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A Book To Self-Teach?

  1. Mar 29, 2010 #1
    I've found that I learn mathematics better by familiarizing myself with the topics through self-study, then taking more formal classes in the subject. Would Larson's Calculus (With Analytic Geometry), 8th edition be a good choice? I'm looking specifically at Larson's because it's a) widely available for extraordinarily low prices, and b) comprehensive, so I'll only have to buy the one book for Calculus I, II and III. Is it a good buy, or would I be wasting my money?
  2. jcsd
  3. Mar 31, 2010 #2
    I would recommend you to take a look at
    "Calculus Lifesaver Tools Princeton."
    It is really good book because it shows you how to solve problem [calculus 1-2]step by step, but I will also recommend you to take some classes at a community college because some of the stuff in those book are not really easy to comprehend.
  4. Apr 1, 2010 #3
    I took a look at The Calculus Lifesaver. It didn't seem comprehensive enough, and its lack of problem sets makes it seem ill-suited as a primary learning tool. I'm going to be going to a university to study calculus I-III, so I figured I'd grab a book that covered most or all of the topics covered in those three courses. Larson's seems to fit the bill, but I wanted some opinions on it before I bought it.
  5. Apr 1, 2010 #4
    Stewart's Calculus was the norm when I took first year calculus. It is very easy to read and focuses on understanding the computational aspect of calculus. Spivak also seems to be popular for pure math students, but I have not read it.

    Understanding Analysis by Abbott is also popular and is a very good introduction to analysis. Even though it is a small book and taken at 1st or 2nd year, it is packed with information and should be read slowly.
  6. Apr 3, 2010 #5
    I recommend Thomas Calculus (which is pretty much the same as Stewart Calculus).

    However, the Princeton book the Calculus Lifesaver is great. I'm flying through it just as a backup to the computational flavouring of calculus and I just wish I had gotten this book sooner.

    If you want an old style theory flavoured calculus book that isn't too taxing (and is free due to the Google Books scheme) I advise you read;

    "Calculus and Linear Algebra. Vol. 1: Vectors in the Plane and One-Variable Calculus"
    Wilfred Kaplan, Donald J. Lewis
    http://scholarlypublishing.org/calculus/ [Broken]

    This is my major book now as it's got that old feeling to it, and it's full of deep information about linear algebra and calc (well, so far it does!).

    I'm only on the limits chapter but I'm going to be finished it in a day or two and I can tell you it is holding my attention. It's the kind of book I wouldn't be so confident in reading had I not suffered through Thomas Calculus and the videos on www.khanacademy.org[/url] and [url]www.justmathtutoring.com[/URL] but to me this is a stepping stone to Apostol and Spivak and a good one at that :biggrin:
    Last edited by a moderator: May 4, 2017
  7. Apr 4, 2010 #6
    For what it's worth, I taught myself Calculus by doing EVERY SINGLE PROBLEM in Larson/Hostetler's Alternate 3rd Edition. I still have that very copy with me today. I do not know what the recent editions have changed, but that particular edition was very good on examples, illustrations, proofs, practice problems, and even biographical blurbs on famous mathematicians. And yes, it was also comprehensive (and quite thick/heavy).
  8. Apr 7, 2010 #7
    I feel the same way about self-teaching, although in my case it's more because I get easily bored with material, and like to learn at my own (much faster than high school math classes) pace. If having a huge number of problem sets isn't very important to you, I recommend that instead of getting a book, you use the video lectures provided through MIT's Open Course Ware (ocw.mit.edu); I think they're either very suited for how you learn or quite the opposite: they don't do many examples, and what they do are very cursory, but the lecturer (David Jerison) is very good about proving absolutely everything he shows you. If you need help, or have questions, there's no one better to ask than a math teacher (I presume you're in high school, is this not the case?).
  9. Apr 11, 2010 #8
    "Calculas for dummies" is best book.
  10. Apr 13, 2010 #9
    I agree with yaseen shah....
  11. Apr 15, 2010 #10
    I learned from Stewart's Calculus, but currently I'm going through Spivak's book. After Stewart's computational, no-nonsense approach I'm looking for more theory and it seems Spivak fills the void nicely. I've heard only good things about Apostol's text as well. And in regards to Larson's text -- I've actually read and have done some work from it and thought it was pretty good.

    So, basically... Take your pick! Good luck.
  12. Apr 23, 2010 #11
    I've been teaching out of the Larson text for 17 years (started with the alternate 4th edition through to the 8th edition and now the early-trans 4th edition). I have to say that whenever I start thinking of changing the text, I never find another that has the quality of exercises as Larson. That guy just keeps getting better!
  13. May 7, 2010 #12


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    Gold Member

    Calculus Made Easy by Silvanus P. Thompson
  14. May 8, 2010 #13
    That is a great one!
  15. May 8, 2010 #14


    User Avatar

    Go to your local public library, there are probably at least three or four calculus textbooks you can take a look at. As far as a book for Calc I - III, my university currently uses Thomas Calculus (just switched to 12th edition) for all three courses.
  16. Jul 27, 2011 #15
  17. Jul 3, 2012 #16
    Hi i like Calculus lifesaver from Adrian Banner. Mainly because it teachs in a down to earth way, and its a non trivial approach at calculus (like for dummies stuff).
    I find elearning videos, boring and like the more active approach that have books.

    My main problem is that i study, work, and need time to resolve the class exercises, and prepare for the exams. I prefer to focus on class exercise material than books exercises because, it shows me more about the exam criteria of the class that im doing.

    Previous to Calculus lifesaver, i was using mainly leithold calculus.
    Had to put down Spivak and Piskunov. Because i dont understood their more formal approach, get bored, and frustrated, and end wasting more time, searching on youtube/ google, on how to read the theory, and apply the procedures to the exercises (with the risks of using internet, like ending in any site, 4chan, 9gag ) than focusing on study.

    Do you know good study guide books, about multivariable calculus, discrete math, linear algebra? with good detailed examples, than exercises? and good books just with exercises, and answers?

    And what can i do to at steps, go near to the more formal approach of math, and understand the real books and theory.
    I would like a more philosophical/ psychological way of showing math, know what inspired the mathematician to stablish a determinated theory. at now the books i read, have just historical facts. Long books arent my problem.

    Thanks, excuse for the errors im a foreign speaker.
  18. Jul 7, 2012 #17
    I would highly recommend you get a hold of a 4th edition of Calculus and Analytic Geometry by George B. Thomas. I think they go for like 15 books on Amazon. It's the best edition of his book.

    If you can't get a hold of that I recommend the Alternate Edition of the same book. It is like the third edition but better.

    Anything higher than the 4th edition of Thomas is just not worth the price when the older editions are available.
  19. Jul 17, 2012 #18
    Hi zxcvbs,
    It would have been better if you had mentioned your current knowledge level however considering you to be in between state of a high schooler and university goer , I highly recommend apostol's calculus volume 1 & 2 for multivariable calculus and other stuff ( though a bit pricey) this is a good choice for deep understanding of the topics in calculus , and linear algebra done right by Sheldon Axler.
  20. Jul 24, 2012 #19
    I'm surprised nobody mentioned Strang's Calculus. I learned from Stewart in school, but then came across Strang and found it better and more comprehensive in every way. Everyone else I've spoken to who is familiar with the two of them agrees with me. It would be worth checking out!
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