1. The author of Calculus Course and Principles of Mathematical Analysis, Fechkin Goltz. The previous book, three volumes in Russian and eight volumes in Chinese; The latter book consists of two volumes in Russian and four volumes in Chinese. This book is a classic. In fact, even the author admits that Calculus Course is not suitable as a textbook, so he gives a set of books that can be used as a textbook, which can be said to be a simplified version. I believe that until today, many teachers will still look for "calculus course" when they start classes, because there are too many examples in it. If you want to lay a solid foundation, you can consider making the example an exercise with an answer. Of course, not every problem can be done this way. Undoubtedly, this set of books represents the highest level of dealing with the contents of mathematical analysis in a classical way (referring to the concept of not introducing real variables and functional).
2.Apostol's Mathematical Analysis is a relatively complete textbook in the west (western Europe and the United States), which talks about Lebesgue integral, but it is not good.
3. The Principles of Mathematical Analysis by 3.W.Rudin (Chinese translation: Rudin's Principles of Mathematical Analysis) is a very good book. Later, we can see that this gentleman has written a series of teaching materials. The presentation of this book (referring to the use of some symbols and terms) is also very good. After studying Advanced Mathematics, you can find a book with advanced calculus level in the west (especially Rubin's book), which can basically meet the requirements of the general mathematics department. Speaking of Advanced Calculus, there is a book under this title that can also be read, that is, Advanced Calculus by L.Loomis and S.Sternberg, which is still very high-minded. After all, it is a textbook of Harvard.
4. Mathematical Analysis (Peking University Edition) Fang, Shen Xiechang, etc. Mathematical Analysis Exercise Set and Mathematical Analysis Exercise Book. This set of textbooks compiled by Peking University is OK, but the best one is about two exercises. As we all know, Jimidovich is not very suitable for students majoring in mathematics. After all, most of them are calculation problems. By contrast, this set of problem sets of Peking University is much better, and it is really worth doing. That exercise textbook is also a very interesting book, including solutions to some rather difficult exercises.
5. Klebauer's "Mathematical Analysis". I remember that it is an analysis book in the form of exercises, and the topic is also very good.
6. Zhang Zhusheng's "New Lecture on Mathematical Analysis" (* * * three volumes). Personally, I think this is the latest mathematical analysis textbook written by China people. Teacher Zhang worked really hard to write this book, and wrote it back and forth for almost five times. Disabled people like him pay much more for doing such a thing than ordinary people, so that he himself quoted "Dou Yun's author is crazy, who can understand the taste" in the postscript. In this set of books, the treatment of many materials is quite different from the traditional methods. This is well worth reading. The only regret is that according to Mr. Zhang himself, Peking University Press found a printing factory that didn't know how to print math books at all, so the typesetting was not very good.
Some of the following books may be novel.
7b。 V.A. zorich's Mathematical Analysis, a textbook of Moscow University. Springer has published an English version, which is a set of quite good teaching materials, especially exercises.
8. Didong's Fundamentals of Modern Analysis (Volume I) is the first volume of a set of textbooks compiled by people in the 20th century, and the terminology used is quite profound. Maybe it will be better for the function to look back after learning about the real change in the future.
9. Say a few words about the high number of non-mathematics majors. It is highly recommended that some math books written by French people be included in Ritu. Because in the French higher education system, for the best students, studying for two years after graduating from high school is not divided into departments, so their advanced mathematics (such as the first volume of Advanced Mathematics by Academician J. Diximir) or General Mathematics is basically between the mathematics courses of the domestic mathematics department and the physics department.
10. Add a technical question. For the convergence of function series, uniform convergence is sufficient, but not necessary. There is a necessary and sufficient condition called "sub-uniform convergence", which is mentioned in Calculus Course. It seems that its detailed discussion can only be found in Lucin's On Functions of Real Variables.
1 1. Mr. Hua's Introduction to Advanced Mathematics, Volume 1. This set of books (in fact, the original plan has not yet been completed) is a handout distributed by Mr. Hua to undergraduates in the early 1960 s with the help of Mr. Hua. At that time, they did an experiment, that is, a professor was in charge of the teaching of the first students, so Mr. Hua's book actually involved many aspects (incidentally, the other two were Mr. Guan and Mr. Wu Wenjun who were in charge of the first students). Also out of
Just try it. There are some things in Mr. Hua's book that do not belong to traditional teaching content, including some applications. You can read it.
12. Mathematical Analysis by He Chen, Shi Jihuai and Xu Senlin. This should be HKUST's textbook. Although it doesn't seem to have much impact, I like it very much. It's the first time for senior one to use this set of books. I feel very organized and practice well. The printing quality is also quite good.
13, Mathematical Analysis by Zou Ying.