For beginners, the most important thing is to understand a few points.

1 is the concept of "limit", that is, "Δ ε-\ Δ" must be studious at first, which means that this definition must be strictly followed, so that you can avoid the questions of "why does this need to be proved" and "why is this so troublesome to prove".

2. ruin your three views. See more counterexamples: continuous but non-derivable, original function exists but Riemann is not integrable, discontinuous everywhere, continuous but not monotonous everywhere, continuous but not derivable everywhere, derivable but not monotonous everywhere. ?

3, do the problem in moderation, don't brush a few Midovic, the efficiency is too low, you can do some simplified versions, first understand, then calculate. Pei Liwen's typical example in mathematical analysis is better, but it is a bit difficult. ?

Many freshmen's mathematics departments have reread Rudin's Principles of Mathematical Analysis. I think Rudin had better learn it again. Also, if you are interested in how to calculate the integral, you can read a book: Paul J. Nahin Inside Interest Integral.

4, the topic is still to be done, learning mathematics is also afraid of that kind of self-knowledge, many high school students claim to have studied mathematical analysis. In order to test yourself, after-school exercises should be done, and at least 80%-90% can be done correctly. Do more proof of understanding and make appropriate calculations.