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Please introduce the characteristics of the review books for the postgraduate entrance examination in Li Yongle.
There are different versions of review books for mathematics postgraduates in Li Yongle. Written by Li Yongle and Wang Shian, it is often called the Li Wang Edition. There is also a version written by Li Yongle and Li Zhengyuan, published by China University of Political Science and Law, called Li Shuang Edition.

Generally speaking, the double plum version is more respected.

Compared with other mathematical reference materials, the review book for Li Yongle Mathematics Postgraduate Entrance Examination emphasizes the foundation, which is suitable for students with weak foundation.

Attached is the second edition catalogue.

First advanced mathematics

chapter one

Limit, continuity and the 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

chapter two

Concept and calculation of derivative and differential of unary function

Content summary and key and difficult tips

Explain the main points of evaluation 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

chapter three

The Concept, Calculation and Application of One-variable 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 four

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 five

Taylor formula of unary function and its application

Content summary and key and difficult tips

Explain the main points of evaluation 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.

Common problems and their solving methods and skills

Problem training

Chapter vi

differential equation

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

I. Basic concepts

Second, the first order differential equation

Third, reducible higher-order equations.

Fourth, the properties and structure of solutions of linear differential equations

Fifth, second-order and some higher-order homogeneous linear equations with constant coefficients

Sixth, second-order non-homogeneous linear equations with constant coefficients

7. Equations with Variable Limit Integrals

Eight. application problem

Common problems and their solving methods and skills

Problem training

Chapter VII

Multivariate differential calculus

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the concept, limit and continuity of multivariate function

Second, partial derivative and total differential of multivariate function

Third, the differential law of multivariate functions

Fourth, the application of derivative method of compound function-implicit function differential method

Fifth, other applications of the derivative rule of composite function.

Six, multivariate function extreme sufficient discrimination method

Seven, the maximum and minimum of multivariate function.

Common problems and their solving methods and skills

Problem training

Chapter VIII

double integral

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the concept and properties of double integral

Secondly, the double integral is transformed into the repeated integral in rectangular coordinate system.

Third, the variable substitution of double integral

Four, how to use the calculation formula to calculate or simplify the double integral?

Common problems and their solving methods and skills

Problem training

The second article

linear algebra

chapter one

decisive factor

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the concept, expansion and properties of determinant

Second, several important formulas about determinant

Third, about Cramer's law.

Common problems and their solving methods and skills

Problem training

chapter two

Matrix and its operation

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

The concept of 1. matrix and several special square matrices.

Second, the operation of matrix

Thirdly, the necessary and sufficient conditions for matrix invertibility.

Fourth, the elementary transformation of matrix and elementary matrix

Equivalence of verb (abbreviation for verb) Matrix

Common problems and their solving methods and skills

Problem training

chapter three

N-dimensional vector

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the concept and operation of N-dimensional vector

Second, linear combination and linear expression

Thirdly, linear correlation has nothing to do with linearity.

Fourth, the relationship between linear correlation and linear expression

5. Rank of vector group and rank of matrix

Six, the important formula of matrix rank

Schmidt orthogonalization.

Common problems and their solving methods and skills

Problem training

chapter four

linear system of equations

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

1. Various expressions of linear equations and related concepts

Second, the concept of basic solution system and its solution

Thirdly, the judgment that homogeneous equations have non-zero solutions.

Fourthly, the determination of solutions of nonhomogeneous linear equations.

Fifthly, the structure of solutions of nonhomogeneous linear equations

six

Properties of solutions of linear equations

Common problems and their solving methods and skills

Problem training

chapter five

Eigenvalues and eigenvectors of matrices

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

The concepts, properties and solutions of eigenvalues and eigenvectors of 1. matrix.

Second, the concept and properties of similarity matrix

Third, the necessary and sufficient conditions and problem-solving steps of matrix similarity diagonalization

Common problems and their solving methods and skills

Problem training

Chapter vi

square

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

The concept of quadratic form and its standard form

Second, positive definite quadratic form and positive definite matrix

Third, the contract matrix

Common problems and their solving methods and skills

Problem training

Attachment: the answers to the training questions in the whole book.

First article

Advanced mathematics

Chapter 1 Limit, Continuity and Method of Finding Limit

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

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

chapter four

Differential mean value theorem and its application

Chapter 5 Taylor formula of univariate function and its application

Chapter VI Differential Equations

Chapter 7 Differential calculus of multivariate functions

Chapter VIII Double Integral

The second article

linear algebra

The first chapter determinant

Chapter II Matrix and Its Operation

Chapter 3 n-dimensional vector

Chapter IV Linear Equations

Chapter V Eigenvalues and Eigenvectors of Matrices

Chapter vi

square