Advanced Calculus class senior year having finished AP Calculus as juniors, but many more who completed "regular" AP Calculus as seniors also ended up in STEM fields.

I took Advanced Calc and AP Stats senior year, which in retrospect was a mistake :P

> limits, derivatives, integration (Newton), maybe even some high level talk about ODEs

My son is taking high school BC Calculus (one step above "AP" calculus) this year. It includes limits, derivatives, integration (including integration by parts and partial fraction decomposition), ordinary differential equations, infinite series and taylor/mcluarin series.

> My son is taking high school BC Calculus (one step above "AP" calculus) this year.

BC Calculus is the advanced version of AP calculus, not "one step above". Ideally people are moved into AB or BC Calculus based on skill level, but only take one AP course.

Ah, you're correct - I was mixing up AP with AB. My mistake.

At my US school around the year 2000, precalc was one option for seniors, which primarily focused on limits and derivatives. The more advanced pace AP calc course also went into integrals. Beyond that I don't really recall, but by that point you also had gone through courses focusing on basic geometry, basic algebra (using variables, factoring), and a course dedicated to trigonometry (mostly memorizing the rules around figuring out angles).

There were some other courses that had math involvement, but were more business oriented (finance / accounting type stuff) and I don't recall if they counted towards core math credit requirements.

Limits, derivatives, and integrals mostly, plus many applications. There is also a heavy emphasis on computation and very little emphasis on proof.

Calculus without analysis, so the mechanical rules and recipes of real analysis of well behaved scalar functions that an engineering course might use (and that were used by the developers of Newtonian mechanics in the pre-modern era), limits on intervals, Riemann integration, etc.

Yes, they talk about the normal things average high school students learn about derivatives and integrals all over the world.