<p>I think that most large universities offer a Calc for Science and Engineering and a Calc for social science/business majors. I had a look at the University of Michigan Math department and they do offer a proof-based course.</p>
<p>I also had a look at the University of Vermont and they do offer a variety of calc courses but I didn’t see anything involving proofs. My offhand guess is that most universities don’t offer the proof-based courses. If you want that, you get it later courses.</p>