The applicable disciplines are: in economics, except for two disciplines and majors that must take Math III, the other two disciplines and majors can choose Math III or Math IV; In the first-level discipline of management business administration, except for the two disciplines and majors of Math III, the majors of the other two disciplines can choose Math III or Math IV. Among the first-class disciplines of agricultural and forestry economic management, two disciplines and majors have lower requirements for mathematics.
Calculus, Linear Algebra, Probability Calculus, the concept, limit and continuous examination content function of function and its representation; The properties of basic elementary functions such as boundedness, monotonicity, periodicity, odd-even inverse function, composite function, implicit function and piecewise function; The definition of sequence limit and function limit of graphic elementary function: the concepts of left limit and right limit of its property function, infinitesimal and infinite; The basic nature of the relationship between them and the comparative limit of order; And two standards with operational limitations.
The concepts of function continuity and discontinuity; Continuity of elementary function; Properties of continuous functions on closed intervals.
Test requires 1. Understand the concept of function and master the representation of function.
2. Understand the boundedness, monotonicity, periodicity and parity of functions.
3. Understand the concepts of compound function, inverse function, implicit function and piecewise function.
4. Grasp the nature and graphics of basic elementary functions and understand the concept of elementary functions.
5. Will establish a functional relationship in a simple application problem.
6. Understand the concepts of sequence limit and function limit (including left and right limits).
7. Understand the concept and basic properties of infinitesimal, master the comparison method of infinitesimal order, and understand the concept of infinity and its relationship with infinitesimal.
8. To understand the nature of limit and two criteria for the existence of limit, and to master the nature of limit and four algorithms, two important limits will be applied.
Understand the concept of functional continuity (including left continuity and right continuity).
10. Understand the properties of continuous functions and the continuity of elementary functions. Understand the properties of continuous functions on closed intervals (boundedness, maximum theorem, minimum theorem, intermediate value theorem) and their simple applications.
Second, the geometric meaning of the concept derivative of the differential test content of univariate function and the relationship between the derivability and continuity of economic significance function. Four operations of basic elementary function derivatives, concepts and operation rules of inverse function derivatives and implicit function derivatives, Rolle theorem and Lagrange mean value theorem and their applications. The concavity and convexity of the extremum function diagram of the monotone function of Robida's rule function, the examination of the maximum and minimum values of the inflection point description function, and the requirement of Zhejiang nearline function diagram 1. Understand the concept of derivative and the relationship between derivability and continuity, and understand the geometric and economic significance of derivative (including the concepts of margin and elasticity).
2. Master the derivation formula of basic elementary functions, the four operation rules of derivatives and the derivation rules of compound functions; Master the derivative method of inverse function and implicit function, and understand the logarithmic derivative method.
3. In order to understand the concept of higher derivative, we can find the second derivative and n derivative of simpler function.
4. Understanding the concept of differential, the relationship between derivative and differential, and the invariance of first-order differential form will lead to the differential of function.
5. Understand the conditions and conclusions of 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 and its simple application, and master the solution of extreme value, maximum value and minimum value (including solving simple application problems).
8. We can judge the concavity and inflection point of the function graph by derivative, and find the asymptote of the function graph.
9. Master the basic steps and methods of drawing functions, and be able to draw some simple functions.
3. The concept of original function and indefinite integral, the basic properties of indefinite integral, the concept and basic properties of indefinite integral, the mean value theorem of definite integral of legal integral, the Newton-Leibniz formula, the concept of definite integral and generalized integral of partial integral, and the application of calculating definite integral are all required in the examination. 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 for calculating indefinite integral .56666.666666666666
2. Understand the concept and basic properties of definite integral, understand the mean value theorem of definite integral, master Newton-Leibniz formula, and the substitution integral method and partial integral of definite integral; Understand the function that defines the extreme point on a variable and find its derivative.
3. Will use definite integral to calculate the area of plane figure and the volume of rotator, and will use definite integral to solve some simple economic application problems.
4. Understand the concept of convergence and divergence of generalized integral, master the basic method of calculating generalized integral, and understand the conditions of convergence and divergence of generalized integral.
