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Suggestions for Multivariable Calculus

  1. Aug 24, 2014 #1
    Hi, I took Advanced Calculus and we used 'Calculus, a complete course' by Adams. However, I couldn't learn most of the topics actualy. So, I want to learn Multivariable Calculus; double-triple integrals, Stoke's, Green's Theorem etc. What are the good books you know that I can follow easily? Thanks.
  2. jcsd
  3. Aug 24, 2014 #2


    Staff: Mentor

    Last edited by a moderator: May 6, 2017
  4. Aug 26, 2014 #3
    Thanks. Any other suggestions?
  5. Aug 26, 2014 #4
    There's Vector Calculus, Linear Algebra, and Differential Forms by Hubbard ,the very difficult Advanced calculus by Loomis and Sternberg ,that's free on Sternberg's website.For something unusual and good there's Advanced Calculus: A Geometric View (James J. Callahan) and Harold M. Edwards' Advanced Calculus- A Differential Forms Approach.
    Last edited: Aug 26, 2014
  6. Aug 27, 2014 #5
    Thanks, whyevengothere , I'm having trouble with understanding the concepts. I will check these today.
  7. Aug 27, 2014 #6
    This is just one personal opinion but I think that most modern lower level textbooks suck. They seem to have a lot of pictures and worked problems but shy away from proofs and intuition. It's as if they begin with the assumption that you will find it too difficult. I would recommend going to a used bookstore and getting an older book. I still have the 3rd edition of Thomas' Calc and Analytical Geometry on my shelf but when I was handed a current copy of Thomas I thought it was a joke. Same goes for Stewart. I can't figure out how a student who uses those books is prepared to study math. I'm familiar with this one and would highly recommend it:


    Hey, you can't really lose for a penny plus $3.99 shipping.

    If you're good with single variable and just want to focus on multi-variable and other topics I recommend this for a penny:


    or this or this for another penny:


