Book recommendation for "intermediate level"problem book on calculus.

Question

I finished calculus books like Thomas and currently reading a book on advanced calculus and another one on real analysis.

I noticed recently that I don't solve enough "hard problems". I usually just solve the exercises on my books. so I figured that I need problem book(s) on calculus.

I want a book(s) that has many exercise on calculus topics like Limits(without l'hopital) ,derivatives, integrals , series and sequence , multiple integrals etc... I also want them to be challenging and interesting problems and not "too hard" I consider myself on an intermediate level as the advanced exercises on Thomas book seems very easy to me, I also don't want "forward substitute questions" which is plugging numbers in formulas or straight forward use of a theorem or equation as I want to increase my problem solving skills.

I will appreciate any suggestions ,thank you in advance .

Answer 1

My recommendation would be "Problems in Mathematical Analysis" by Demidovich. The book was written in Russian, but you can find the English translation online. In total there are over 3,000 problems with solutions in the book ranging from complete beginner problems to intermediate/advanced.

Answer 2

The following might be helpful:

Problems and Theorems in Analysis I and Problems and Theorems in Analysis II by G. Pólya and G. Szegö

This two volume book is a problem based classic (first edition from 1925). It is a highly inspiring source of many interesting problems in different fields of analysis together with detailed solutions. The AMS-review might be interesting.

Answer 3

GN Berman, A Problem Book in mathematical analysis is your best bet, no other book comes close for questions related to calculus but not analysis. https://www.scribd.com/document/557039546/A-Problem-Book-in-Mathematical-Analysis-G-N-Berman-1977#

Answer 4

I recommend you check out these books;

1. "Calculus for JEE (Advanced) - Cengage" by G. Tewani, see here

The above book is for the specific exam known as the JEE advanced, however the book does come with intermediate level calculus questions.

2. For Multiple Integrals and other calculus content, I recommend "Higher Engineering Mathematics" by B.S Grewal see here and "An introduction to Harmonic series and logarithmic integrals" by Ali Shadhar - see here.

3. "Problems in calculus of one variable" by I.A Maron -see here

4. "Black Book" by Vikas Gupta - see here

Also, to solve "Hard" problems, the best task would be to solve math contest papers, there are plenty exams and their archives you can find online.

You can find online pdfs for them. .

Answer 5

I recommend you check out (Almost) Impossible Integrals, Sums, and Series written by Cornel Ioan Valean. Instead of paying for the book, you could click on the link and get it in PDF form. The way the problems are written is unique in that there is a chapter for questions, a chapter for hints, and a chapter for solutions.

Answer 6

Sounds like you may be ready for Rudin's "Principles of Mathematical Analysis" -- it has a reputation for having challenging questions but within a limited domain in calculus -- may be good for grounding what you already know.

If that looks too intimidating then I'd recommend Ross' "Elementary Analysis" as a good intro to rigorous proofs in analysis.

One other book that may be helpful is Advanced Calculus by Buck -- it has a more problem-set feel but covers a lot of ground.