1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculus Mike Spivak Math Textbooks

  1. Apr 1, 2015 #1
    Hi, everyone

    I was directed here by a poster in another thread and thought I'd post my question to you guys in this area of the forums.

    I had some questions about Mike Spivak's math textbooks. It was alluded to in another thread that his books are quite difficult. Yet, from what I can gather, they seem to also be popular.

    I'm curious what makes his books difficult and how they may differ from other math textbooks used in college. And, secondly, if I'm just starting Calculus, which of his books (if any) would fit my level of math (beginning Calculus I next Fall 2015 semester).

    Thank you all much!
  2. jcsd
  3. Apr 1, 2015 #2
    They are more proof based then your average calculus book and its more of a real analysis textbook then a calculus textbook. If you are familiar with writing proofs then you may be fine but I would recommend reading it after your first calculus course and possibly a proof writing class. I feel it would be a better textbook to read before taking real analysis or to compliment that class rather then before calculus or to compliment it.

    Its popular because spivak is great mathematical expositor.
  4. Apr 2, 2015 #3
    In my opinion, only his calculus book is good, I don't like the rest. But I can see why some people like them.

    That said, if you never studied calculus before, then you probably shouldn't be doing Spivak. Once you're a bit comfortable with the intuitive concepts of limits, derivatives and integrals, and once you can calculate them pretty adequately, you can try Spivak (and it'll still be difficult). For your situation, I recommend "A first course in calculus" by Lang. It's a terrific book and very well written.
  5. Apr 2, 2015 #4


    User Avatar
    Science Advisor
    Homework Helper

    I like all of mike's books, but they are very different. to give a goldilocks justification for micromass' view, the multivariable book is in a sense too short, and the diff geom book too long, while the Calculus book is just right. In my opinion also, the Calculus book benefits greatly by being, in some sense, a more entertaining rewrite of Courant's great calculus book. You also need to be careful what you mean by "difficult". Spivak presents difficult material, but does it so clearly, that if your goal is actually to learn what is in his Calculus book, he makes learning it about as easy as it can be made. However if you want to understand Stokes' theorem, I feel that the version in Lang's Analysis 1 (for simplices), is clearer and easier to read than the one in Mike's Calculus on Manifolds. I like that latter book though for a clear and precise presentation of differentiation and integration in several variables and of forms over chains.
    Last edited: Apr 2, 2015
  6. Apr 3, 2015 #5
    Some helpful responses guys. Thanks very much. I'll check out the Lang book, but was curious what the name of the good Spivak Calculus book was? I'll look it up when I get the chance.
  7. Apr 3, 2015 #6
    Last edited by a moderator: May 7, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Mike Spivak Math Date
Prob/Stats Books on Machine Learning without a strong math background required Feb 7, 2018
Calculus Will this be enough preparation for Spivak's Calculus book? Nov 12, 2017
Calculus Spivak's Calc book? Nov 11, 2017
Calculus What are some good resources for studying Spivak's Calculus? Aug 30, 2017
Calculus Spivak Calculus Math Question Feb 19, 2017