3 14 Outline of Mathematics and Agriculture Postgraduate Entrance Examination
20 14 outline for postgraduate entrance examination in mathematics and agriculture
Examination subjects: advanced mathematics, linear algebra, probability theory and mathematical statistics.
Examination form and examination paper structure
First, the perfect score of the test paper and the examination time
The full mark of the test paper is 150, and the test time is 180 minutes.
Second, the way to answer questions
The answer methods are closed book and written test.
Third, the content structure of the test paper
Advanced mathematics is about 56%
Linear algebra accounts for about 22%
Probability theory and mathematical statistics account for about 22%
Fourth, the question structure of the test paper
8 multiple-choice questions, each with 4 points and ***32 points.
Fill in the blanks with 6 small questions, with 4 points for each small question and 24 points for * *.
Answer 9 small questions (including proof questions), ***94 points.
Advanced arithmetic
I. Function, Limit and Continuity
Examination content
The concept and representation of function, boundedness, monotonicity, periodicity and parity of function, the properties of basic elementary functions of inverse function, piecewise function and implicit function, and the establishment of functional relationship of graphic elementary function.
Definitions and properties of sequence limit and function limit, left limit and right limit of function, concepts and relationships of infinitesimal and infinitesimal, properties of infinitesimal and four operational limits of infinitesimal, two important limits: monotone bounded criterion and pinch criterion;
Concept of Function Continuity Types of Discontinuous Points of Functions Continuity of Elementary Functions Properties of Continuous Functions on Closed Interval
Examination requirements
1. Understanding the concept of function and mastering the expression method of function will establish the function relationship in application problems.
2. Understand the boundedness, monotonicity, periodicity and parity of functions.
3. Understand the concepts of compound function and piecewise function, inverse function and implicit function.
4. Grasp the nature and graphics of basic elementary functions and understand the concept of elementary functions.
5. Understand the concepts of sequence limit and function limit (including left limit and right limit).
6. Understand the nature of limit and two criteria for the existence of limit, master four algorithms of limit, and master the method of finding limit by using two important limits.
7. Understand the concept and basic properties of infinitesimal, master the comparison method of infinitesimal, and understand the concept of infinitesimal and its relationship with infinitesimal.
8. Understanding the concept of function continuity (including left continuity and right continuity) can determine the type of function discontinuity.
9. Understand the properties of continuous function and continuity of elementary function, understand the properties of continuous function on closed interval (boundedness, maximum theorem, mean value theorem), and apply these properties.
Second, the differential calculus of unary function
Examination content
The concept of derivative and differential, the relationship between derivability and continuity of geometric meaning function; Four operations of tangent, normal derivative and differential of plane curve; Differential method of derivative of basic elementary function: differential mean value theorem of higher derivative of implicit function: L'H?pital hospital rule; Discrimination of monotonicity of function; Maximum and minimum values of extreme function graph, inflection point and asymptote function.
Examination requirements
1. Understand the concept of derivative, the relationship between derivability and continuity, and understand the geometric meaning of derivative, and you will find 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 derivative rule of compound function, and you can find the derivative of piecewise function and implicit function.
3. Understand the concept of higher derivative and master the solution of second derivative.
4. Understand the concept of differential and the relationship between derivative and differential, and find the differential of function.
5. Understand Rolle theorem and Lagrange mean value theorem, and master the simple application of these two theorems.
6. Will use the Lobida rule to find the limit.
7. Master the method of judging monotonicity of function, understand the concept of function extreme value, and master the solution and application of function extreme value, maximum value and minimum value.
8. The concavity and convexity of the function graph can be judged by the derivative (note: in the interval, let the function have the second derivative. At that time, the figure was concave; At that time, the graph was convex), and the inflection point and asymptote (horizontal asymptote and vertical asymptote) of the function graph were found.
3. Integral calculus of unary function
Examination content
The concept of original function and indefinite integral The concept and basic properties of definite integral formula The function of upper limit of definite integral and its derivative Newton-Leibniz formula The substitution integration method of indefinite integral and definite integral and the application of partial integral Abnormal (generalized) integral definite integral.
