Calculus course written by F.M. Fichkingolz. This book is a classic of mathematical analysis, which can be said to be difficult and thorough, without too many exercises. It is a set of high-level textbooks. It can be said that a considerable number of modern mathematicians in China have been trained by this textbook, which is worth reading for two or three years.

The second book is the mathematical analysis of East China Normal University, and this textbook should do the questions. I can only tell you that it is impossible to master any knowledge, especially mathematics, without doing problems.

The third book is Chen Jixiu, Fudan's mathematical analysis, which is very distinctive. The content of the textbook is comprehensive and not out of touch. In the preface, it is said that Teacher Su has done about 10,000 calculus exercises, and now it is mathematical analysis, in the traditional sense.

The fourth is the mathematical analysis of Zorich, who is also Russian. This is an innovation, which is very difficult, especially the supporting exercises. This is not easy to do. If you do well, you will be a super-high-level undergraduate, which will lay the best foundation for your future research and application.

Fifth, the typical problems and methods in Pei's mathematical analysis are difficult and classic problems. We must do it in a down-to-earth manner. If we want to learn well, we should do it more often.

The sixth book is Qin Xin's Eight Lectures on Mathematical Analysis, which is the only book on basic mathematical analysis written by a great mathematician (really good). The content is very detailed. It's wonderful. You must read it after learning it, so as to eliminate all previous misunderstandings about mathematics, or you will be laughed at. After reading this book, maybe you won't ask such a question now, and you won't ask what the essence of calculus is, because there is no answer to this question, or you don't ask it like this. I feel that you still haven't learned enough, so I won't say much here. See for yourself.

Also, there are so many books, just choose one of the first four books to read one, and don't ask for more, improve. Also, be sure to do more questions, that is, the fifth book, which contains very good questions, which is definitely different from what you are doing now. Don't do that skill when you do the problem. There is no need to practice integral all day. You can only learn skills, not math and calculus.

By the way, I don't recommend the book of Peking University, because it is not very clear, and the system needs you to read it realistically. Almost equal to relearning.