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
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