Book Recommendation: Series and Sequences of Functions

Question

I would like recommendations on calculus books that explain series and sequences of functions that clearly cover:

• pointwise convergence
• uniformly convergence
• uniformly convergence in compact sets
• normal convergence for series of functions
• the implications of those convergences (e.g. the limit of the integral of a sequence/series of functions is the integral of its limit, and the same for derivatives)
• Abel's criterion
• power series of functions

For reference, I am a second year undergrad maths student

Answer 1

From your reference to "normal convergence" I suspect you're learning mathematics in French.

You ought to find most of what you need in Chapters 1 to 3 of Volume 4 of Cours de mathématiques spéciales by Ramis.