Best Books to Learn Calculus in 2021

[Alfin Abu]

I have just started to learn calculus.Can you suggest the best book to grasp the concepts and to teach myself the true calculus.

 

[fresh_42]

I have just started to learn calculus.Can you suggest the best book to grasp the concepts and to teach myself the true calculus.

Well, you really should have explained a bit where you currently stand and which goals you have. For the "gap" between school and college or university, I usually recommend the books on https://openstax.org/subjects which are free. They might contain stuff you already know, but you can skip these parts, and have many exercises for practice. My recommendation would be a different one, if you, say, want to build a personal library or study calculus in deep, which again would depend on your goals: physicists might have different emphases than statisticians. However, for the basic concepts the books on OpenStax are fine and cheap.

 

[jedishrfu]

There's Keisler's book on Calculus that uses the hyper-reals approach in addition to limits. Hyper-reals allow you to evaulate limiting expressions in an algebraic way.

https://www.math.wisc.edu/~keisler/calc.html

and there's the collection of math videos at www.mathispower4u.com on Calculus 1,2,3 and other related math from high school to first year college. Each video is a short 10 minutes.

 

[Scrumhalf]

I have not had personal experience with reading it, but a lot of people whose opinion I respect have suggested "Calculus Made Easy" by Silvanus Thompson. I flipped through it at the bookstore and it does seem like a nice introduction to the subject, emphasizing the concepts rather than the "tricks" on how to solve a particular integral or whatever.

 

[mathwonk]

I may be wrong, but as I read the question, the OP wants a deep grasp of calculus concepts, including theory, for which my best recommendations are still Courant, Spivak, and Apostol.

 

[Scrumhalf]

I may be wrong, but as I read the question, the OP wants a deep grasp of calculus concepts, including theory, for which my best recommendations are still Courant, Spivak, and Apostol.

He did say that he was just starting off, which is why I think that Spivak or Apostol would be too much. I really like the Silvanus Thompson book. I picked up a copy myself yesterday and it is really quite brilliantly written. It is an excellent introduction to the concepts.

 

[mathwonk]

Yes I am familiar with that book, first encountering it in 1960, when a friend who was also taking a spivak level course showed it to me (spivak's book not yet having been written). I later bought a lovely leather bound copy from many years ago and cherished it until i gave it as a present to a young student struggling with calculus. I still own a paperback copy of the newer edition that Martin Gardner produced, which to me has less charm than the original. I must say however that in all those years I never really learned anything from it, but greatly enjoyed the lighthearted attitude and modesty of the author, who was apparently a fellow of the royal society. I do not recommend it to anyone who actually wants to understand anything about calculus though. (But I see I did recommend it way back in post #8 of my thread "Who wants to be a mathematician?", now retitled "Should I become a mathematician?" for some reason, in the academic guidance section.) In that same post, I recommnded another book I think would be better to actually learn from as a beginner, namely "lectures on freshman calculus" by Cruse and Granberg, if it can be located.

Well I just located one on Amazon for $859, that's right, (not a typo, not mine anyway), and one on abebooks for about $40, for a book worth maybe $25. Maybe that used book dealer asking $859 was bought out by Martin Shkreli? no i guess in that case it would have been $1250.