Filipuk G. Analysis with Mathematica, Vol 1...2019

Textbook in PDF format

A computer algebra system such as Mathematica is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica represents domains, qualifiers and limits to implement actual proofs a requirement to unlock the huge potential of
Mathematica for a variety of applications
Number systems
Recursive sequences, discrete dynamical systems and their limits
Series
Limits of functions and continuity
Differentiation
Sequences and series of functions
Integration