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