I would like to buy a book to study multivariable calculus. Currently, the texts I have in mind are:
- Vector Calculus, Linear Algebra, and Differential Forms A Unified Approach by Hubbard & Hubbard
- Multivariable Calculus with Applications by Lax & Terrell
- Functions of Several Real Variables by Moskowitz & Paliogiannis
I want a book that has a clear expositions of the subjects of multivariable calculus. Also, I would like a book that avoids leaving proofs as excercises to the reader, or at least that does not do it most of the time. If possible, a book that also contains multiple examples/exercises with (fully) detailed explanations/solutions to at least some of the examples/exercises. I do not mind a rigorous approach to the subject as long as the content is explained with detail.
Which of the books mentioned above fits best the description? Also, if you have other books in mind, feel free to recommend them as well. Thanks in advance!
Note: I have taken two proof-based calculus classes and one proof-based linear algebra class.
How about Multivariable Calculus, by Don Shimamoto? It is a rigorous text, free, suitable for proof-based multivariable calculus, and has solutions to odd-numbered problems in the back.
I just took a quick browse through the book. It's true that he does leave some proofs of important theorems to the exercises, but it looks like he also leaves a number of hints. Still, I think it's a good choice.
When I took Multivariable Calculus, we used the book by Colley, but I think I would have preferred learning from Shimamoto's book.