The discussion centers on recommendations for rigorous textbooks for a Calculus 2 course in Brazil, which includes Ordinary Differential Equations and multi-variable differential calculus. Participants suggest checking the specific textbook used in the course first. For self-study, the Schaum's Outline series is mentioned as a good resource due to its affordability and numerous examples, though not considered rigorous. Other recommended texts include "Vector Calculus" by Marsden and Tromba for its depth, and Apostol's second volume of Calculus for its rigor. The conversation also touches on the suitability of rigorous texts like Spivak's "Calculus on Manifolds" and Munkres' "Analysis on Manifolds," questioning if such rigor is necessary for a first course. Additionally, Serge Lang's "Analysis I" is highlighted as a valuable resource.
