Does the content of the third postgraduate entrance examination of mathematics include the higher order differential equation that can reduce the price

Does the content of the third postgraduate entrance examination of mathematics include the higher order differential equation that can reduce the price

2 test content
Calculus
Function, limit, continuity
Examination requirements
1. Understand the concept of function, master the representation of function, and be able to establish the functional relationship of application problems
2. Understand the boundedness, monotonicity, periodicity and parity of functions
3. Understand the concept of compound function and piecewise function, understand the concept of inverse function and implicit function
4. Master the properties and graphs of basic elementary function, and understand the concept of elementary function
5. Understand the concepts of sequence limit and function limit (including left limit and right limit)
6. Understand the nature of limit and the two criteria of limit existence, master the four operation rules of limit, and master the method of using two important limits to find limit
7. Understand the concept and basic properties of infinitesimal. Master the comparison method of infinitesimal. Understand the concept of infinitesimal and its relationship with infinitesimal
8. Understand the concept of function continuity (including left continuity and right continuity), and be able to distinguish the types of function discontinuities
9. Understand the properties of continuous function and the continuity of elementary function, understand the properties of continuous function on closed interval (boundedness, maximum and minimum theorem, intermediate value theorem), and be able to apply these properties
Differential calculus of functions of one variable
Examination requirements
1. Understand the concept of derivative and the relationship between differentiability and continuity, understand the geometric and economic significance of derivative (including the concepts of margin and elasticity), and be able to solve the tangent equation and normal equation of plane curve
2. Master the derivative formula of basic elementary function, the four operation rules of derivative and the derivation rules of compound function, be able to find the derivative of piecewise function and the derivative of inverse function and implicit function
3. Understand the concept of higher derivative and be able to find the higher derivative of simple function
4. Understand the concept of differential, the relationship between derivative and differential, and the invariance of first-order differential form, and be able to find the differential of function
5. Understand Rolle theorem, Lagrange mean value theorem, Taylor Theorem and Cauchy mean value theorem, and master the simple application of these four theorems
6. Be able to use the law of lobita to find the limit
7. Master the judgment method of function monotonicity, understand the concept of function extremum, and master the solution and application of function extremum, maximum and minimum
8. Be able to judge the concavity and convexity of function graph with derivative (Note: in the interval, let the function have the second derivative. At that time, the graph is concave; at that time, the graph is convex), and be able to find the inflection point and asymptote of function graph
9. Can describe the graph of simple function
Integration of functions of one variable
Examination requirements
1. Understand the concept of original function and indefinite integral, master the basic properties and basic integral formula of indefinite integral, master the integral method of changing elements and integral method by parts of indefinite integral
2. Understand the concept and basic properties of definite integral, understand the mean value theorem of definite integral, understand the function of the upper limit of integral and be able to find its derivative, master Newton Leibniz formula, and the integral method of substitution and division of definite integral
3. Be able to use definite integral to calculate the area of plane figure, the volume of revolving body and the average value of function, and be able to use definite integral to solve simple economic application problems
4. Understand the concept of abnormal integral and be able to calculate abnormal integral
Calculus of multivariate functions
Examination requirements
1. Understand the concept of multivariate function and the geometric meaning of binary function
2. Understand the concepts of limit and continuity of bivariate function, and understand the properties of bivariate continuous function on bounded closed domain
3. Understand the concept of partial derivative and total differential of multivariate function, be able to find the first and second partial derivatives of multivariate composite function, be able to find the total differential, and be able to find the partial derivative of multivariate implicit function
4. Understand the concepts of extreme value and conditional extreme value of multivariate function, master the necessary conditions for the existence of extreme value of multivariate function, understand the sufficient conditions for the existence of extreme value of binary function, be able to find the extreme value of binary function, use Lagrange multiplier method to find conditional extreme value, be able to find the maximum and minimum value of simple multivariate function, and be able to solve simple application problems
5. Understand the concept and basic properties of double integral, master the calculation method of double integral (rectangular coordinates and polar coordinates), understand the simple abnormal double integral on unbounded region and be able to calculate
Infinite series
Examination requirements
1. Understand the convergence and divergence of series and the concept of the sum of convergent series
2. Understand the basic properties of series and the necessary conditions of series convergence, master the geometric series and the conditions of series convergence and divergence, master the comparison and ratio criteria of positive series convergence
3. Understand the concepts of absolute convergence and conditional convergence of arbitrary series, the relationship between absolute convergence and convergence, and the Leibniz criterion of staggered series
4. Be able to find the convergence radius, convergence interval and convergence region of power series
5. Understand the basic properties of power series in its convergence interval (continuity of sum function, term by term derivation and term by term integration), and be able to find the sum function of simple power series in its convergence interval
6. Understand the Maclaurin expansion of the power X of E, SiN x, cos x, ln (1 + x) and the power a of (1 + x)
Ordinary differential equation and difference equation
Examination requirements
1. Understand differential equation and its order, solution, general solution, initial condition and special solution
2. Master the solution methods of variable separable differential equations, homogeneous differential equations and first-order linear differential equations
3. Be able to solve second order homogeneous linear differential equations with constant coefficients
4. Understand the properties and structure theorem of solutions of linear differential equations, and be able to solve second-order non-homogeneous linear differential equations with constant coefficients whose free terms are polynomials, exponential functions, sine functions and cosine functions
5. Understand the concepts of difference, difference equation, general solution and special solution
6. Understand the solution method of the first order constant coefficient linear difference equation
7. Be able to solve simple economic application problems with differential equations
linear algebra
determinant