    Don't buy new editions because when authors of popular books die someone else takes over and waters it down. I also second the recommendation of Schaum's outlines. I probably have 20 of them on my shelf and they were fantastic when I was a student.
    Last edited by a moderator: May 6, 2017
  8. Aug 28, 2014 #7
    Thanks a lot, alan2.
    I borrowed Schaum's Advanced Calculus outlines from the library and I will check those 3 books you recommended.
  9. Oct 9, 2015 #8
    Get a very comprehensive manual on "calculus" (i.e. differential & integral calculus) and analytic geometry; and get the sudent /teacher solutions manual ( or its photocopy, 10% of pages at a time per respect to copyright owner) if the answers aren't included therein. Adam's "Calculus, a complete course" is one of the two best textbooks in the world now. This manual and the solutionary are worth /represent up to twelve credits of recognized academic study for beginners. By "beginner" I mean a person who has a complete mastery of the secondary school mathematic curriculum, plus the optional "discrete mathematics" course, plus the optional "geometry and linear algebra" course. You will have to teach yourself, study by yourself, and get initiated to a graphing calculator or a software of your choice: the most recommendable ones are the colour graphing calculator Casio and the Maple software. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Always read the manual and solutionary, and always get acquainted with the relevant usage of your prefered graphing calculator or prefered software, before you start a academic course /laboratory in mathematics. Always. Once you have thus gotten well prepared, and afterwards once you have taken and succeeded a "Calculus 3" or equivalent, the time come for you to consider buying "Advanced Calculus: a Geometric View" and to seek for its answers on Internet. It is worth 6.5 more credits. Henceforth /furthermore, the best preparation for future two-semester course in "honours advanced calculus III" or "differential-form calculus", is the purchase and the thoroughly study by your own of "Advanced Calculus, A Differential Form Approach". Which has a 6.5 credit value. There are courses that corespond to the two last textbooks, in some universities.
  10. Oct 9, 2015 #9
    Thomas & Finney's "Calculus and Analytic Geometry" (recent edition) is the other best in the world textbook for beginners in "calculus". With its solutionary in two tomes, it is worth 12 crédits .
  11. Oct 9, 2015 #10
    I used Adams: A Complete Course 8th edition for single and multi variable calculus, I thought it was a really good book for both in class and self study. I had Calculus of Several Variables by Serge Lang as well, I thought it was a good book.
  12. Oct 13, 2015 #11
    Most of the people worldwide, even with a very well preparation in maths of high-school and in college-pre-calculus, cannot follow and understand easily Lang's textbooks. I don't recommend the authors Folland, Lang, Marsden and Rubin which are very excellent mathematicians. The most recent and foremost popular method of teaching infinitesimal calculus, Is American. It includes some study of differential equations since the very first course in "calculus"; it goes on in teaching some more materials on ordinary differential equations (ODEs) in the 2nd, 3rd and 4th courses, with a glimpse of partial differential equations (PDEs) from the 2nd trimester in calculus. Textbooks shall adapt themself to the curriculum; and rarely the curricula are adapted or modulated or up-dated to the new and brilliant textbooks, manuals & treaties on the idealized academic mathematics. This new trend is an logic response to the college-level physics books which have gained a mathematical maturity and an incredible beauty. ______________________________________________________ After Adam, and after Thomas & Finney, I consider Stewart as the third best author of textbooks on basic / intermediate calculus, in the world. With Stewart one can earn /gain 9 credits in calculus. Same credentials with Mizrahi & Sullivan with their "Calculus and Analytic Geometry", who come in fourth position. _______________________The highly gifted in maths who plans to become mathematician, will learn also from Folland, Lang , Marsden and Rubin.
  13. Oct 13, 2015 #12
    I don't believe you have to be highly gifted to learn from Lang. Over the years math texts seem to have taken a hand-holding approach. So when students take a look at Lang or Spivak texts (the way math should be written in my opinion) they may find it hard to follow.
  14. Oct 23, 2015 #13
    Se the reviews of "tech boy guy" on Spivak's "Calculus, 4/e" and of Lang's introduction of calculus. The first is rather a book for Analysis I (3 crédits) as admitted by the author; while the second needs to be supplemented by a big student's workbook, as Springer editor makes uninteresting books _ "Advanced Calculus: A Geometric Approach" and "Partial Differential Equations: A Visaual Approach" are amongst the very rare exceptions_.
  15. Oct 31, 2015 #14
    My "highly gifted" isn't politically correct; so in their introduction/preface, the manuals, textbooks & scientific books read the acceptable & cool phrase "very motivated" (student/reader); sometimes combined further on, by "honours or graduate course". Only a private school/college can afford to maintain a "honours curriculum" in calculus & advanced calculus. For such curricula, the authors Lang and Spivak merit to be chosen. Optional courses in mathematics could appear from the last quadrimester of elementary school, through secondary school, and more numerous through college and institutes of superior technology. Too much time and energy is spent in learning the usage of softwares for mathematics. A graphic in colours Casio calculator, later on complemented by a recent version of Maple software (in campus), is my preference for any student of any level.
  16. Nov 1, 2015 #15
    Use 'Vector Calculus' by Matthews if you are not learning it as part of the analysis course. I recommend this book from my heart, the clearest I have ever seen.
  17. Nov 5, 2015 #16
    It is raisonnable to read only the textbook designated for the course you are registered in. No time to read a more friendly book. The average student should prevent stress & overwelming difficulties, by pre-reading his/her next compulsery textbook during the summer prior to the course. For any course on calculus and advanced calculus, this preparation is obviously necessary. Nowadays, vector calculus is absolutly in the third course of calculus. And many teachers do tutoring (which costs money). Nowadays calculus and advanced calculus contains enough stock to design 7 seven courses of 3 credits each. I am not thinking of courses on differential equations nor integral equations nor numerical analysis nor analysis. Adam's thick textbook represents, with all the solutions to exercises / problems, a 12-credits safe foundation.
  18. Nov 5, 2015 #17
    Taking at the same quadrimester, a 3rd course in calculus (multivariable calculus) and a course in analysis is stupid and dangerous. The 5th , 6th and 7th courses in advanced/hounpartially someors calculus should contain a part of analysis. Logically, any serious first 3-credit course in analysis, requires as prerequisites, at least 3 credits of post-college algebra, 3 credits of linear algebra II, 3 credits of ODE. Analysis is no necessary tool for high-school and 1st-year college maths teachers; nor for engineers except those in physics speciality. The curricula are designed to allow the maximum profits$ to the colleges & universities.
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