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Calculus Books for self studying calculus as a beginner

  1. Jul 3, 2015 #1
    I have a knowledge of precalculus (Algebra II, basic Trig), and I was wondering what would be a few good books for self studying calculus, primarily introductory calculus (Calculus I, Single Variable Calculus).

    The books I'm currently looking at right now are Thomas and Finney, Swokowski, and Calculus: An Intuitive and Physical Approach. Are these books good choices for self study?

    I am not trying to prepare for a calculus class in college, I am just trying to self teach myself.

    So, what would be a few good books for learning calculus?

  2. jcsd
  3. Jul 4, 2015 #2
    It is hard to know how well a book will match your learning style and background before you try a few sections. A lot of the free course materials are pretty good and come with the advantage of being able to drop one book and choose another without financial penalty if it doesn't work out well or isn't helping you move toward your educational goals.
  4. Jul 4, 2015 #3
    I recommend Keisler: https://www.math.wisc.edu/~keisler/calc.html The book is free (not unimportant), and takes a very beautiful approach to calculus. It takes the infinitesimal approach which is very nice, but nonstandard. He covers the standard formalism too, but he doesn't focus on it. The infinitesimal approach is nice because it is useful in a lot of geometry and physics.
  5. Jul 4, 2015 #4
    Micromass suggestion is a solid one. However, I do not like to read books on a computer screen unless it is a novel. Of the current textbooks you own i will give my opinion.

    Thomas and Finney 9th edition is a good book, however it fails in comparison to Thomas Calculus with Anylitical Geometry 3rd ed. The latter is clearer and the proofs are intuitive and easier to understand. The author goes to great efforts to explain every line, so the reader is not left wondering were the mathematical steps came from. Diagrams to not clutter the page and are well chosen. I do like the problems in Thomas and Finn however.

    Swokloski is a theorem/ proof approach. Has a formal style. It is better than say Stewart, however the Thomas book you currently have is a lot better.

    Kline is great, however it is too verbose at times. I see it as book, one reads at leisure after learning single variable calculus from another book. In order to gain an intuitive understanding of how calculus is used as a tool in physics.

    I strongly recommend Thomas 3rd ed (it is the red book not to be confused with other 3rd ed versions of Thomas).

    Simmons also is a great book. Although Simmons can be hand wavy at times. I would use Thomas 3rd ed as the main book and Simmons as a supplement. These books complement each other nicely.

    Simmons alone for the appendix and explanation of Sequences and Series justifies its price.

    Paul's Online Calculus notes are also good for explaining a few topics. Note: these notes should be used as a supplement not as a replacement for a calculus book.
  6. Jul 4, 2015 #5
    Actually, I have looked and read a few parts of the Keisler calculus book. For me, it was a little bit difficult to understand the way he explained hyperreals and infinitesimals.
    I was thinking I may supplement that book with Infinitesimal Calculus by Henle and Kleinberg to try to understand hyperreals and infinitesimals. That is a book that is based on infinitesimals and is mainly for an introductory calculus course, but it does not fully teach calculus at all, as it does not show you how to apply methods of calculus.
    Does that seem to be a good idea?

    Link for Henle and Kleinberg: https://www.amazon.com/Infinitesimal-Calculus-Dover-Books-Mathematics/dp/0486428869
  7. Jul 4, 2015 #6
    Yes, you may supplement it with that, but in my opinion Henle and Kleinberg is harder than Keisler.
    For Keisler, the first chapter is a bit tricky, but afterwards it becomes quite straightforward. So make sure you understand the concept of infinitesimals, the rest should be easy.
  8. Jul 4, 2015 #7


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    Einstein23, the 9th edition of Thomas & Finney (the blue lighthouse one) focuses on the applications, applying the methods to problems. I would choose that if you want to focus on method. It is one of the only books to take related rates seriously and related rates are IMHO the most important concept in calculus.
  9. Jul 11, 2015 #8
    I second what Verty wrote above. I would recommend Thomas Calculus. We used it in high school and it was comprehensive. It lists out all the theorems and examples are very detailed and thought-provoking. It is also used in half of the Ivy League schools (the other half use Stewart I believe). I was able to get a 5 on the BC exam largely due to using Thomas and exempt Calculus III using it as well. You can't go wrong with either Thomas or Stewart.

  10. Jul 11, 2015 #9
    I have to disagree with that particular edition. That book is mediocre. It is extremely dumb down compared to previous editions. Generic Calculus txt.

    There is a difference between editions of thomas. The best being the 3RD ed of Thomas Calculus with Analytical Geometry or the 9th which verty pointed out. Both are great and are really cheap. They are essentially a different book. I suggest buying both and using the 3rd ed as the main txt.
  11. Jul 16, 2015 #10


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    another book to look at is Calculus, the Elements, by Michel Comenetz. I suggest you go to a library that has these books on the shelf and read until you find the one you can understand best.
  12. Jul 17, 2015 #11
    I am surprised no one mentioned Serge Lang's "A First Course in Calculus". Incredibly clear book with good problems.
  13. Jul 17, 2015 #12
    I did, however I mentioned that the 3rd ed of Thomas was better for a self study. Enough for a self study of apostol later.
  14. Jul 18, 2015 #13
    I stand corrected. I mentioned it in another post.
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