Hi, I am currently in the first year of my undergraduate mathematics degree and I am taking a course in vector calculus. The course content is: line integrals, conservative field, divergence, gradient, curl, the divergence theorem, green’s formula, Stokes' them., field theory. I have seen that a lot of books are treating those subjects using differential forms. The course I am taking doesn't use differential form. When asked the lecturer about it, he also said that differential forms are the right way to deal with those subjects. My question is, should I study this course using differential forms? Is the transition from one to another approach is that hard? The course is using the book Adams and Essex(calculus, a complete course), but we can see that even the lecturer doesn't like the course book. What should I do? Thank you.