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