Failure at the entrance to university is a major social issue, particularly for science majors, whose graduation rates in Licence are lower than average. This phenomenon is multi-causal, and we study only a facet of it: the difficulties faced by science (but non-math) majors in mathematics. Research in this field has already identified that the mathematics used in the first-year physics courses at university differ from those encountered by students in mathematics courses and may cause issues for students. We take this observation as a starting point and show how to characterize the gaps between mathematics in mathematics courses and mathematics in mechanics courses. This allows us to better understand potential and effective difficulties faced by first-year physics majors.