In my school, to get the CS degree you only need as much calculus as needed to get to the second Physics course, which covers electromagnetism. You don't need a deep understanding of calculus. A lot of applications of calculus in the course can be handled by rote memorization.
I took extra calculus classes from the math department. Those are way harder than what you need for introductory physics.
Not op but for fwiw, in my university you only needed about as much calculus for ComSci as you would learn in IB/AP High school courses with a good prof anyway. Maybe a bit more but it was mostly a repeat.
(I recall one day in 3rd year calculus course realizing "wait a second... I don't need to be here!". I just kept signing up for calculus every year since 11th grade and suddenly realized I don't need, don't want, and don't like the class nor the prof I was in, and that was one pain less I could instill upon myself :)
As others have mentioned 'calculus' can mean one of five or six classes (I, II, III, advanced, diffyQ, probably more), basic differentiation is not hard, most of calc is some tricks a computer can learn or do better.
At least to my knowledge there is no 'theory of calculus' which allows one to solve generic integrals or differentials, calc is as much an unrelated art to comp sci as learning to play chess will help with accounting.
