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[Calculus] Lost and what book to Use Next

  1. Jul 21, 2014 #1

    I have used Stewart's Calculus for the last year of Calculus and we made it through Taylor and MacLaurin Series. Next year we will be continuing. Since I really enjoyed calculus and I'm thinking of studying math/physics/computer science in college, I was looking for a good textbook to review calculus so far yet not feel boring. I was reading through Kline's Calculus: An Intuitive and Physical Approach, but it felt too easy and not even as rigorous as Stewart's, which I know is mainly an application based book. I read online that both Apostol and Spivak provide a rigorous review of calculus and will allow me to try my hand at proofs.

    Which book will feel less like a review and more exciting to do even though I've learned quite a bit of calculus already? I was so bored reading through Kline and I want something hard but accessible (I'm a smart kid but I wasn't doing calculus in the womb or anything like that...).


    Edit: Just want to mention that I have no idea what happened to my title :-p
    Last edited: Jul 21, 2014
  2. jcsd
  3. Jul 21, 2014 #2


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    Homework Helper

    It sounds like you know calculus. So what I recommend is trying the problems here, there are not a lot of them and they are very good. There are lecture notes and videos in case you get stuck.

    For review, that is what I recommend. Or if you want a book, try https://www.amazon.com/Calculus-Ana...id=1405977681&sr=8-16&keywords=edwards+penney or one of their newer editions to get many problems.

    Now, you asked about Spivak and Apostol. Apostol will surely not be exciting enough for you. Spivak will be but it is really a book about theorems and proofs. If that is what you want and you want to be challenged, try it. You can also look at Courant which is available online. I must admit, this one looks pretty good to me. Thank you to Mathwonk for this one. It is slightly less accessible but don't be frightened by it, read carefully and do all the questions, it would suffice as well.

    Or, you could learn most of this from almost any real analysis book, if that is something you are interested in.
    Last edited by a moderator: May 6, 2017
  4. Jul 21, 2014 #3
    Last edited by a moderator: May 6, 2017
  5. Jul 22, 2014 #4
    But there are no solutions online...? I always like to have solutions so I don't think I'm doing the right thing the whole time and meanwhile I'm completely wrong.
  6. Jul 22, 2014 #5


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    Personally, I think answers are a hindrance to learning. If you can't answer a question, go back to the notes/readings. I always like to say, for any homework problem there is a very similar example that you have already seen. Go back to it, study it. In this case, the examples are in the lecture notes and additional reading notes. The information is there, you just need to find it. That is so much better than looking at an answer.
  7. Jul 22, 2014 #6

    But what if I feel sure that I am right, thus I don't look back over the lecture notes, and pick up bad habits? I agree that answers can cripple creativity and learning, but I also feel like they are necessary when someone is learning on their own.
  8. Jul 22, 2014 #7
    You can always ask on the forums whether you did it right.
  9. Jul 23, 2014 #8
    Another really good one is Calculus by Michael Spivak. Very in depth, very rigorous; much more so than the Stewart text.
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