Advanced mathematics
I. Function, Limit and Continuity
Examination content: the concept and expression of function: boundedness, monotonicity, periodicity, parity, composite function, inverse function, piecewise function and implicit function.
Second, the differential calculus of unary function
Examination contents: the relationship between the geometric meaning of derivative and differential concept derivative and the derivability and continuity of physical meaning function, and the tangent sum of plane curves; Four operations of linear derivative and differential basic elementary function derivative compound function, inverse function, implicit function and differential method The higher derivative of the function determined by parametric equation.
Invariant Differential Mean Value Theorem in First-order Differential Form Lobida's Rule Function Monotonicity Discriminates the Concave-convex, Inflexion and Asymptote of Extreme Value Function Graph Description of Maximum and Minimum Value of Function Graph Concept of Curvature Circle and Arc Radius Differential Curvature
4. Vector Algebra and Spatial Analytic Geometry
Exam content: concept vector of vector, mixed product of quantity product and cross product vector of linear operation vector, condition of vertical parallelism of two vectors, coordinate representation of included angle vector of two vectors, and concepts of cosine surface equation and space curve equation for operation unit vector direction number and direction.
Plane equation Straight line equation The angle between plane and plane, plane and straight line, straight line and straight line, the distance between parallel and vertical conditions point to plane and straight line Common quadratic equation of spherical cylinder surface of revolution and its parametric equation of graphic space curve and projection curve equation of general equation space curve on coordinate plane.
Verb (abbreviation of verb) Differential calculus of multivariate functions
Examination contents: the concept of multivariate function, the geometric meaning of bivariate function, the limit and continuity of bivariate function, the properties of multivariate continuous function in bounded closed region, the necessary and sufficient conditions for the existence of partial derivative and total differential of multivariate function, the derivation method of multivariate composite function, the directional derivative of second-order partial derivative of implicit function, the tangent of gradient space curve and the second-order Taylor formula of tangent plane and normal plane of bivariate function, the maximum and conditional extreme value of multivariate function and its simple application.
Six, multivariate function integral calculus
Examination content: the concept, nature, calculation and application of double integral and triple integral; The concept, properties and calculation of two kinds of curve integrals: Green's formula; The condition that the plane curve integral is independent of the path; The primitive function of the total differential of binary function; The concept, properties and calculation of two kinds of surface integrals: Gaussian formula; Stokes formula; The concepts of divergence and curl; And the calculation of curve integral and surface integral.
Seven, infinite series
Basic properties and necessary conditions of convergence of constant series and conceptual series; Methods for judging the convergence and divergence of geometric series, series and positive series: absolute convergence and conditional convergence of staggered series and Leibniz theorem: convergence domain, convergence radius, convergence interval and convergence domain of sum function series.
The basic properties of power series sum function in its convergence interval: the solution of simple power series sum function; the Fourier coefficient of power series expansion function of elementary function and Dirichlet theorem of Fourier series; Sine series and cosine series of Fourier series function above.
Eight, ordinary differential equations
Examination content: Basic concept of ordinary differential equation Differential equation with separable variables Homogeneous differential equation First-order linear differential equation Bernoulli equation Total differential equation Some differential equations that can be solved by simple variable substitution can be simplified to higher-order linear differential equations. The properties and structure theorems of solutions of second-order homogeneous linear differential equations with constant coefficients are higher than those of second-order homogeneous linear differential equations with constant coefficients. Simple application of second-order homogeneous linear differential equation with constant coefficients Euler differential equation
linear algebra
I. Determinants
The concept and basic properties of determinant of examination content; The expansion theorem of determinant by row (column)
Second, the matrix
Examination contents: the concept of matrix, linear operation of matrix, the concept and properties of transposed inverse matrix of determinant matrix of multiplication matrix, necessary and sufficient conditions for matrix reversibility, elementary transformation of matrix, equivalent block matrix of rank matrix of elementary matrix and its operation.
Third, the vector
Examination content: the linear combination of the concept vectors of vectors and the linear correlation of linear representation vector groups are equivalent to the maximum linear independent group of linear independent vector groups. The relationship between the rank of vector group and the rank of matrix vector space and its related concepts. Base transformation and coordinate transformation of vector inner product of transfer matrix. Orthogonal normalization method and its properties of orthogonal matrix of linear independent vector group specification orthogonal basis.
