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How to learn mathematical analysis
Arrangement of recommending reference books for mathematics majors

Starting with mathematical analysis:

Mathematical analysis is the most important course in the department of mathematics, and often a point will lead to future courses, which is the basis of most courses in the department of mathematics in the future. It is also a difficult course for beginners. The difficulty here is mainly the inadaptability to the ideas and methods of mathematical analysis. In fact, it will become easier with the deepening of the course. You will feel much more relaxed when you review for the postgraduate entrance examination in senior three. Mathematical analysis in the Department of Mathematics is taught in three semesters, with 15 credits and 270 class hours. Delete the difficult part of mathematical analysis and add some simplest ordinary differential equations, that is, advanced mathematics for non-mathematics majors in China, or the high number part of mathematics one.

Mathematical analysis book:

A reference book is basically enough for beginners to choose a textbook. 1 1 is highly recommended, and 1, 2, 7, 8 is recommended. In addition, it is suggested to take a look at16,20 that cannot be used as a textbook.

Written by China people themselves:

1 Mathematical analysis Chen, Jin Fulin, Zhu Xueyan, Ouyang Guangzhong (the new version is in reverse order).

It should be a concise course of mathematical analysis from Qin Xin, which is the longest and most used book in the department of mathematics, and also the designated teaching material for graduate students in most schools. I used the second edition when I was a freshman, and now I have the third edition, but there are still some typographical errors in it, but Dick can tell at a glance. Reference answers to after-class exercises can be found online, but it is recommended to do it yourself. Many economic engineering schools also use this book. Some places are difficult to understand and lack one or two knowledge points compared with other books. For example, it seems that stolz theorem is not mentioned, and the definition of real number is not clear. But it is still a good book. It must have some advantages to be widely used.

2 "Mathematical Analysis" Mathematics Department of East China Normal University

Teachers use the most books in class, and the exercises after class are well arranged, which is also a lot of books used for postgraduate entrance examination. At the end of the textbook, I talked about some calculus on manifolds. Although it is a teacher-training book, it is a little less difficult than the last one, but it is still worth reading.

3 "Mathematical Analysis" Chen Jixiu is waiting

The above three books are the three most used for postgraduate entrance examination.

4' Mathematical Analysis' Li Chengzhang, Huang Yumin.

It is a series of mathematical analysis volumes of Nankai University. This set of teaching materials is often used and is generally good. It is the teaching material of various courses in mathematics department after the reform.

5 Liu Yulian "Mathematical Analysis Lecture"

A book recommended by the math analysis teacher, but I didn't read it. A new version should be released recently, like the fifth edition? Version, originally a correspondence teaching material, should be written in detail and easy to understand. Don't look down on correspondence teaching materials. In fact, the first communication was done by the best professors. It's far away to elaborate, just have a brief look.

6 "Mathematical Analysis" Cao Zhijiang is waiting

The textbooks in the mathematics base of Inner Mongolia University emphasize the realization of physics, which will lay a good foundation and will not be blindly extended to N dimensions. Suitable for beginners. Textbooks of national excellent courses.

7 "New Lecture on Mathematical Analysis" Zhang Zhusheng

It is recognized as a novel book, and there is no practice after class. The treatment of materials is quite novel. The author has passed away.

8 "Mathematical Analysis Course" Chang Gengzhe and Shi Jihuai

The textbooks of Chinese University of Science and Technology are extremely difficult to exercise after class.

9 Xu Senlin "Mathematical Analysis"

With the above one out of a door, Tsinghua University textbooks. Students with good level can try it. This book is very thick and looks slow.

10 Deng Dongao's concise course of mathematical analysis

It is also a book that can be read often. The author has passed away. Textbooks of national excellent courses.

1 1 Xu Shaopu's Mathematical Analysis Course, Nanjing University Press

These books should be enough, so I won't list the others one by one. Choose any one as a teaching material.

Foreign textbooks of mathematical analysis;

1 1 fik hin Geerds's calculus course.

The first masterpiece of mathematical analysis, don't be scared by its voluminous works. I started reading in the first half of senior one, and found that I wrote clearly and read quickly. I strongly recommend you to have a look, even if you buy a collection. It is not recommended to look at the price when buying books, but to read books. A good textbook can lay a solid foundation and affect future study.