# Multivariable Calculus

## Main Question or Discussion Point

Do any of you know of excellent advanced multivariable calculus textbooks? If so please list them. (Don't mention James Stewart)

Thanks

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Nusc said:
I was wondering if anyone here has used Multivariable Calculus - James F. Hurley.

In addition to that, do any of you know of excellent advanced multivariable calculus textbooks? If so please list them. (Don't mention James Stewart)

Thanks

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

HungryChemist, 4th or 5th edition (Tromba) and which one uses with the solutions manual?

Would you please speculate the difference between courses in advanced calculus (multivariable/vector) and watered down multivariable and vector calculus? Then speculate the difference between the textbooks used for these courses, I am already familiar with James Stewart's text.

Thanks

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Nusc said:
HungryChemist, 4th or 5th edition (Tromba) and which one causes with the solutions manual?

Would you please speculate the difference between courses in advanced calculus (multivariable/vector) and watered down multivariable and vector calculus? Then speculate the difference between the textbooks used for these courses, I am already familiar with James Stewart's text.

Thanks
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.

Thanks

And can you compare the use of proofs between Stewart's and Tromba's textbooks?

In the appendix for Stewart's textbook, there is a couple proofs but there has to be more than that!

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

I don't like the excessive use of figures and all the unecessary spam/junk the producer puts in textbooks just to profit off of it. ie University Physics 11th - Young & Freedman. That textbook has seriously so much garbage in it that I find it distasteful especially with the ISEE sections and the "Active Physics Online" computer software. Also, let us not forget the useless Applied Projects at the end of some sections for Stewart or even maybe even your DE's text. How many professors do you think use this? Students are mostly assigned even/odd numbered problems anyway. I find these distracting. People need to write books like Griffith. Not only can they save some pages but it makes the book much less heavy. Some would agree that older textbooks are better and I could say so myself since I like to read continuously through texts. Newer editions are getting so elementary that I might as well take some crayons and doodle like a baby. :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl: :rofl:

(Do you get my drift?)

Multivariable Calculus - James F. Hurley is a good book and he writes clearly without having to refer to figures repeatedly but the author keeps refering to advanced calculus textbooks. It is almost as if he treats his own book as obsolete but then again most good authors that I have read refer to other textbooks in their own! I wonder if this is a trend.

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mathwonk
Homework Helper
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.

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Junk Shelf.

That's awesome.

https://www.amazon.com/exec/obidos/...104-6731615-7315960?v=glance&s=books&n=507846

In the last review Kishan Yerubandi says, "Minimal preparation for approaching Spivak would be at least a year of Graduate real analysis (lebesgue integration and differential forms). Also, a mastery of undergraduate linear algebra is crucial; and some topology is beneficial."

If that is true I won't get it. Bad reviews came from Tromba as well. But it is not surprising.

What textbook would be best to learn from an advanced calculus text as an undergraduate student? Or are most of these textbooks written in such a way that it makes a great reference to graduates but hard to learn from as an undergraduate? If the later is the case, then what provides the stepping stone?

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Nusc said:
In the last review Kishan Yerubandi says, "Minimal preparation for approaching Spivak would be at least a year of Graduate real analysis (lebesgue integration and differential forms). Also, a mastery of undergraduate linear algebra is crucial; and some topology is beneficial."
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.

hypermorphism said:
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.
I thought advanced calculus should precede real analysis though. I'll just get Tromba.

arildno
Homework Helper
Gold Member
Dearly Missed
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)

Nusc said:
What textbook would be best to learn from an advanced calculus text as an undergraduate student? Or are most of these textbooks written in such a way that it makes a great reference to graduates but hard to learn from as an undergraduate? If the later is the case, then what provides the stepping stone?
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

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mathwonk