Well our (meaning physics students) 2 math-related subjects of the first semester are calculus and linear algebra. I've understood a lot about calculus from high school, but the curriculum there didn't include sequences or any any material from real analysis. I'll try to find and study the books you've suggested to get an idea and hopefully to answer questions that I may have.

Concerning integrations, I've had trouble finding the detailed solution of some integrals in calculus books. These integrals are:

and

What I don't understand is how the "h" gets into the solution..