Looking for Advanced Single Variable Calculus textbooks (NOT REAL ANALYSIS)

Question

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.

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. — Silver, Feb 25 '21 at 23:08
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. — Ted Shifrin, Feb 25 '21 at 23:08
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. — Silver, Feb 25 '21 at 23:09
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. — Paramanand Singh, Feb 26 '21 at 02:06
If you just want challenging problems, do visit the tags related to calculus here. — Paramanand Singh, Feb 26 '21 at 02:06
Some books in the answer to Joseph Kitchen's Calculus (reference) might be what you're interested in. However, their focus is mostly on rigor and proofs, not contest-level formal manipulation (which seems to be what you want), so maybe look in some of the old classics (from the 1800s) listed in my answers to Extremely “hard” books (or handouts) for undergrad studies and Tables of primitives with indication of solution method. — Dave L. Renfro, May 30 '21 at 16:36
Also, several of my answers give, or cite references to, what one might consider as "contest level" calculus manipulation stuff: Example 1 and Example 2 and Example 3 and Example 4 and Example 5 and Example 6 and Example 7 (continued) — Dave L. Renfro, May 30 '21 at 16:38
and Example 8 and Example 9 and Example 10 and Example 11 and Example 12 and Example 13 and Example 14 and Example 15 and Example 16 (continued) — Dave L. Renfro, May 30 '21 at 16:39
and Example 17 and Example 18 and Example 19 and Example 20 and Example 21 and Example 22 and Example 23 and Example 24 and Example 25 (continued) — Dave L. Renfro, May 30 '21 at 16:40
and Example 26 and Example 27 and Example 28 and Example 29 and Example 30. — Dave L. Renfro, May 30 '21 at 16:40

score 3 · Answer 1 · answered Feb 26 '21 at 08:39

3

I would like to recommend

Irresistible integrals
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)
Inside interesting integrals

answered Feb 26 '21 at 08:39

Aditya Dwivedi

1,345

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. – user6262 Mar 05 '21 at 07:21
@user1055 I think inside interesting integrals is reccomended for undergraduates only – Aditya Dwivedi Mar 05 '21 at 08:12
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) – user6262 Mar 05 '21 at 08:17
Still Inside intersting integral has very good single variable calculus problems. – user6262 Mar 05 '21 at 08:31

user0102 · Answer 2 · 2021-02-26T17:16:48.120

1

I think the MIT calculus book may fit your needs.

edited Feb 26 '21 at 17:16

answered Feb 25 '21 at 22:59

user0102

21,572

The book is a bit hard to read, but definitely will be using some of this. Thank you! – Silver Feb 25 '21 at 23:10
You are welcome ! I am glad to help. – user0102 Feb 25 '21 at 23:17

Looking for Advanced Single Variable Calculus textbooks (NOT REAL ANALYSIS)

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