Finding Calculus Books for Understanding Asymptotes

[fgyamauti]

Hi, I´m trying to find out some calculus books that explain asymptotes (not only 10 lines, someone that explains formally and intuitivelly too) and demonstrate formally every theorem (including Weiertrass-Bolzano, Cauchy, Weiertrass, Lagrange, Roller theorem and L´Hopital´rule absent more advanced concepts in analysis, like compactness). I tried some analysis books, like Rudin, Terence Tao, however they are too advanced for me.
Furthermore, I´m searchig for some book that explains how to prove formally, because I´m having troubles to deal with the mathematical formalism. Any Advice?
Thanks.

 

[micromass]

Hi fgyamauti

What you are looking for is actually quite difficult. Books that prove every theorem tend to be quite rigourous and difficult and they don't tend to give much intuition. On the other hand, books that supply a lot of intuition, will certainly not prove anything.

I quite agree that Rudin is too much, that book already deals with real analysis, which is calculus++.

Here is some advice that I can give you:
1) Go check out the videos of khan academy. They're great in building intuition. They won't prove anything of course, but you first need intuition before you can do your proofs.
2) Check out the calculus books by Spivak or Stewart. I think that these books could be good for you. Spivak proves everything, but I wouldn't immediately call this book "easy". Check them out and let us know what you think of them!

 

[zooxanthellae]

I second micromass's suggestion of Spivak's Calculus. You might not be able to do some (or even many) of the problems on your own if this is your first time with proofs (proofs are, in my experience, aren't easy to self-study), but Spivak is certainly pretty rigorous but accessible even to a person who is seeing Calculus for the first time. Many universities use Spivak as a stepping-stone to Rudin.

I am finishing up a first-year Honors Calculus sequence that uses Spivak and have been pretty pleased with it.

 

[fgyamauti]

Hi, thanks for the answers.
I´ve already tried Spivak, but it does not talk about asymptotes. I´ve tried Apostol too, however I want something more formal (like russian books, Demidovich for instance). I will try analysis next semester, so I have to understand those formal concepts and learn how to prove rigorously by myself.
Thanks again.

 

[Skrew]

You want an introductory analysis book.

Abbots, Understanding Analysis or Ross's, Elementary Analysis or Lays Introduction to Real Analysis.

Also a book can't both provide proofs and not be mathematically formal.

 

[Chaostamer]

I can't say for sure since I've not finished reading the book, but Fitzpatrick's "Advanced Calculus" is fairly accessible, so it might have what you're looking for.

 

[QuarkCharmer]

I have a difficult time reading through Spivak's "Calculus". Many here suggested I pick up this book, https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20 and it's making the Spivak book a bit more understandable.

 

[fgyamauti]

Thanks. Any other suggestions about books related to demonstrations, proofs? How to improve it? Techniques about proving ?