Fourth, the content of multivariate function calculus exam The concept of multivariate function, the geometric meaning of binary function, the limit and continuity of binary function, and the properties of binary continuous function on bounded closed regions (maximum theorem and minimum theorem)
The concept of partial derivative of multivariate function and the calculation of derivative method and implicit function derivative method of multivariate composite function The concept and basic properties of extreme value and conditional extreme value, maximum value and minimum value double integral of high-order partial derivative of multivariate function and the calculation requirements of simple double integral in unbounded region 1. Understand the concept of multivariate function and its geometric significance.
2. Understand the intuitive meaning of limit and continuity of binary function.
3. Understand the concepts of the same direction number and total differential of multivariate function, master the solution of the same direction number and total differential of multivariate composite function, and use the derivative rule of implicit function.
4. Understand the concepts of extreme value and conditional extreme value of multivariate function, master the necessary conditions of extreme value of multivariate function, understand the sufficient conditions of extreme value of binary function, find the extreme value of binary function, find the conditional extreme value by Lagrange multiplier method, find the maximum value and minimum value of simple multivariate function, and solve some simple application problems.
5. Knowing the concept and basic properties of double integral, we can calculate simple double integral (calculated in polar coordinates); Will calculate the simple double integral on the celestial body region.
Linear Algebra I. Determinant Examination Contents The concept and basic properties of determinant Examination requirements 1. Understand the concept of n-order determinant and master the properties of determinant.
2. The properties of determinant and determinant expansion theorem will be applied to calculate determinant.
Second, the concept of matrix test content matrix identity matrix, diagonal matrix, quantization matrix, triangular matrix, symmetric matrix, the concept of transposed inverse matrix of determinant matrix of linear operation matrix and matrix product, the necessary and sufficient condition of invertibility of property matrix, elementary transformation of adjoint matrix, rank block matrix of elementary matrix equivalent matrix and its operation test requirements 1. Understand the concept of matrix, and understand the definitions and properties of several special matrices.
2. Master the linear operation and multiplication of matrices and their operation rules, master the properties of matrix transposition, and master the properties of determinant of square matrix product.
3. Understand the concept of inverse matrix, master the properties of inverse matrix, the necessary and sufficient conditions of matrix reversibility, understand the concept of adjoint matrix, and use adjoint matrix to find the inverse of matrix.
4. Understand the concepts of elementary transformation of matrix and elementary matrix and matrix equivalence, understand the concept of matrix rank, and use elementary transformation to find the inverse sum rank of matrix.
5. Understand the concept of block matrix and master the algorithm of block matrix.
Third, the concept, nature and discrimination of linear combination of concept vectors and linear representation vector groups are linearly related and linearly independent. The maximum linearly independent group of a vector group is equivalent to the relationship between the product of the rank vector group of a vector group and the rank of a matrix. Test requires 1. Understand the concept of vector and master the operation of addition and multiplication to the county.
2. Understand the concepts of linear combination and linear representation of vectors, linear correlation with county groups, linear independence and so on, and master the related properties and discrimination methods of linear correlation and linear independence of vector groups.
3. Understand the concept of maximal independent group of vector group and master the method of finding maximal independent group of vector group.
4. Understand the concept of group equivalence, the concept of rank of vector group, and the relationship between the rank of matrix and the rank of its row (column) vector group, and then find the rank of vector group.
Fourth, the examination content of linear equations: the solution of linear equations; Cramer's law for linear equations: Determination of linear equations with and without solutions; The basic solution system of homogeneous linear equations and the relationship between the solution of nonhomogeneous linear equations and the corresponding solution (derivative subgroup); Examination requirements for general solution of nonhomogeneous linear equations 1. Understand the concept of solution of linear equations, you will use Cramer's rule to solve linear equations, and master the judgment method of linear equations with and without solutions.
2. 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.
3. We have mastered the solution of the general solution of nonhomogeneous linear equations, and we will use its special solution and the basic solution system of the corresponding derivative group to represent the general solution of nonhomogeneous linear equations.
