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Best book on vector calculus

  1. Feb 3, 2010 #1
    Can u suggest a me a really good book on vector calculus and analysis , the book should be more of conceptual nature , because i want to know the indepth concept and meaning of various things like curl, grad, div, various theorems. I mean book shouldn't be problem oriented. I don't need too much problems to practice , i just want to grasp the concept or theory behind. Any classic text or anything related to what i want?
  2. jcsd
  3. Feb 3, 2010 #2
    feynmann lectures on physics - volume 2 - vector calculus comes to life through electromagnetic theory.
  4. Feb 4, 2010 #3
    For Vector Calculus I like J. Marsden (CalTech) & A. Tromba (UCSC). But like wolfsy said, if you are trying to conceptualize things, a book on E&M. Feynmann isn't super mathematically intensive. Griffith is a standard undergrad E&M text; some people love it some people hate it. Jackson is a grad text, but a large portion of the book is devoted to learning the math.
  5. Feb 4, 2010 #4
    I think Div, Grad, Curl, and All That by H.M Schey is good for beginners ^^
  6. Feb 5, 2010 #5
    i would suggest the book by Leithold "the calculus 7".
  7. Jun 10, 2011 #6
    The book: Mathematical Methods for Physicists, 6th Edition - A Comprehensive Guide By George B. Arfken, Hans J. Weber & Frank Harris is an excellent book. Its over 1000 pages and covers quite a great deal of material in a very elegant and superb manner. I strongly, strongly recommend having this book. I found Vector Calculus from James Stewart, Joel Hass, and similar authors seemed to be based off a single source and felt more like a cook book than a text. Painfully frustrating.

    Have a look at the first chapter of Mathematical Methods for Physicists (its free from the publisher) and you will see what I'm trying to say.

    Publishers link to book - http://www.elsevierdirect.com/product.jsp?isbn=9780120598762

    Link to sample chapter: http://www.elsevierdirect.com/samplechapters/9780120598762/9780120598762.PDF
  8. Jun 11, 2011 #7
    I just had a discussion about vector calculus in a thread today that started out about coordinate systems:


    I listed some books that don't cover the Cylindrical and Spherical coordinates much. Hope that might be useful to you.....At least to put on avoid list!!!.

    Yes If you work on the Introduction to electrodynamics by David Griffiths, you will get a very good workout on vector calculus. I have been working on chapter 10 and 11, I have to really go back and review a lot of the vector calculus, I really feel I am learning vector calculus with this.

    Div, Grad, Curl, and All That by H.M Schey is the only one that cover what I want but I yet to read it to know how good it is. But choose a book that really cover cylindrical and spherical coordinates. Rectangular coordinates are quite easy, the kicker is when you get into cyl and sph co. particular mix in time as the forth variable.
    Last edited: Jun 11, 2011
  9. Jun 11, 2011 #8
    I really like the Griffiths book. I am on the electronic side of it and I studied a few of the Electromagnetics for engineers book, they don't go very deep and they avoid difficult vector calculus at all cost. Griffiths really get into it. I really feel I am working on a vector calculus class.....a difficult one!!!
  10. Jun 12, 2011 #9


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    Feynmann's Lectures on Physics Book2.
  11. Jun 12, 2011 #10
    If you really want to understand the concept and see them in action, you should enroll in the undergrad electrodynamics class, a class that use Griffiths book would be the best. You can see first hand how electric field tend to have divergent property and magnetic field tends to have the curl property.

    I am a self studier and I buy a lot of books. Most third semester calculus concentrate on vectors, VVF, surface and volume integrals. Most spent maybe 2 weeks in the final parts of the vector fields, line intergrals Green's, Divergence and Stoke's theorems. That by themselves are like double the amount of study. You enroll in the ED class, you get to learn the other coordinate systems, their div and curl. Then from work problem, you get to set up the equation yourself.....And that really show whether you really understand or not.

    Just reading math books is not enough, I,ve done that. I study 2 books, worked through all the problems. Re-studied two more times. I can easily get A's on it even the first time. It is not until I work on Griffiths cpt 10 and 11 that I really find out how little I understand and I feel I really study a new vector calculus class. All the multi-variables calculus books( which I have a lot) barely touch these topics. The first few chapters of the Griffiths are quite basic and you can just read and work a few problems to get the "feel" of the electric and magnetic field in terms of calculus. Then when you get to the later chapters, it can get quite tough. In chapter 10 some of the problems take me a whole day and still do get it. You can do a search using my name here on the post in the last two months, they are 90%+ vector calculus and verify understanding of concepts. The part that involve retarded fields and potential which add the time component in can really get you going!!!!
  12. Jun 12, 2011 #11
    I've used coffin a bit as a reference & so far I like it. I haven't seen gibbs/wilson yet but I bet it's good too. They're two of the all-time classics singled out by crowe in his history. (no surprise that they were both written by physicists) I also think doing vector analysis in parallel with E&M (haha) is probably a good idea but I haven't got around to it yet.
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