Mathematical Analysis I By Claudio Canuto And Anita Tabacco -

This final chapter covers convergence tests (comparison, ratio, root, integral test) and improper integrals. The highlight is the treatment of for series, including a proof of the Riemann rearrangement theorem (a mind-bending result that conditionally convergent series can be rearranged to converge to any real number).

: Covered in Chapters 9 and 10, including techniques for computing primitives and definite integrals. mathematical analysis i by claudio canuto and anita tabacco

Buy the physical copy. Keep a notebook dedicated solely to rewriting its proofs. By the end of the book, you will no longer be a calculus student; you will be a nascent analyst. you will be a nascent analyst.