What Are the Best Books for Learning Calculus Proofs?

In summary, the conversation is about recommendations for books that focus on proofs in calculus, specifically for topics such as limit properties and the epsilon-delta theorem. The suggested books are Calculus by Apostol and Calculus by Spivak, both of which have exercises for practicing proofs. The participants in the conversation all agree that these books are helpful for learning about proofs in calculus.
  • #1
jessjolt2
16
0
Hey,

I know that questions about learning materials (like books) are supposed to be posted in the learning materials category but for some reason it is saying i cannot post there (it is saying i do not have privilieges/am trying to access administrative stuff?)...so i will just ask here

Does anyone know about any good books that focus on proofs in calculus (especially calc I and II..i haven't taken calc III yet)? Like explaining the limit properties using the epsilon-delta theorem, explaining why limit of sin x/x is 1 as x approaches 0, etc. Also would be great if the book had a bunch of exercises making you prove things.

Thanks!
 
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  • #2
You should try calculus by Apostol. It contains everything you want, and even more.
Calculus by Spivak is also good.
 
  • #3
i agree.
 
  • #4
I also agree. I learned a huge amount from Spivak. Apostal is also very good.
 

FAQ: What Are the Best Books for Learning Calculus Proofs?

What is the best book for learning calculus proofs?

The answer to this question may vary depending on personal preferences, but some popular choices among scientists and mathematicians include "How to Prove It: A Structured Approach" by Daniel J. Velleman, "Understanding Analysis" by Stephen Abbott, and "Introduction to Real Analysis" by Robert G. Bartle and Donald R. Sherbert.

Is it necessary to study calculus proofs?

If you are pursuing a degree in mathematics or a related field, it is highly recommended to study calculus proofs as they are essential for developing a strong understanding of the subject. However, if you are simply interested in learning calculus for practical applications, you may not need to focus on proofs as much.

Can I learn calculus proofs without a formal course?

Yes, there are many resources available such as textbooks, online courses, and video lectures that can help you learn calculus proofs on your own. However, having a strong foundation in basic calculus concepts is important before diving into proofs.

How can I improve my skills in solving calculus proofs?

The best way to improve your skills in solving calculus proofs is to practice regularly. Start with simple proofs and gradually move on to more complex ones. It is also helpful to study different proof techniques and strategies, and to seek help from peers or online forums if you get stuck on a problem.

Are there any online resources for learning calculus proofs?

Yes, there are many websites and online courses that offer resources for learning calculus proofs. Some popular ones include Khan Academy, Coursera, and MIT OpenCourseWare. These resources often provide video lectures, practice problems, and interactive quizzes to help you learn at your own pace.

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