So these are "quarterly" classes? How weird.
The topics you listed in Calculus 3 are a subset of what's covered in Calculus 2 at this university (and most others I'm familiar with). Those don't seem as necessary for engineering topics, but they're certainly useful.
Your Calculus 4 is a subset Calculus 3 here (semesters are ~4 months). Those are the topics that I were saying were useful/necessary to engineers.
There's a "Calculus 4" here, but I'm pretty sure it's just lovingly called that by the people that take it. I have no idea what it's really called, but I've been told that it's going into painful depth in the proofs of concepts used in Calculus.