I am terribly confused as to why you are call referring to "Calc II" and "Calc III" as if you all went to the same university :-/
Me too, but that's probably due to all the US students here, who for some reason seem to have a lot of identical courses all over the country.
It confused me at the beginning too. I actually go to a US school, but my school is on quarter system. At my school, it's more like I - Differential Calculus, II - Integral Calculus, and
III - Sequence and Series (with a few additional topics), and multivariable calculus was a two-quarter sequence, calling them multivariable calculus I and II. But I guess most of the schools use semester system, so I had to figure these out on my own.
I know, and that's what's sad. We spent almost all semester "parameterizing" curves again and again and again and then spent the last week on the important culminating theorems. I don't know them at all, neither does anyone else in that class, which is why I can't even read Maxwell's Equations in their differential forms with grads and curls and stuff.
The experience with me in multivariable calculus was kind of similar--although we certainly did spent more than a week to cover those materials! I felt like multivariable calculus was just a bunch of long and tedious computations until we got to the vector analysis chapter at the end, even though I felt like we should have spent more time on those stuff. The textbook I used for that course (Stewart) wasn't necessary great at that chapter--I felt like he just squeezed every detail of vector analysis into just one chapter so that he can save some pages. Fortunately, I had a pretty good instructor who went into more details than what the book covered.