Examination requirements
1. Understand the concepts of original function and indefinite integral, master the basic properties and basic integral formula of indefinite integral, and master the substitution integral method and integration 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 upper limit of integral and find its derivative, and master Newton-Leibniz formula, method of substitution and integration by parts of definite integral.
3. Will use definite integral to calculate the area of plane figure and the volume of rotator.
4. Understand the concept of generalized integral on infinite interval and calculate the generalized integral on infinite interval.
Four, multivariate function calculus
Examination content
Concept of multivariate function, geometric meaning of binary function, concept of limit and continuity of binary function, concept and calculation of partial derivative of multivariate function, derivative method of multivariate composite function and derivative method of implicit function, concept, basic properties and calculation of extreme value and conditional extreme value of second-order partial derivative of multivariate function.
Examination requirements
1. Understand the concept of multivariate function and the geometric meaning of bivariate function.
2. Understand the concepts of limit and continuity of binary functions.
3. Knowing the concepts of partial derivative and total differential of multivariate function, we can find the first and second partial derivatives of multivariate composite function and the total differential and partial derivative of multivariate implicit function.
4. Understand the concepts of multivariate function extremum and conditional extremum, grasp the necessary conditions for the existence of multivariate function extremum, and understand the sufficient conditions for the existence of binary function extremum.
5. Understand the concept and basic properties of double integral, and master the calculation methods of double integral (rectangular coordinates and polar coordinates).
Verb (abbreviation for verb) ordinary differential equation and difference equation
Examination content
Basic concepts of ordinary differential equations; separable variable differential equations; first-order linear differential equations.
Examination requirements
1. Understand differential equations and their concepts such as order, solution, general solution, initial condition and special solution.
2. Master the solution methods of differential equations with separable variables and first-order linear differential equations.
linear algebra
I. Determinants
Examination content
The concept and basic properties of determinant The expansion theorem of determinant by row (column)
Examination requirements
1. Understand the concept of determinant and master its properties.
2. The properties of determinant and determinant expansion theorem will be applied to calculate determinant.
Second, the matrix
Examination content
Concept of matrix, linear operation of matrix, multiplication matrix, product of power matrix, concept and properties of inverse matrix of determinant matrix, necessary and sufficient conditions for matrix reversibility, elementary transformation of matrix, equivalence of rank matrix of elementary matrix.
Examination requirements
1. Understand the concept of matrix, the definitions and properties of identity matrix, diagonal matrix and triangular matrix, and the definitions and properties of symmetric matrix, antisymmetric matrix and orthogonal matrix.
2. Master the linear operation, multiplication, transposition and its operation rules of matrix, and understand the determinant properties of square matrix power and square matrix product.
3. Understand the concept of inverse matrix, grasp the properties of inverse matrix and the necessary and sufficient conditions of matrix reversibility, understand the concept of adjoint matrix, and use adjoint matrix to find inverse matrix.
4. Understand the concepts of elementary transformation of matrix and elementary matrix and matrix equivalence, understand the concept of matrix rank, and master the method of finding the inverse matrix and rank of matrix by elementary transformation.
Third, the vector
Examination content
The linear combination of concept vectors of vectors and the linear representation of vector groups; the equivalent relationship between the rank of the largest linearly independent vector group of linearly independent vector groups and the rank of matrices.
Examination requirements
1. Understand the concept of vectors and master the operations 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 concepts of maximal linearly independent group and rank of vector group, and find the 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 the rank of its row (column) vector group.
Fourth, linear equations.
Examination content
Cramer's law for linear equations: Determination of existence and nonexistence of solutions of linear equations; The basic solution system of homogeneous linear equations and the relationship between the solution of non-homogeneous linear equations and the solution of corresponding homogeneous linear equations; General solution of nonhomogeneous linear equations.
Examination requirements
1. will use Cramer's rule to solve linear equations.
2. Master the method of judging the existence and non-existence of non-homogeneous linear equations.
3. Understand the concept of basic solution system of homogeneous linear equations, and master the solution and general solution of basic solution system of homogeneous linear equations.
