Looking for a good problem book for PROOF-BASED integration

In summary, for those looking for a book on PROOF-BASED integration, the thread "Integrals with Proofs" on physicsforums.com offers good recommendations such as "Baby Rudin" and "Integral Calculus" by P. Shanti Narayan. These books provide theoretical and abstract integration problems that require a deeper understanding of the integral, making them a good choice for those with a strong motivation for studying analysis. Additionally, "Baby Rudin" also covers Riemann integration, while "Integral Calculus" includes illustrated examples and proofs of identities used in exercises.
  • #1
mathboy
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Looking for a good book for PROOF-BASED integration

Just to be clear, I'm not looking for a book that helps you to exercise calculating integrals, but more like problems that involve doing proofs involving integrals. Theoretical and abstract integration problems like the ones in this thread:

https://www.physicsforums.com/showthread.php?t=36033

Any good recommendation for these types of integration problems?
 
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  • #2
Integration is usually around chapter 6. If you suddenly got the interest in a deeper understanding of the integral the bad news is that it is difficult for most people to skip the first 75% of undergraduate analysis to get to the good part.
But the good news is that if you have a good motivation for studying analysis, the chances are better that you can get through the book (to chapter 6) more quickly. You should at least spend a month on it (and that would be a minimum in the case you are very good at it!).

As for a book, Baby Rudin is the one I read, so that is the one I recommend.
 
  • #3
I use 'Integral Calculus' by P. Shanti Narayan. It has lots of exercises with each exercise succeeded by Illustrated examples and proof of the identities used in subsequent excercise.
 
  • #4
Riemann integration is fairly trivial once you build the machinery. The only interesting questions (in chapter 6 of rudin, at least) are just frustrating since they're much easier with the Lebesgue integral.
 

1. What is a proof-based integration problem book?

A proof-based integration problem book is a collection of mathematical exercises that focus on proving theorems and solving problems related to integration. These problems typically require a deep understanding of calculus and mathematical reasoning skills.

2. Why should I use a proof-based integration problem book?

Using a proof-based integration problem book can help you improve your understanding of integration and develop your skills in mathematical proofs. It can also be a useful resource for students studying calculus or other advanced mathematics courses.

3. How do I choose a good proof-based integration problem book?

To choose a good proof-based integration problem book, look for one that has a variety of problems at different levels of difficulty. It should also have clear explanations and solutions for each problem. Additionally, consider the author's credentials and reviews from other users.

4. Can I use a proof-based integration problem book for self-study?

Yes, a proof-based integration problem book can be a great resource for self-study. However, it is important to have a strong foundation in calculus and mathematical proofs before attempting to work through these problems on your own.

5. Are there any online resources for proof-based integration problems?

Yes, there are several online resources available for proof-based integration problems. These can include websites with practice problems and solutions, video tutorials, and even forums where you can discuss solutions with other students and experts.

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