I am asking this question as a question similar to what has been asked previously for other topics as well as math in general. But I'd like to ask for text references specifically in the domain of multivariable/vector calculus.
So my question shares a similar spirit to other questions such as
Learning through guided discovery https://mathoverflow.net/questions/119621/learning-through-guided-discovery
Big list of guided discovery textbooks Big list of "guided discovery" books
Are there any books that take a 'theorems as problems' approach? https://mathoverflow.net/questions/12709/are-there-any-books-that-take-a-theorems-as-problems-approach
The discussions and responses on all those discussions are great, but they did not talk about anything for multivariable calculus.
I would greatly appreciate it if anyone could share any books they know that would fulfill some of the characteristics of a guided discovery text. Just to give a clearer sense of what kind of book I'm looking out for, the books
Excursions in Calculus http://www.amazon.com/Excursions-Calculus-Continuous-Mathematical-Expositions/dp/0883853175
Excursions in Classical Analysis www.maa.org/press/maa-reviews/excursions-in-classical-analysis
are great books which I've been looking for in the topic of single variable calculus, and have found them. I just hope that there exists something similar in multivariable calculus.
To start off the sharing and listing, I thought I would say that the book
Div, Curl and All That www.amazon.com/Div-Grad-Curl-All-That/dp/0393925161
to be a possible candidate, but from what I've seen from it so far, it looks like it does not have the same level of mathematical rigor as what the other two textbooks have (for the topic single variable calculus that they address).
Thank you very much!
- I wanted to post up the links completely for all the other references, but I couldn't because my reputation isn't high enough. So pardon the incomplete links :p