I'm teaching for a small group of future undergraduate science students. I'm from Brazil, so here, we don't see any calculus in school, Just definition of function and some properties of most known functions of a real variable, everything very simplified.
I) I want to reintroduce this functions in a way that it will be more useful for a future calculus course at university. (Pre Calculus or first chapter of calculus books).
II) I want to teach the concepts of limits, and derivatives with some formal approach.(Because they will study sciences). I want to give some interesting applications of functions, limits and derivatives(Because they are not going to a pure math course).
What I need It's a list (1,2 or 3) of books that fits in:
1)Mathematically strong calculus books, with some good pre calculus on it: (Write your list 1, 2 or 3 books).
2)Book of calculus that has some good applications in physics/economics: (Write another list 1,2 or 3 books ).
OBS: I don't know english language calculus books, so I don't even can compare this books.