Discussion Overview
The discussion revolves around recommendations for rigorous multivariable and vector calculus textbooks. Participants share their experiences and suggest various texts based on their perceived rigor and accessibility, considering the mathematical background of the original poster.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
Main Points Raised
- One participant suggests Tom Apostol's "Calculus: Vol 2" and Spivak's "Calculus on Manifolds" but expresses concern about their density and suitability for the original poster's background.
- Another participant recommends C. H. Edwards, Jr.'s "Advanced Calculus of Several Variables" as a friendlier alternative to Spivak.
- A participant endorses Spivak's "Calculus on Manifolds" but advises that it is better complemented with prior knowledge of vector calculus, suggesting Hubbard/Hubbard's "Vector Calculus, Linear Algebra, and Differential Forms" as a good resource.
- One participant acknowledges the quality of Hubbard/Hubbard's text after reviewing it.
- A suggestion is made to consider "Vector Calculus" by Marsden and Tromba, noting that it omits many proofs, which may affect its rigor.
- Another participant points out that Apostol's Vol. 2 and Spivak's text cover different subjects, questioning the recommendation from the original poster's math teacher. They also mention Munkres' "Analysis on Manifolds" as a less dense alternative to Spivak.
Areas of Agreement / Disagreement
Participants express differing opinions on the suitability and rigor of the recommended texts, indicating that there is no consensus on which book is the best choice for the original poster.
Contextual Notes
Some participants note the density of certain texts and the importance of prior knowledge in vector calculus, which may affect the choice of book. There is also mention of the varying subjects covered by the recommended texts, which could lead to confusion regarding their interchangeability.
Who May Find This Useful
This discussion may be useful for students or self-learners seeking rigorous multivariable and vector calculus resources, particularly those with a background in calculus looking for advanced texts.