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Calculus: An Intuitive and Physical Approach

  1. Sep 23, 2011 #1
    I've been searching for a good book on Calculus that is great for self-study, and at the same time, walks the reader through the WHY behind the math. I am farely upset at how today's educational institutions teach math as plug-n-chug subject without walking the students through the underlying process and concepts. After some research, I've managed to find a book on amazon:

    Calculus: An Intuitive and Physical Approach (Second Edition) [Paperback]
    Morris Kline

    As a student who is currently enrolled in precalculus, but who wants to study ahead, would this be the right choice for a self-study book, and does it cover the topics that a college course would cover? The reviews seem very good, but I really want to get your opinions before investing the money and time.

    The same goes for:

    Practical Analysis in One Variable (Undergraduate Texts in Mathematics) [Paperback]
    Donald Estep (Author)

    which was recommended by another member of PF. I personally believe that an analysis book would be too difficult/rigorous for a first time learner of Calculus, but I would still like to hear your opinions on this book.

    Please recommend any other books (no websites please, I'm well aware many of them) you might think would help me in my pursuit to learn and understand Calculus.

    Thank you!
  2. jcsd
  3. Sep 25, 2011 #2
    There's one calculus book that was the one that young Einstein learned the stuff from, I can't remember the title, though.
  4. Sep 25, 2011 #3
    When I taught myself Calculus while taking PreCal (or before I took it), I was watching MIT video lectures with David Jerison. For a book though, I would suggest James Stewart Calculus. Calculus is not a plug and chug type of math. If you feel comfy, you should prove the formulas yourself (though I have to say that you won't prove much in Calculus).

    MIT Calculus I Video Lectures:http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/

    James Stewart Calculus: https://www.amazon.com/Calculus-Jam...=sr_1_1?s=books&ie=UTF8&qid=1316934744&sr=1-1
  5. Sep 26, 2011 #4
    Last edited by a moderator: Apr 26, 2017
  6. Sep 26, 2011 #5
    I used this book myself, and would recommend it too. But first get it from a library first and see if it fits your style as different books suit different people.

    ***Edit: How could I forget Calculus by Thomas. Also look that one up too in the library (http://www.amazon.co.uk/Calculus-An...0154/ref=sr_1_3?ie=UTF8&qid=1317066202&sr=8-3)***
  7. Sep 26, 2011 #6
    Thanks guys,
    But I've heard that James Stewart Calculus is not good for self-study, and is more of a plug-n-chug book. Calculus Made Easy is also too superficial for understanding Calculus.
    How about the books mentioned above in my original post?
  8. Sep 26, 2011 #7


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    That is the wrong characterization of his book. Many of the exercises involve some analytical thinking. Also he presents many proofs well (at least some of them presented well).

    "plug-n-chug"? No. Many of the exercises are not too dull, and require some thinking and understanding.

    "not good for self-study"? I have recently been using the single variable Calculus book by Stewart to review a few sections of the book, and this book is very acceptable for self-study review. So far, chapters 2 through 4 have good development.
  9. Sep 26, 2011 #8
    Perhaps you're thinking of Feynman, who learned from Calculus For the Practical Man.
  10. Oct 4, 2011 #9
    I'd say Kline is also a 'plug-and-chug' text. But Kline is different cause he explains things in a lot more detail (albeit, not rigorously). I use two texts, Thomas' and Kline's. If there's something I don't quite understand intuitively in Thomas', I'll look it up in Kline's. I also use Thomas' for the problems.

    If you had to choose one, I'd pick Kline's book (assuming you're going to take Calculus anyway). It's different from other Calculus texts, not rigorous but like the title suggests, it'll help you understand the subject intuitively

    I'm not sure what a standard college course covers in the US, but I think the book is mostly single-variable calculus and a bit of multivariable. It's a big book, cause most of the pages are spent trying to solidify your understanding with lots of exposition and applications . It 'holds your hand' so to speak (some people don't like that).

    Also, a detailed solutions manual is available free from the publisher upon request!
  11. Oct 4, 2011 #10
    If you want a more deep calculus book, go to either Apostol, or Spivak or Courant. My personal taste is Apostol.
  12. Oct 4, 2011 #11
    James Stewart book, despite what some people say, is good, the problem with it is that you can use it well or badly. You can skip all the proofs and still solve most problems.
    But you can study it through and learn calculus very well, but it's a very big book.

    Books like Apostol on the other hand kind of force you to understand the reasoning behind it.

    So, if you just want to learn calculus to do well on your engineering exams and maybe learn some thing deeper, stewart is the way to go. If you want to learn it as a mathematician, stick with Spivak and etc.

    Courant is a personal favorite because it not only teaches you very well but it's also presented in a more informal way, like a dialogue between him and you, I find it very good for self-study. So it may be better for a beginner, self-studying but wanting to learn more than the average non-math student.
    On the other hand, courant is a very old book, so it's not filled with pretty images, modern examples and the like.
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