[tropo]

No, partial differential equations would be the fourth semester.

Calculus I is differentiation. Calculus II is integration. Calculus III is vector calculus, with stuff like curvature in 3 dimensions. Differential Equations would be the next class.

The AP test covers differentiation and, optionally, integration. It's the first semester or two. This is what a good high school student will do unless the school itself is really bad or really small.

[rmah]

I remember Calc I (1st semester) being limits, differentiation and integration. And Clac II (2nd semester) being partial differential equations. This was in the engineering school though... it may have been different for other schools in the university.

This is the original poster's point. There is no consistency. Even in university. Some schools use quarters, some semesters, some trimesters. Some have letter grades, some percentages. Some are pass/fail freshman year, but are graded in subsequent years (e.g. MIT). What makes up "Calc I" at university varies tremendously.