As commented, the actual answer is real analysis.
Now, you say you want to know why calculus works. There are proofs in most calculus books, you know. Those proofs do explain why things work.
Finally, Spivak Calculus is an excellent calculus book, with much more emphasis on proofs than usual.
manpreet
Best Answer
2 years ago
What branch of mathematics should someone study to really understand why calculus works ? I know basic calculus but for me it seems really more like apply the tools to compute stuff. I would like to know why it is true.
Any help ?