Transferring without completing a specific course?

Hey everyone, so I have a couple of friends at my community college that have been accepted to some universities and will be transferring for Fall 2017. The thing is that, one of them was required to take a math and got accepted, but was told he could take his class at their school for next semester. My other friend who is a Chem major, was required to take O-chem and is also doing the same, finishing her O-chem at the campus.

How does this work? I need to take Calc now and was wondering if I could possibly do the same for my transfer? I was looking at some UC’s and Cal States. Also, if I do begin taking Calc, can I do a semester here and finish off at the campus?