Calculus Seeking Recommendation on Multivariable Calculus (theories)

[bacte2013]

Dear PF personnel,

I am a college sophomore with double majors in mathematics and microbiology. I wrote this email to seek your advice on selecting a theoretical, proof-based textbook on the multivariable calculus. I will be taking a multivariable calculus on this Summer but it unfortunately is a computational one with little theories. I would like one that comprehensively covers the theories of multivariable calculus and perhaps including sections on the applications too (but not necessary). Couple of textbooks I have in my mind are ones written by Serge Lang, Apostol, Marsden, Hubbard, and Fleming. Which one is good for self-learning?
PK

 

[robphy]

I'd vote for Marsden. As an applied-mathematician, he had good illustrative examples (in my opinion) on many topics, introductory and advanced.

http://www.cds.caltech.edu/~marsden/
http://www.cds.caltech.edu/~marsden/math1c-10/home/

 

[bacte2013]

^
Thank you for the vote! Is this better textbook than Hubbard or Lang for the contents, explanation, and problem sets quality? I heard some bad reviews about it, more frequent than Hubbard and Lang.

 

[robphy]

From those authors, I have only used Marsden (for Complex Analysis)...
and have referred to more advanced physics texts by Marsden.
The Hubbard text looks interesting with its treatment of differential forms.
I haven't used any of them for vector calculus.

 

[bacte2013]

^
Thank you very much for the explanation. However, I am not sure if Marsden's book will be in similar quality to his other books...I am awaiting for more responses. Unfortunately, available books for Marsden in my college library are all checked out..I read some portions of Lang and Hubbard, and I feel like I miss something in Lang while Hubbard covers less contents in vector calculus than other books.

 

[Xiuh]

In my opinion Marsden isn't that bad, but the other ones are much better. Fleming is one of my favorites, but perhaps it is not super-friendly for self learning.
Other books I highly recommend are
- Munkres. Analysis on Manifolds
https://www.amazon.com/dp/0201315963/?tag=pfamazon01-20
- Edwards. Advanced Calculus
https://www.amazon.com/dp/0486683362/?tag=pfamazon01-20

 

[bacte2013]

^
Thank you very much for the recommendation! Do they cover traditional topics in vector calculus? I took a look on them and they seem to only cover the theories behind vector calculus? Vector calculus course I will be taking on Summer is purely computational, and my aim is to get a book on vector calculus that covers both theories and applications. I have two volumes of Apostol's Calculus but the second volume (covering multivariable and linear algebra) seems very outdated...Currently, my mind is on Marsden but I am not sure if this textbook can be a standalone.

 

[Xiuh]

Yes, they cover all the traditional topics. There are some computational aspects covered in both texts, but there is more emphasis on the theoretical side, so I guess it's up to you. Check them out and see if you like them.