I found a book that will be my first contact, however I do not know if it covers the introductory topics. I would like to know if it is enough for a first contact. Its topics are:
- Ordered fields and Dedekind's postulate; Real number sequences; Bolzano-Weierstrass theorem and Cauchy sequences; Initial notions about numerical series; Criteria for convergence of series; Limits of functions; Continuous functions; Maxima and minima and the intermediate value theorem; The derivative; The mean value theorem and applications; L'Hospital's rules; Polynomial approximation; Power series: elementary notions; Riemann's integral: initial notions; The fundamental theorem of calculus; Logarithmic and exponential functions.
And I thought about studying one of the following books after the book with the mentioned topics. I'm torn between Apostol, Carothers and Roselicht (I think Rudin is too much for me). Which one would complement the previous topics well? I want to have a solid foundation to get to analysis at the graduate level (Measure Theory and, finally, Functional Analysis).