Recommend a Vector Calculus book

[rubrix]

Recommend a "Vector Calculus" book

- by "Vector Calculus" i do not mean Calc III (multivariate). What i mean is the Calculus course that follows after Calc III and consists of topics such as Stokes's and divergence theorems, Cartesian tensors.

- Wel'll be using Vector Calculus by Jerrold E. Marsden and Anthony Tromba as our textbook. I'm reading some amazon reviews and the book sounds a bit hard to follow.

- I want another book which is relatively easier to follow but covers pretty much same material. I'll be self-studying from this book so recommend a good one please ;)

- I have ran into two books: Vector Calculus by Paul C. Matthews (Springer) and Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, Fourth Edition by H.M.Schey. Would you recommend them?

P.S. What *SPECIFIC* topics from Calc III should I review before taking this course?

 

[physicsnoob93]

I used Vector Calculus by Paul C. Matthews. It's nice and quick but it doesn't cover some things a standard Calc III book will cover but it also covers topics such as cartesian tensors and the divergence theorems etc. In all it's quite a good book.

 

[qspeechc]

I think the Marsden & Tromba book is terrific actually. Yea it's difficult, but this is usually because the student is not prepared enough, but then that's the instructor's fault for using the book and not the students fault. I learned vector calculus out of the watered-down book by Stewart. I found out very soon it did not meet my vector calculus needs in physics. Now that I have Marsden & Tromba I never use Stewart; it's being used as an expensive and large door-stop somewhere...
The best preparation for Marsden & Tromba is a rigorous calc course, e.g. Spivak. If you have such a background you'll be fine. If not, well I suggest you try reading a good rigorous calc book first.
The book by Schey is informal but very good, but doesn't cover as many topics as the Marsden & Tromba book.
Marsden & Tromba is difficult, but I promise you it will leave you well prepared for further studying in mathematics and physics.

 

[Nabeshin]

I think the Marsden & Tromba book is terrific actually. Yea it's difficult, but this is usually because the student is not prepared enough, but then that's the instructor's fault for using the book and not the students fault. I learned vector calculus out of the watered-down book by Stewart. I found out very soon it did not meet my vector calculus needs in physics. Now that I have Marsden & Tromba I never use Stewart; it's being used as an expensive and large door-stop somewhere...
The best preparation for Marsden & Tromba is a rigorous calc course, e.g. Spivak. If you have such a background you'll be fine. If not, well I suggest you try reading a good rigorous calc book first.
The book by Schey is informal but very good, but doesn't cover as many topics as the Marsden & Tromba book.
Marsden & Tromba is difficult, but I promise you it will leave you well prepared for further studying in mathematics and physics.

/agree

 

[n!kofeyn]

The book you want is http://matrixeditions.com/UnifiedApproach3rd.html" by John Hubbard. I have been wanting to go back and fresh up my vector calculus, and this will be the book I use. The best part about it is that it builds up the required prerequisites and has a very modern treatment. By that I mean he shows the relationship between classical vector calculus and differential forms, which is not done all too often or possibly at all. The Marsden/Tromba book doesn't even bother with differential forms until the last 15 pages or so. This is a shame because the language of differential forms generalizes the div, grad, and curl, as well as Stoke's Theorem. The Hubbard book introduces manifolds and a unique way of teaching the Lebesgue integral. If you are planning on doing higher mathematics, then Hubbard's book is the best bet when it comes to this material. He covers much more material than Marsden/Tromba. Even if you want to become a physicist, you will eventually have to go back and relearn vector calculus from the differential form viewpoint anyway.

There is also Advanced Calculus: A Differential Forms Approach by Harold Edwards that is very good. Although, he does not integrate vector calculus like Hubbard does.

By the way, the 4th edition of Hubbard is now out. You can browse excerpts from the book in the link above.

 

[rubrix]

@physicsnoob93, that's what i thought. Springer books are usually easy to follow but they lack exercises BIG TIME. How did you cope with that problem, did you use any other resources?

@qspeechc, i have a pretty good Calclus background...well except for 2nd half of Calc III. All those 3D stuff, double/triple integral did not appeal to me then. But now i realize how important it...hence is why I'm asking for *SPECIFIC* topic from Calc III that i should review for Vector Calculus course.

by rigorous calculus course are you referring to one that involves proofs? In that case i have done Analysis course.

@n!kofeyn, John Hubbard book sounds good but i want the book covering only Vector Calculus. I also checked table of content of Edwards @ amazon and it seems different than what i'll be learning in the course.

thnx everyone for the input so far, really appreciate it :)

edit: here is table of content of the book our class will be using google books link

I'm surprised by how this detailed table of content looks like. There really isn't much new in there. I can group buncha topics from that book into what we did in Calc I, II, and III.

Vectors in 2D & 3D, Cylindrical & Spherical Coordinates, Gadient and Directional Derivatives, Partial Derivatives, Vector Fields, Double/ Triple Integral, Line Integral (Calc III)
Taylor's Theorem, Improper Integral (Calc II)
Limits and Continuity, Differentiation, Properties of the Derivative (Calc I)

so is "Vector Calculus" like an in-depth study of the same thing (and a few new things)?

 

[qspeechc]

It sounds like you have a solid background so you should have no problems with Marsden & Tromba. I think you will like it, it is a good book (Marsden is a famous applied mathematician).
I think H.Edwards book has more on differential forms than Hubbard & Hubbard. I think you should read those books AFTER Marden & Tromba, since most of the books you will encounter yet will not use differential forms and will be closer in style to the MArsden & Tromba book.
If you have studied these topics already

Vectors in 2D & 3D, Cylindrical & Spherical Coordinates, Gadient and Directional Derivatives, Partial Derivatives, Vector Fields, Double/ Triple Integral, Line Integral (Calc III)
Taylor's Theorem, Improper Integral (Calc II)
Limits and Continuity, Differentiation, Properties of the Derivative (Calc I)

M&T covers the same stuff pretty much, but a bit more material, and at what level did you study it? M&T is more rigorous than Stewart.

 

[rubrix]

kool thanks for the info qspeechc ;)