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Review content of senior three in postgraduate entrance examination
20 10 Postgraduate Mathematics 3 Mathematics (Mathematics 3) Economic Review Book

catalogue

First calculus

Chapter 1 Function, Limit and Continuity

Content summary and key and difficult tips

Explain the main points of evaluation 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 comparison

Fourth, the method of finding the limit

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

Properties of continuous function of intransitive verbs

Common problems and their solving methods and skills

Problem training

Chapter 2 Differential calculus of univariate function

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

1. Derivative and differential of unary function

Second, 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

Seven, differential mean value theorem

Eight, using derivatives to study the behavior of functions.

Nine, the geometric application and economic application of differential calculus

X. Maximum and minimum values of functions.

Taylor formula of 1 1. unary function

Twelve, use piano remainder to solve Taylor formula.

Thirteen, the application of Taylor formula of unary function

Common problems and their solving methods and skills

Problem training

Chapter 3 Integral calculus of unary function

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the concepts and basic properties of primitive function and indefinite integral.

Second, the calculation of indefinite integral

Third, the concept, basic properties and basic theorems of definite integral.

Fourth, the calculation of definite integral

Generalized integral of verb (abbreviation of verb)

Six, the geometric application of definite integral

Seven, the simple economic application of definite integral

Common problems and their solving methods and skills

Problem training

Chapter IV Multivariate Function Calculus

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

I. Limits and continuity

Second, partial derivative and total differential

Third, the extreme value of multivariate function

Fourth, the maximum and minimum values of multivariate functions.

Five, the concept and calculation of double integral

Common problems and their solving methods and skills

Problem training

Chapter 5 has no research series.

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

First, the concept and basic properties of constant term series

Second, the determination of convergence and divergence of positive series

Third, the discrimination method of convergence and divergence of staggered series

Fourthly, absolute convergence and conditional convergence.

5. Convergence domain of power series

6. Operation of Power Series and Properties of Functions

Seven. Power series expansion of function

Common problems and their solving methods and skills

Problem training

Chapter VI Ordinary Differential Equations and Difference Equations

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

I. Basic concepts

Second, the first order differential equation

Third-order and second-order homogeneous linear differential equations with constant coefficients

Fourth, the second order non-homogeneous linear differential equation with constant coefficients

The concept and nature of verb (verb's abbreviation) difference

Sixth, the first-order linear difference equation with constant coefficients

Common problems and their solving methods and skills

Problem training

The second part of linear algebra

The first chapter determinant

Content summary and key and difficult tips

Explain the main points of evaluation 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 II 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 inversion.

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 3 n-dimensional vector

Chapter IV Linear Equations

Chapter 5: Characteristics and eigenvectors of matrices.

Chapter VI Quadratic Form

The third part is probability theory and mathematical statistics

Chapter 1 Random Events and Probability

Chapter II Random Variables and Their Distribution

Chapter III Multidimensional Random Variables and Their Distribution

Chapter IV Numerical Characteristics of Random Variables

Chapter V Law of Large Numbers and Central Limit Theorem

Chapter VI Basic concepts of mathematical statistics

Chapter VII Parameter Estimation