Multivariable Calculus

I thought James Stewart was a good book. Anyway, my school uses a book called Vector Calculus written by Tromba. It's one step more formal than most other introductory Calculus text.

 

howard anton's multi-variable calculus is the best i have seen

 

Sorry for the late reply, let me be as straight forward as I can but I should warn you mean while general opinion on one text book to another has wide range of difference. ex) I didn't particulary like Calculus book written by Anton.

You said Advanced Calculus (multivariable/vector) and I would like to say that in general Advanced Calculus is not equal to multivariable/vector calculus rather the later is the subset of Advanced Calculus.

If you're familar with Stewart then studying Advanced Calculus is good way(and that is what I am doing now). It covers most of topics covered by Stewart in much more compact form plus some P.D.E, Fourier, Special Integrals and so on.(At least for most of the text book).

Vector Calculus is the topics that are covered in Stewart from Ch12 to Ch13(but not so sure).

Vector Calculus text written by tromba is little advanced in a sense their definition of limit and derivative (and so on ) are much more precise but basically covers the same topics(does not cover Ch1 to Ch10) as in Stewart although it is almost as thick as Stewart. I do not know which edition of Tromba comes with solution manual.

It's all up to you man, if you're ready to go on to something new, then study Advanced Calculus but if you want to rebuild upon vector calculus to get good feeling of what you're doing in a class like E&M,Classical Dynamics and so on, then try another Vector Calculus such as Tromba.

 

Personally I like Stewart's book. However you sound like you need something a bit more advanced.

 

a much better book than stewart is spivaks little "calculus on manifolds". this is the book that gives you the version that mathematicians use, and grad students should have in Pre PhD math. read every word and do every problem. but first learn what a linear map is.

other good books are by fleming, or courant vol 2, or loomis - sternberg (probably too abstract), or even dieudonne (foundations of modern analysis, for someone who already has read courant vol2), or lang analysis I (in 1970, new title now?). Is that enough? you probably won't need your crayons for these.

I still have all of these books on my working shelf, not my junk shelf.

 

This is overkill. A minimum is knowledge of linear algebra (like the back of your hand) and undergraduate real analysis. An exposure to complex variables adds to the experience. I don't see any need in the text for pre-knowledge of topology, though a basic knowledge is nice.

 

Marsden&Tromba's "Vector Calculus" isn't particularly rigorous, but it is clearly written and has a good set of exercises (at least the edition I had)

 

I've not read, Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications by Tom Apostol, but it seems to me to be the type of book you're asking for.

https://www.amazon.com/exec/obidos/...2/sr=2-3/ref=pd_bbs_b_2_3/002-8368934-3692846

Apostol's approach is a bit more rigorous than the standard North American textbook approach (e.g. Stewart). I'm basing that opinion on what I know of Apostol's Calculus, Volume I. While Amazon reviews of the first volume seem to be unanimously positive, the reviews of the second volume seem to be a little more mixed

One other consideration is that MIT uses the Apostol books and you can obtain extensive course notes for volume's I and II via the opencourseware project website. The volume II stuff is here:

http://ocw.mit.edu/OcwWeb/Mathematics/18-024Calculus-with-Theory-IISpring2003/LectureNotes/index.htm

 

mr yerubandi does not know what he is talking about. the only prerequisite is linear algebra. it is a good book. i recommend you get it. but if you are scared off by a silly review like that maybe you do not have what it takes.