3

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?

nihaljp
  • 161
  • 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. – spaceisdarkgreen Jun 10 '17 at 06:56
  • Is there any book that covers everything from basics to the top? – nihaljp Jun 10 '17 at 06:58
  • I heard someone say that Thomas' book covers all of it – nihaljp Jun 10 '17 at 06:58
  • 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. – Paramanand Singh Jun 10 '17 at 07:35
  • 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. – Andrew D. Hwang Jun 10 '17 at 09:23
  • I recently answered a question similar to yours: https://math.stackexchange.com/questions/2315374/how-can-i-improve-my-problem-solving-critical-thinking-skills-and-learn-higher-m/2315457#2315457 – user49640 Jun 10 '17 at 21:23
  • There are different kinds of calculus books. The ones by Spivak and Apostol are very good on both theory and practice. Others, like Stewart's and Thomas's books, are not good for learning theory, but they are much easier if you're only interested in practical applications at a relatively low level of difficulty. If you want to study from a non-rigorous calculus book, then Basic Mathematics by Lang or Algebra and Trigonometry by Axler will be sufficient preparation. If you want to study from a book like Spivak, you may find that you need additional preparation. The books that I linked to... – user49640 Jun 10 '17 at 21:33
  • in my previous comment are good preparation. However, some highly able students will find that they don't need much additional preparation after basic algebra and trigonometry, and they are able to learn from a book like Spivak directly. This is highly variable. – user49640 Jun 10 '17 at 21:35
  • Guys you made me confused, let me tell something about myself. I'm not a math genius, am average but I know I could excel at it with enough practice and if I stop being lazy. As i said in the question I took khan academy's course in precalculus. So I know about some trig and conic sections. So finally, which book should I read? The current options are A course of pure mathematics(is it beginner friendly though?), Calculus made easy, Thomas' calculus or any other one? – nihaljp Jun 11 '17 at 04:56
  • @nihaljp I don't know what Khan Academy's courses are like. I don't know if someone who has learned math from videos can have the same level of proficiency as someone who has done it using a book and doing problems. If you believe that you've learned precalculus reasonably well that way, here is what I can suggest. Try starting calculus with Calculus I by Marsden and Weinstein. They have some self-tests at the beginning to tell you whether you need to go back and take an algebra class, read the review sections in their book, or jump straight into calculus. Their book can be downloaded... – user49640 Jun 12 '17 at 09:25
  • legally and for free from the Caltech website here: http://www.cds.caltech.edu/~marsden/volume/Calculus/ Their book is not a rigorous, theory-focused book like Spivak, but it is reasonably good for applications. I like it much better than Stewart.Go to the "orientation quizzes" on page 13. – user49640 Jun 12 '17 at 09:28
  • Does this answer your question? What books are prerequisites for Spivak's Calculus? –  Jul 02 '21 at 06:49
  • Does this answer your question? What are the prerequisites to smoothly reading Spivak's "Calculus"? – user33704 Oct 04 '23 at 00:54

1 Answers1

1

If you're curious about theory, then use Spivak. But here are some drawbacks. Although he proves everything, some of his proofs are too slick. He develops the theory of differential and integral calculus BEFORE introducing the trigonometric, exponential, and logarithmic functions so that their properties are easier to derive. But this order does not match history! Spivak fails to motivate them, and how mathematicians figured these functions out. I prefer

James Stewart's Calculus doesn't focus on theory, but its appendices prove some theorems. If you like physics, try Bressoud's Second Year Calculus: From Celestial Mechanics to Special Relativity.

user46157
  • 21