The eigenvalues and eigenvectors of verb (verb's abbreviation) content matrix's eigenvalue and eigenvector's concept property of similar matrix's concept and property matrix's necessary and sufficient condition for diagonalization of similar diagonal matrix and real symmetric matrix of similar diagonal matrix's eigenvalues and eigenvectors are investigated 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, master the properties of similar matrices, understand the necessary and sufficient conditions of matrix diagonalization, and master the method of transforming matrices into similar diagonal matrices.
3. The properties of eigenvalues and eigenvectors of real symmetric matrices are generalized.
Probability theory 1. The relationship between random events and events in the sample space, the operation of random events and their properties, the independence of events, the definition of complete event group probability, the basic properties of probability, the conditional probability addition formula of classical probability, the multiplication formula, the total probability formula and the Bayes formula, and the independent repeated test examination requirements L. Understand the concept of sample space, understand the concept of random events, and master the relationship and operation between events.
2. Understand the concepts of probability and conditional probability, master the basic properties of probability, and calculate the addition formula, multiplication formula, total probability formula and Bayesian formula that account for typical probability.
3. Understand the concept of event independence, grasp the probability calculation with event independence, understand the concept of single city retest, and master the calculation method of related event probability.
Second, random variables and their low-level distribution The concept and nature of the distribution function of random variables, the probability distribution of discrete random variables, the probability density of continuous random variables, and the probability distribution requirements of common random variables are 1. Understand the concept of random variables and their probability distribution, and understand the distribution function f (x) = p {x x.
2. Understand the concept and probability distribution of discrete random variables, and master 0-L distribution, binomial distribution, hypergeometric market division, Poisson distribution and its application.
3. Understand the concept of continuous random variables and their probability density, master the relationship between probability density and distribution function, and master normal distribution, uniform distribution, exponential distribution and their applications.
4. Master the basic method of finding the probability distribution of its simple function according to the probability distribution of independent variables.
Three. Two-dimensional random variables and their probability distribution examination content Joint probability distribution and edge distribution of two-dimensional discrete random variables Joint probability density and edge density of two-dimensional continuous random variables Common independence of two-dimensional random variables Probability distribution test of joint distribution of random variable functions 1. Understand the concept of two-dimensional random variables, the concept, properties and two basic forms of joint distribution of two-dimensional random variables: discrete joint probability distribution and edge distribution; Continuous joint probability density and edge density. Two-dimensional probability distribution will be used to find the probability of related events.
2. Understand the concept of independence of random variables, and master the conditions of independence of discrete and continuous air defense variables.
3. Grasp the two-dimensional uniform distribution, understand the density function of the two-dimensional normal distribution, and understand the probability meaning of the parameters.
4. Will find the probability distribution of a simple function of two random variables.
Fourth, the test content of digital characteristics of random variables, mathematical expectation, variance and standard deviation of random variables and their basic properties, mathematical expectation of random variable function, covariance of random variables and its properties, correlation coefficient of random variables and its properties 1. Understand the concept of digital characteristics of random variables (mathematical expectation, variance, standard deviation, covariance, correlation coefficient), calculate the digital characteristics of its specific distribution by using the basic properties of digital characteristics, and master the digital characteristics of common distributions.
2. According to the probability distribution of the random variable x, the mathematical expectation eg (x) of its function g (x) will be found.
Verb (abbreviation of verb) central limit theorem examination content Poisson theorem De Moivre-Laplace theorem (binomial distribution takes normal distribution as the limit distribution) Levy-lindberg theorem (central limit theorem of independent and identical distribution).
Test requires 1. Master the conditions of Poisson theorem and its application, and use Poisson distribution to approximately calculate the probability of binomial distribution.
2. Understand the conclusions and application conditions of the nuclear prize-Laplacian central limit theorem and Levi-Lindbergh central limit theorem, and use relevant theorems to approximately calculate the probability of random events.
Test paper structure (1) Content proportion Calculus is about 50% Linear algebra is about 25% Probability theory is about 25% (2) Proportional fill-in-the-blank and multiple-choice questions are about 30% Analytical questions (including proof questions) are about 70%.