Rigorous Calculus Textbook

Question

As a reader of I. M. Gelfand's algebra/trigonometry and A. P. Kiselev's geometry textbooks, I am struggling to find an equally rigorous calculus textbook. I've tried Stewart's "Calculus: Early Transcendentals", but it's way too (for lack of other words) fluffy. I enjoyed Gelfand/Kiselev books because of their succinctness and rigor, where the few exercises were never the same (i.e. solving 2 quadratic equations where $a$, $b$, and $c$ are just different numbers).

I'm looking into Tom Apostol's book, but there the only editions I've seen have terrible formatting and many typos. I attempted Thompson's book (the one Richard P. Feynman studied by), but there are typos even in the answer key, which confused me severely as a self-learning student new to calculus.

Also, as a bonus, but not a requirement, if the book includes some linear algebra (like Apostol's), that would be a plus.

Answer 1

I've decided on Introduction to Calculus and Analysis by Richard Courant. So far, so good!

Answer 2

Maybe you could consider The How and Why of One Variable Calculus, by Amol Sasane. Here is the publisher's homepage for the book: http://eu.wiley.com/WileyCDA/WileyTitle/productCd-1119043387.html , while a google preview can be found at : https://books.google.se/books?id=mHOwCQAAQBAJ&pg=PP1&lpg=PP1&dq=Sasane+Calculus&source=bl&ots=N9FS3lmhkF&sig=GzOv3aYbETCCaTH6LgEDKRaVdgo&hl=sv&sa=X&ved=0ahUKEwjwyrTtobXRAhVFOxoKHZJHAvkQ6AEIQDAD#v=onepage&q=Sasane%20Calculus&f=false

Answer 3

Consider getting Apostol's Calculus: Volume-I. Later, if you make it through Volume-I, you can continue with Multivariable Calculus using the Volume-II of the same writer. His books are very rigorous with the proofs.