In our university both math and engineering students attend in the same calculus classes. There are arguments in our department about the possible influences of this approach on students. It seems based on the students' needs in their future career they need different types of calculus. For example in a calculus class for the math students, the teacher should emphasize on the abstract aspects, proofs, generalizations and the interactions with the other fields of mathematics and in a calculus class for engineering students, the applications and calculation are more important features of the course.
Question. Is there any difference in teaching calculus for the math and engineering students? Should math and engineering students attend in separated calculus classes?