1 and part of the third edition have been appropriately adjusted;

2. Some changes have taken place in the order in which the basic theorems of real number theory appear;

3. The concept of inner closed uniform convergence is added, and the related contents are adjusted;

4. In order to facilitate students' study, some examples with high skill requirements have been added.

Extended data

Compared with the third edition, the fourth edition of mathematical analysis in China Normal University has not changed much. Since the first edition was published in 1980, it was published in 1990 and 200 1.

The second edition is very mature, and there will be no major changes. The fourth edition is only a partial deletion of the third edition.

The content of the book is more substantial and the structure is more stable, which is conducive to improving the quality of teaching. The contents of this revision (relative to the third edition) mainly include:

(1) In order to solve the problem that the limit theory in Chapter 7 is too concentrated and lagging behind, in Chapter 2, we first prove "arbitrary sequence".

Firstly, the compactness theorem is obtained. Using this tool, the completeness of continuous functions on closed intervals is obtained.

The fourth chapter can prove the quality.

(2) In view of the fact that many colleges and universities no longer offer mathematical analysis problems separately, some slightly difficult examples have been appropriately added in this revision.

Ask questions to help students develop their ability to solve problems.

(3) In the chapter of function term series, the concept of "internal closed uniform convergence" is added, which is beneficial to the in-depth discussion of uniform convergence. (4) The relationship between the two curves (surfaces) is changed from "selected content" to "required content". (5) In chapter 2 1 "Proof of transformation formula of multiple integral variables under general conditions", the author gives a new method which is different from the previous method.

(5) In chapter 23, the contents about vector function differentiation in the first three sections are retained, and the original G4 (outer product differential form and generalized S) is deleted.

And the title of this chapter is changed to "Vector Function Partition".

Like the first two editions, marking "mouth" means the end of proposition proof or example solution; For the chapter "*", teachers can use it flexibly in teaching.

Flexible choices make books more suitable for the needs of all levels.

Mathematical Analysis, Fourth Edition, Volume 1