Examination content: the concept and basic properties of determinant
Examination requirements
1. Understand the concept of determinant, master the nature of determinant
2. Be able to use the properties of determinant and determinant to calculate determinant according to row (column) expansion theorem
matrix
Examination requirements
1. Understand the concept of matrix, the definition and properties of identity matrix, quantity matrix, diagonal matrix and triangular matrix, and the definition and properties of symmetric matrix, antisymmetric matrix and orthogonal matrix
2. Master the linear operation, multiplication, transpose of matrix and their operation rules, and understand the properties of determinant of power and product of square matrix
3. Understand the concept of inverse matrix, grasp the properties of inverse matrix and the necessary and sufficient conditions for matrix reversibility, understand the concept of adjoint matrix, and be able to use adjoint matrix to find inverse matrix
4. Understand the concepts of elementary transformation of matrix, elementary matrix and matrix equivalence, understand the concept of rank of matrix, and master the method of solving inverse matrix and rank of matrix with elementary transformation
5. Understand the concept of block matrix and master the algorithm of block matrix
vector
Examination requirements
1. Understand the concept of vector and master the algorithm of vector addition and multiplication
2. Understand the concepts of linear combination and linear representation of vectors, linear correlation and linear independence of vector groups, and master the related properties and discrimination methods of linear correlation and linear independence of vector groups
3. Understand the concept of maximal linearly independent group of vector group, and be able to find maximal linearly independent group and rank of vector group
4. Understand the concept of vector group equivalence and the relationship between the rank of matrix and its row (column) vector group
5. Understand the concept of inner product. Master the Schmidt method of orthogonal normalization of linear independent vector system
System of linear equations
Examination requirements
1. Be able to solve linear equations with Cramer's rule
2. Master the judgment method of non-homogeneous linear equations with and without solutions
3. Understand the concept of basic solution system of homogeneous linear equations, and master the solution method of basic solution system and general solution of homogeneous linear equations
4. Understand the structure of solutions and the concept of general solutions of non-homogeneous linear equations
5. Master the method of solving linear equations with elementary row transformation
Eigenvalues and eigenvectors of matrices
Examination requirements
1. Understand the concept of matrix eigenvalue and eigenvector, master the properties of matrix eigenvalue, and master the method of solving matrix eigenvalue and eigenvector
2. Understand the concept of matrix similarity, grasp the properties of similar matrix, understand the necessary and sufficient conditions for matrix to be similar diagonalized, and master the method of transforming matrix into similar diagonal matrix
3. Master the properties of eigenvalues and eigenvectors of real symmetric matrix
Quadratic form
Examination requirements
1. Understand the concept of quadratic form, express quadratic form in matrix form, and understand the concepts of congruent transformation and congruent matrix
2. Understand the concept of rank of quadratic form, the concepts of standard form and normal form of quadratic form, the inertial theorem, and transform quadratic form into standard form by orthogonal transformation and formula method
3. Understand the concept of positive definite quadratic form and positive definite matrix, and master its discriminant method
probability statistics
Random events and probability
Examination requirements
1. Understand the concept of sample space (basic event space), understand the concept of random events, and master the relationship and operation of events
2. Understand the concepts of probability and conditional probability, master the basic properties of probability, calculate classical probability and geometric probability, master the addition formula, subtraction formula, multiplication formula, total probability formula and Bayes formula of probability, etc
3. Understand the concept of event independence, and master the probability calculation with event independence; understand the concept of independent repeated test, and master the calculation method of event probability
Random variable and its distribution
Examination requirements
1. Understand the concept of random variables, understand the concept and properties of distribution function, and calculate the probability of events associated with random variables
2. Understand the concept of discrete random variable and its probability distribution, master 0-1 distribution, binomial distribution, geometric distribution, hypergeometric distribution, Poisson distribution and its application
3. Master the conclusion and application conditions of Poisson's theorem, and be able to approximate binomial distribution with Poisson's distribution
4. Understand the concept of continuous random variable and its probability density, master uniform distribution, normal distribution, exponential distribution and its application, in which the probability density of exponential distribution with parameter is
5. Be able to find the distribution of random variable function
Multidimensional random variable and its distribution
Examination requirements
1. Understand the concept and basic properties of the distribution function of multidimensional random variables
2. Understand the probability distribution of two-dimensional discrete random variables and the probability density of two-dimensional continuous random variables, and master the marginal distribution and conditional distribution of two-dimensional random variables
3. Understand the concepts of independence and irrelevance of random variables, grasp the conditions of mutual independence of random variables, and understand the relationship between irrelevance and independence of random variables
4. Master two-dimensional uniform distribution and two-dimensional normal distribution, and understand the probability significance of parameters
5. Be able to find the distribution of function according to the joint distribution of two random variables, and find the distribution of function according to the joint distribution of several independent random variables
Numerical characteristics of random variables
Examination requirements
1. Understand the concept of digital characteristics of random variables (mathematical expectation, variance, standard deviation, moment, covariance, correlation coefficient), use the basic properties of digital characteristics, and master the digital characteristics of common distribution
2. Be able to find the mathematical expectation of random variable function
3. Understand Chebyshev inequality
Law of large numbers and central limit theorem
Examination requirements
1. Understand Chebyshev's law of large numbers, Bernoulli's law of large numbers and schinchin's law of large numbers (Law of large numbers for sequences of independent and identically distributed random variables)
2. Understand demover Laplace central limit theorem (binomial distribution takes normal distribution as limit distribution), levy Lindbergh central limit theorem (central limit theorem of independent and identically distributed random variable sequence), and use relevant theorems to approximate the probability of relevant random events
Basic concepts of mathematical statistics
Examination requirements
1. Understand the concept of population, simple random sample, statistics, sample mean, sample variance and sample moment, and its application