4. Understand the structure of nonhomogeneous linear equations and the concept of general solution.
5. Master the method of solving linear equations with elementary line transformation.
Eigenvalues and eigenvectors of verb (abbreviation of verb) matrix
Examination content
Concepts of eigenvalues and eigenvectors of matrices, concepts of similar matrices and necessary and sufficient conditions for similar diagonalization of property matrices, eigenvalues and eigenvectors of similar diagonal matrices and their real symmetric matrices.
Examination requirements
1. Understand the concepts of matrix eigenvalues and eigenvectors, master the properties of matrix eigenvalues, and master the methods of finding matrix eigenvalues and eigenvectors.
2. Understand the concept of matrix similarity and the properties of similar matrices, understand the necessary and sufficient conditions of matrix similarity diagonalization, and turn matrices into similar diagonal matrices.
3. Understand the properties of eigenvalues and eigenvectors of real symmetric matrices.
Probability and mathematical statistics
I. Random events and probabilities
Examination content
The relationship between random events and sample space events and the basic properties of operation probability; The basic formula of classical probability conditional probability; Independent repeated testing of events.
Examination requirements
1. Understand the concept of sample 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 master the addition formula, subtraction formula, multiplication formula, total probability formula and Bayesian formula of probability.
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 related event probability.
Second, random variables and their distribution
Examination content
Concept and properties of distribution function of random variables Probability distribution of discrete random variables Probability density of continuous random variables Distribution of common random variables Distribution of random variable functions
Examination requirements
1. Understand the concepts of random variables and distribution functions.
The concept and properties of will calculate the probability of events related to random variables.
2. Understand the concept and probability distribution of discrete random variables, and master distribution, binomial distribution, Poisson distribution and their applications.
3. Understand the concept of continuous random variables and their probability density, and master uniform distribution, normal distribution, exponential distribution and their applications, in which the probability density of exponential distribution with parameters is
4. Find the distribution of simple functions of random variables.
Three, multidimensional random variables and their distribution
Examination content
Two-dimensional random variables and their distributions Probability distribution and edge distribution of two-dimensional discrete random variables Probability density and marginal probability density of two-dimensional continuous random variables Independence and irrelevance Distribution of two simple functions of common random variables.
Examination requirements
1. Understanding the concept of two-dimensional random variables, the concept and properties of two-dimensional random variable distribution, the probability distribution and edge distribution of two-dimensional discrete random variables, and the probability density and edge density of two-dimensional continuous random variables will lead to the probability of related events of two-dimensional discrete random variables.
2. Understand the concepts of independence and irrelevance of random variables, and understand the conditions of independence of random variables.
3. Understand the probability density of two-dimensional uniform distribution, two-dimensional normal distribution and the probability meaning of parameters.
4. Find the distribution of the sum of two independent random variables.
Fourth, the numerical characteristics of random variables
Examination content
Mathematical expectation (mean), variance, standard deviation and their properties of random variables Mathematical expectation moment, covariance and correlation coefficient of simple functions of random variables and their properties
Examination requirements
1. Understand the concept of numerical characteristics of random variables (mathematical expectation, variance, standard deviation, moment, covariance, correlation coefficient), and use the basic properties of numerical characteristics to master the numerical characteristics of common distributions.
2. Know the mathematical expectation of simple functions of random variables.
Law of Large Numbers and Central Limit Theorem
Examination content
Chebyshev Inequality Chebyshev's Law of Large Numbers Bernoulli's Law of Large Numbers De Morville-Laplace Theorem Levy-Lindbergh Theorem
Examination requirements
1. Understanding Chebyshev Inequality.
2. Understand Chebyshev's law of large numbers and Bernoulli's law of large numbers.
3. Understand de moivre-Laplace Theorem (binomial distribution takes normal distribution as the limit distribution) and Levi-Lindbergh Theorem (central limit theorem of independent identically distributed random variable sequence).
Basic concepts of mathematical statistics of intransitive verbs
Examination content
Sample mean, sample variance and sample moment distribution of simple random sample statistics of individuals in the population Common sampling distribution of quantile normal population.
Examination requirements
1. Understand the concepts of population, simple random sample, statistics, sample mean, sample variance and sample moment, where sample variance is defined as
2. Understand the concept and nature of distribution, distribution and distribution, understand the concept of quantile and look it up.
3. Understand the common sampling distribution of normal population.