The "line generation king" who is widely trusted by students, the leader of the "golden team" of Wenhai's postgraduate mathematics counseling, and the leader of Beijing's mathematics marking group, the real "line generation" is also affectionately called "modern locomotive" by students. Professor, Department of Applied Mathematics, Tsinghua University, Vice Chairman, Mathematics Research Association, Beijing Higher Education Society. The most famous linear algebra tutor in graduate mathematics in China has participated in the revision of graduate mathematics teaching syllabus and the proposition of national mathematics examination for many times, and was received by the leaders of the Ministry of Education. Teacher Li Yongle compiled many reference books on mathematics for postgraduate entrance examination, which enjoyed a high reputation among candidates and were out of stock year after year. Teacher Li knows the questions and the key points of the exam like the back of his hand. His thinking of solving problems is extremely flexible, his counseling is highly targeted, his effect is excellent, and his achievements are remarkable, which is well received by the majority of students. In recent years, the Comprehensive Book of Mathematics Review for Postgraduate Entrance Examination, Guidance Notes on Linear Algebra, 400 Questions of Mathematical Simulation, 660 Questions of Mathematical Basis, and Final Sprint of Mathematics 135, edited by him, have been recognized as the authority of mathematics review by the majority of candidates and are deeply loved by the majority of students!

In order to make students who take the postgraduate entrance examination review mathematics comprehensively in a relatively short period of time, reach the required mathematical ability in the master's study stage, improve the level of postgraduate entrance examination, and be selected by the state with qualified mathematical results, the author has thoroughly studied the characteristics and trends of postgraduate entrance examination propositions in recent years according to the requirements and the latest spirit of the mathematics examination syllabus formulated by the Ministry of Education, and combined with the author's years of mathematics marking and counseling experience in most cities across the country, compiled this book for postgraduate entrance examination mathematics review and its supporting equipment. When writing, the author pays special attention to the combination with the students' reality and the requirements of postgraduate entrance examination.

Each chapter of this book consists of the following four parts:

First, content summary and tips on important and difficult points-the purpose of writing this part is mainly to make candidates clear about the key points, difficulties and common test sites in this chapter, and to make candidates clear about the relationship between various knowledge points, so as to have an overall understanding and grasp of the contents of this chapter.

2. Explain the main points of exam knowledge-this part comprehensively expounds the knowledge points required by the syllabus, analyzes the key points, difficulties and common test sites of the exam, points out the common problems and mistakes of previous candidates when using basic concepts, formulas, theorems and other knowledge to solve problems, and gives corresponding precautions, so as to deepen the understanding and correct application of key contents such as basic concepts, formulas and theorems.

Third, common questions and their problem-solving methods and skills-this part summarizes the common questions in the unified examination over the years, summarizes the problem-solving methods of various questions, and pays attention to multiple solutions to one question, so as to broaden the candidates' problem-solving ideas, make the knowledge they have learned comprehensive and solve problems comprehensive and flexible.

Fourth, the question training and solution-this part selects the right amount of self-test questions and has detailed answers. Only a proper amount of practice can consolidate the knowledge learned, and math review must be done. In order to make candidates better consolidate their knowledge and improve their practical problem-solving ability, the author specially optimized and designed practical training questions similar to the real questions to be written in the book "400 classic questions of fully simulated mathematics for postgraduate entrance examination" for candidates to choose.

What needs to be emphasized in particular is that this book is written for candidates who apply for math 1. It is a new attempt, and I hope it will be helpful for the majority of candidates to prepare for the exam.

This book is a good teacher and friend for candidates who take the postgraduate entrance examination, and also a valuable reference book for students in various colleges to learn mathematics by themselves, improve their mathematics level and provide teaching guidance for teachers. First advanced mathematics

Chapter 1 Limit, Continuity and Method of Finding Limit

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the concept and nature of limit

Second, the discrimination of the existence of limit (two criteria for the existence of limit)

Third, infinitesimal and its order

Fourth, the method of finding the limit

The continuity of verb (verb's abbreviation) function and its judgment

Common problems and their solving methods and skills

Problem training

The second chapter is the concept and calculation of derivative and differential of unary function.

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

1. Derivative and differential of unary function

Second, according to the definition of derivative and its applicable occasions

Third, the basic elementary function derivative table, the fourth derivative operation rule and the compound function differential rule.

Fourth, the application of the derivative method of composite function-the differential rule derived from the derivative rule of composite function.

Fifth, the derivative method of piecewise function

Sixth, the solution of higher derivative and N derivative

7. Simple application of differential calculus of univariate function

Common problems and their solving methods and skills

Problem training

The third chapter is the concept, calculation and application of unary function integral.

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the concept, properties and basic theorem of unary function integral

Second, the law of integration.

Third, the integration method of various functions

Fourth, generalized integral (generalized integral)

Fifth, the basic method of integral calculus application-differential element analysis.

6. Geometric application of unary function integral

Seven, the physical application of unary function integral.

Common problems and their solving methods and skills

Problem training

Chapter 4 Differential Mean Value Theorem and Its Application

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the differential mean value theorem and its function

Second, study the change of function by derivative.

Third, the maximum and minimum values of unary functions.

Common problems and their solving methods and skills

Problem training

Chapter 5 Taylor formula of univariate function and its application

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

1. Taylor formula of order n with piano remainder and Lagrange remainder.

Second, use piano remainder to solve Taylor formula.

Thirdly, some applications of Taylor formula of unary function.

……

The second part of linear algebra

The third part is probability theory and mathematical statistics