I just finished a theoretical calc3 course, the main text for the course was Spivak's Manifolds. I supplemented with Munkres, Analysis on Manifolds. The course heavily focused on the geometry of things. I' looking for a textbook for self-study, considering either Calculus of Several Variables by Serge Lang or Functions of Several Variables by Wendell H. Fleming. What's the core difference between the two and what would be the better choice?
Edit: I'm an applied mathematics student doing a lot of machine learning related courses (also what I want to do in the future). I think it's very important to understand the theoretical base behind the computational stuff (also generally love math), which is what I'm looking to learn either from Lang or Fleming. The course that I did was designated for pure math majors and was very heavily differential geometry centered, which was interesting, but it kind of grazed over the other stuff assuming that the math majors will be leaning that in real analysis