Does anyone know any other good advanced calculus textbooks that have much more advanced or rigorous problems?

Textbooks like: Spivak, JEE Main, Advanced Calculus Explored, Problems in Mathematical Analysis (Demidovich), AoPS Calculus, Examples & Problems in Advanced Calculus, Advanced Calculus of a Single Variable, I.A. Maron, etc.

Textbooks that aren't what I'm looking for: Rudin, Apostol, Courant, Folland, G.H. Hardy, etc.

Again, I'm not looking for Real Analysis, I'm looking for like a very "honors" type calculus book without proofs. Please, no proofs, just a calculus book with challenging or advanced problems.

I tried looking through other common Mathexchange questions and they're just proofs and answer the same exact thing that I'm not looking for.

  • $\begingroup$ The majority of olympiads don't do calculus problems, and most undergraduate contests are just proofs or real analysis. But mainly I'm looking for more textbooks that teaches those calculus contest problems and advanced/rigorous kinds of problems like AoPS and "Advanced Calculus Explored" does. $\endgroup$ Feb 25, 2021 at 23:08
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    $\begingroup$ Spivak is all about proofs, and yet you list him. I taught the AoPS Calculus course a few years ago and found the exercises in that book very uninspired. You should probably take a standard university calculus book (like Edwards & Penney, Rogowski, Stewart, etc.) and find the advanced/challenging problems in them. $\endgroup$ Feb 25, 2021 at 23:08
  • $\begingroup$ Actually, Spivak has a lot of fun exercises that does not require proofs. Yes there are some chapters and topics that are proofs, but I don't use those sections. $\endgroup$ Feb 25, 2021 at 23:09
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    $\begingroup$ Why are you so against proofs? Problem solving uses proofs implicitly in the sense that the confidence you have in applying some technique is based on the proof that the technique works and is valid. $\endgroup$
    – Paramanand Singh
    Feb 26, 2021 at 2:06
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    $\begingroup$ If you just want challenging problems, do visit the tags related to calculus here. $\endgroup$
    – Paramanand Singh
    Feb 26, 2021 at 2:06

2 Answers 2


I would like to recommend

  1. Irresistible integrals
  2. Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis(This does have some multivariable stuff but it is challenging book to solve, especially the challenge problems)
  3. Inside interesting integrals
  • $\begingroup$ Both Irresistible Integrals(By Victor Moll) and Inside intersting integrals(By Paul J Nahin) Contains many many integrals way beyond single variable calculus syllabus. Both are mostly recommended For Graduate students. $\endgroup$
    – user6262
    Mar 5, 2021 at 7:21
  • $\begingroup$ @user1055 I think inside interesting integrals is reccomended for undergraduates only $\endgroup$ Mar 5, 2021 at 8:12
  • $\begingroup$ Inside Intersting integrals has somewhat less use of multivariable calculus than Irresistible integrals but still It can't be fully recommended for single variable calculus(As OP asks) $\endgroup$
    – user6262
    Mar 5, 2021 at 8:17
  • $\begingroup$ Still Inside intersting integral has very good single variable calculus problems. $\endgroup$
    – user6262
    Mar 5, 2021 at 8:31

I think the MIT calculus book may fit your needs.

  • $\begingroup$ The book is a bit hard to read, but definitely will be using some of this. Thank you! $\endgroup$ Feb 25, 2021 at 23:10
  • $\begingroup$ You are welcome ! I am glad to help. $\endgroup$
    – user0102
    Feb 25, 2021 at 23:17

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