Which course will provide me with a rigorous re-introduction to calculus?

Question

I took the standard calculus 1, 2, and 3 and was very dissatisfied with all the ambiguity. I especially have bad memories of very ambiguously defined differentials. Which course starts from the basics and proves everything rigorously? I won't be taking the class soon for any such course, but I plan to buy the book and study it myself.

Is the course I'm looking for called real analysis? Are there any prerequisites I should take a look at, especially since I am not familiar with most of the logic notation/symbols? What would be a good textbook for me to learn from by myself?

Answer 1

Two things required to learn Real Analysis

$1.$ Love for Mathematics

$2$. Logical Thinking which you will develop more as time passes.

Get the book Introduction to Mathematical Analysis by Tom. M. Apostol as it is a very detailed book with tons of exercises and examples.

Now Enjoy...

Answer 2

Prof. Leonard's lectures on Calculus 1 and 2 are awesome. here. Believe me, you will never forget calculus after watching his videos. Good Luck!

Answer 3

Pice of advice: Don't even touch Rudin's "Principles of mathematical analysis" before you reach Riemann-Stiltjes integral. That book is just painful. But R-S integral is done very well, it was very helpful at my second semester at uni.

Answer 4

After reading your post.. I feel that you need a good introductory book that can develops your logical thinking as well as love in mathematics . So I'll suggest you to follow 1) real analysis by Terrence Tao - volume 1 2) mathematical analysis by Goldberg after reading upto continuity from it.. You go through metric spaces then you try tom M. apostol its a great book .. N you can also try rudin.. Its a good book to read..