Current location - Training Enrollment Network - Mathematics courses - Catalogue of works in mathematics review book
Catalogue of works in mathematics review book
First calculus

Chapter 1 Function, Limit and Continuity

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 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 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

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 evaluation 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 evaluating knowledge.

I. Limits and continuity

Second, partial derivative and total differential

Third, the extreme value of multivariate function

Fourthly, find the maximum and minimum of multivariate function.

Five, the concept and calculation of double integral

Common problems and their solving methods and skills

Problem training

Chapter V Infinite Series

Content summary and key and difficult tips

Explain the main points of evaluating 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, the nature and structure of solutions of linear differential equations

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

Fifth, second-order non-homogeneous linear differential equations with constant coefficients

The concept and nature of intransitive verb difference

Seven, 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 evaluating knowledge.

First, the concept, expansion and properties of determinant

Second, several important formulas about determinant

Three. On 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 evaluation 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 3 n-dimensional vector

Content summary and key and difficult tips

Explain the main points of evaluation 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

Seven, Schmidt orthogonalization

Common problems and their solving methods and skills

Problem training

Chapter IV Linear Agenda Group

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

Sixth, the properties of solutions of linear equations.

Common problems and their solving methods and skills

Problem training

Chapter V 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 Quadratic Form

Content summary and key and difficult tips

Explain the main points of evaluating 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

The third part is probability theory and mathematical system

Chapter 1 Random Probability and Probability

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First, the relationship and operation of random events

Second, the probability of random events.

Three, the total probability formula and Bayesian formula

Fourth, the independence of events and Bernoulli formula.

Common problems and their solving methods and skills

Problem training

Chapter II Random Variables and Their Distribution

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

I. Random variables and distribution functions

Second, discrete random variables and continuous random variables

Third, several common distributions.

Fourth, the solution of random variable function distribution

Common problems and their solving methods and skills

Problem training

Chapter III Multidimensional Random Variables and Their Distribution

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

1. Joint distribution function and edge distribution function of multidimensional random variables.

Second, two-dimensional discrete random variables

Three, two-dimensional continuous random variables

Four, the distribution of two common two-dimensional continuous random variables

Verb (abbreviation for verb) independence of two-dimensional random variables

6. Solving the function distribution of two-dimensional random variables

Common problems and their solving methods and skills

Problem training

Chapter IV Numerical Characteristics of Random Variables

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

1. Numerical characteristics of one-dimensional random variables

Second, the numerical characteristics of two-dimensional random variables

Common problems and their solving methods and skills

Problem training

Chapter V Law of Large Numbers and Central Limit Law

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

I. Law of large numbers

Second, the central limit theorem

Common problems and their solving methods and skills

Problem training

Chapter VI Basic concepts of mathematical statistics

Content summary and key and difficult tips

Explain the main points of evaluation knowledge.

First, the population, the sample and the digital characteristics of the sample.

II. Statistics and sampling distribution

Common problems and their solving methods and skills

Problem training

Chapter VII Parameter Estimation

Content summary and key and difficult tips

Explain the main points of evaluating knowledge.

First of all, the concept of estimator

Second, two commonly used methods for estimating quantity

Common problems and their solving methods and skills

Problem training