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Can someone recommend a Calculus book that emphasizes and clarifies the intuition behind the theorems to the maximum, while at the same time is fairly rigorous?

During my bachelor's in computer science, we used Stewart. I didn't like it as it was far from rigorous. Besides, I don't just want a lot of numerical examples, but rather to clarify the concepts, with a minimum number of examples.

I have read about 1/3 of Spivak, and to me it's an introduction to analysis, not Calculus. Although I understood almost all what I read in Spivak, I felt that my intuition wasn't strengthened and that he could have gave more insight to the ideas and concepts, not just mechanical proofs, I felt I didn't get the big picture. (For example, he gave no intuition behind the chain rule where in fact there is a good one, also he barely mentioned Riemann sums, which is important to intuition in my humble opinion)

So does such a book exist?

N. F. Taussig
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Loai Ghoraba
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  • I've read much of Simmons' Calculus, and he is explicit about writing the textbook to highlight the historical development of topics and the intuition behind the concepts, and I think he succeeds on both counts. – RobinSparrow Mar 22 '24 at 19:55
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    "Calculus 2nd Ed." Volumes 1 and 2, Tom Apostol, 1966. – user2661923 Mar 22 '24 at 20:34
  • Would you care to explain what is a “good intuition behind the chain rule”? – user1551 Mar 23 '24 at 07:34
  • @user1551 As I read it in Stewart, if you think of the derivative as the physical rate of change, then the chain rule is indeed natural, see also: https://math.stackexchange.com/a/62747/573453 – Loai Ghoraba Mar 23 '24 at 19:19

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Short calculus, Serge Lang. There are no epsilon-deltas, but this does not imply that the book is not rigourous. Lang learned this attitude from Emil Artin, around 1950.

Stéphane Jaouen
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