I am a 15-year-old kid with no prior knowledge of calculus, although I learned some precalculus from Khan Academy. But I decided to move to books and many people on the internet are recommending Spivak's calculus, Stewart's Calculus and Thomas' Calculus. Which one is better for me and are there any other prerequisites?

  • $\begingroup$ Spivak is a great book, but it's rigorous and proof-based so if you don't have any experience with that it could be too hard for a first book. I'd grab one of the other two. If you've been good at learning math from reading textbooks thus far you should continue to have good luck with either of those. You just need to know typical precalc stuff... trig functions, logarithms, etc. If you decide to go on to learn analysis Spivak will be a nice bridge that way. $\endgroup$ – spaceisdarkgreen Jun 10 '17 at 6:56
  • $\begingroup$ Is there any book that covers everything from basics to the top? $\endgroup$ – nihaljp Jun 10 '17 at 6:58
  • $\begingroup$ I heard someone say that Thomas' book covers all of it $\endgroup$ – nihaljp Jun 10 '17 at 6:58
  • $\begingroup$ There is no single book that covers from basics to top, because the top is ever growing. In my opinion you should go for Hardy's A Course of Pure Mathematics which is written in an informal style and especially suited for self study. I read it when I was 16 and it should work for you also. Spivak is more in the formal style. Both Spivak and Hardy's books are available online if you search enough. $\endgroup$ – Paramanand Singh Jun 10 '17 at 7:35
  • $\begingroup$ To echo Paramanand, the Mathematics Bookshelf at Project Gutenberg has a number of gratis pre-1923 books typeset in LaTeX (typos fixed, some modernized notation), including Sylvanus Thompson's Calculus Made easy (MacMillan 2nd Ed. 1914) and G. H. Hardy's A Course of Pure Mathematics (Cambridge 3rd Ed. 1921). A few of these have been converted to HTML5 by the Sayahna Foundation from the Gutenberg sources. $\endgroup$ – Andrew D. Hwang Jun 10 '17 at 9:23

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