Fourth, linear equations.
Examination contents: Cramer's rule for linear equations, necessary and sufficient conditions for homogeneous linear equations to have nonzero solutions, necessary and sufficient conditions for nonhomogeneous linear equations to have solutions, properties and structure of solutions, basic solution system of homogeneous linear equations and general solutions of nonhomogeneous linear equations in general solution space.
Eigenvalues and eigenvectors of verb (abbreviation of verb) matrix
Examination contents: the concepts of eigenvalues and eigenvectors of matrices, the transformation of similar properties, the concept of similar matrices and the necessary and sufficient conditions for similar diagonalization of property matrices, and the eigenvalues and eigenvectors of similar diagonal matrices and their real symmetric matrices.
Sixth, quadratic form
Examination content: Quadratic form and its matrix represent the rank inertia theorem of contract transformation and the quadratic form of contract matrix. The canonical form and canonical form of quadratic form are transformed into canonical quadratic form and the positive definiteness of its matrix by orthogonal transformation and matching method.
Probability and mathematical statistics
I. Random events and probabilities
Test content: the relationship between random events and events in sample space and the basic properties of concept probability of complete operational event group probability; Classical probability, geometric probability, basic formula of conditional probability; Independent repeated testing of events.
Second, random variables and their distribution
Examination content: the concept and properties of random variable distribution function; Probability distribution of discrete random variables; Probability density of continuous random variables; Distribution of common random variables; Distribution of functions of random variables.
Three, multidimensional random variables and their distribution
Test contents: multidimensional random variables and their distribution probability distribution, edge distribution and conditional distribution probability density of 2D discrete random variables, marginal probability density and conditional density of 2D continuous random variables, and distribution of two or more simple functions of commonly used 2D random variables.
Fourth, the numerical characteristics of random variables
Test content: mathematical expectation (mean), variance, standard deviation and their properties of random variables; Mathematical expectation moment, covariance, correlation coefficient and their properties of random variable function.
Law of Large Numbers and Central Limit Theorem
Examination content: Chebyshev inequality Chebyshev's law of large numbers, Bernoulli's law of large numbers, DeMoivre-Laplace theorem, Levy-Lindberg theorem.
Basic concepts of mathematical statistics of intransitive verbs
Test content: sample variance and sample moment distribution of population sample mean Quantile normal population Simple random sample statistics of commonly used sampling distribution.
Seven. parameter estimation
Examination contents: concept of point estimation, moment estimation method of estimator and estimated value, maximum likelihood estimation method, selection criteria of estimator, concept of interval estimation, interval estimation of mean and variance of a single normal population, interval estimation of mean difference and variance ratio of two normal populations.
Eight, hypothesis testing
Test content: significance test, hypothesis test, two kinds of errors, hypothesis test of mean and variance of single and two normal populations.
Extended data:
First, you must use math I as your enrollment major.
1. Mechanics, mechanical engineering, optical engineering, instrument science and technology, metallurgical engineering, power engineering and engineering thermophysics, electrical engineering, electronic science and technology, information and communication engineering, control science and engineering, network engineering, electronic information engineering, computer science and technology, civil engineering, surveying and mapping science and technology, transportation engineering, ship and ocean engineering, aerospace science and technology.
2. A first-class discipline in management science and engineering, with an engineering degree.
Second, you must use the enrollment major of Mathematics II.
Textile science and engineering, light industry technology and engineering, agricultural engineering, forestry engineering, food science and engineering are all two disciplines majors.
Three, you must choose a math or math two enrollment major (decided by the admissions unit).
Among the first-class engineering disciplines, such as materials science and engineering, chemical engineering and technology, geological resources and geological engineering, mining engineering, oil and gas engineering, environmental science and engineering, there are two disciplines. Whoever has higher requirements for mathematics should choose mathematics as the major and mathematics as the minor.
Fourth, we must use the enrollment major of Mathematics III.
1. The first-level discipline of economics.
2. Management of business administration, agriculture and forestry economic management level discipline.
3. First-class discipline of management science and engineering, with a degree in management.
References:
Baidu Encyclopedia-Mathematics Postgraduate Entrance Examination Outline