Discussion Overview
The discussion revolves around recommendations for mathematically rigorous textbooks suitable for a Calculus 2 course that includes Ordinary Differential Equations and multi-variable differential calculus, particularly in the context of a Brazilian university curriculum.
Discussion Character
- Exploratory, Technical explanation, Debate/contested
Main Points Raised
- One participant seeks recommendations for challenging and rigorous Calculus 2 textbooks.
- Another suggests checking the specific textbook used in the course before selecting additional resources.
- A participant mentions that while Marsden and Tromba's Vector Calculus is not rigorous by mathematical standards, it offers more substance than typical introductory multi-variable calculus books.
- Another recommendation is Apostol's Calculus, specifically its second volume.
- A participant questions whether a rigorous approach is suitable for a first course, suggesting that books like Spivak's Calculus on Manifolds or Munkres' Analysis on Manifolds may be too advanced.
- One participant recommends Serge Lang's Analysis I, noting its historical context and potential relevance to the current discussion.
Areas of Agreement / Disagreement
Participants express a variety of opinions on what constitutes a rigorous textbook, with some advocating for more accessible options and others suggesting more advanced texts. There is no consensus on a single recommended book.
Contextual Notes
Participants have differing views on the level of rigor appropriate for a first course, and there are assumptions about the background knowledge of the students involved.