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