2009年数学考研大纲（Mathematics postgraduate entrance examination outline in 2009）

2009年数学考研大纲（Mathematicspostgraduate entrance

examinationoutline in 2009）

Thesyllabus of postgraduate mathematics count in 2009

Advancedmathematics

Function,limit, continuity

Examinationcontent

Theconcept of function and establishment of function is a

functionof the nature and pattern of elementary function of

boundedness,monotonicity, periodicity and parity composite

function,inverse function, piecewise function and implicit

functionof the basic elementary function

Thetwo standards are four computing limit comparison limit

propertiesof infinitesimal limit on the left and right limit

ofinfinitesimal and Infinity Concept and the relationship

betweenthe definition and properties of function series limit

andfunction limit and the infinitesimal of the monotone: there

aretwo important limit circle criterion and squeeze rule:

,

Theconcept of function continuity, the type of function

discontinuitypoint, the continuity of elementary function,

theproperty of continuous function on closed interval

Examinationrequirements

1.understand the concept of function, grasp the representation

offunction, will establish the functional relationship of

applicationproblem

2.understand the function of the boundedness, monotonicity,

periodicityand parity.

3.understand the concept of composite function and piecewise

function,and understand the concept of inverse function and

implicitfunction

4.grasp the basic elementary function properties and graphics,

understandthe concept of elementary functions.

5.understand the concept of limit, understand the concept of

theleft limit and the right limit of function, and the

relationshipbetween the existence of function limit and the

leftand right limit

6.grasp the nature of the limit and four arithmetic operations.

7.master the two criteria of limit existence, and use them to

findthe limit, master the method of using the two important

limitsto find the limit

8.understand the concept of infinitesimal, infinite quantity,

graspthe method of comparison of infinitesimal, will use the

equivalentinfinitesimal to find the limit

9.understanding the concept of function continuity (including

leftcontinuity and right continuity) will judge the type of functiondiscontinuity point

10.understand the properties of continuous functions and the continuityof elementary functions, understand the properties of continuousfunctions on closed intervals (boundedness, maximum and minimumtheorems, intermediate value theorems), and apply these properties

Two.Differential calculus of unary function

Examinationcontent

Thegeometric and physical meaning of the concept of function derivativeand differential of the relationship curve between the plane and thecontinuity of the tangential and normal derivative and differentialfour computing elementary
functionsof implicit function derivative compound function, inverse functionand differential method of high order derivative function determinedby parameter equation of first order differential form invariance ofdifferential mean value theorem "(L'Hospital) depicts thefunction extremum function graph discriminant function rule ofmonotone functions of the concavity, inflection point and asymptoticfunction graph minimum and maximum values of the arc differentialconcept of curvature and curvature radius of curvature circle

Examinationrequirements

1.understanding of derivative and differential concept, understand therelation between derivative and differential

geometry,meaning derivative, tangent equation and normal

equationfor the plane curve, to understand the physical

meaningof the derivative, will describe some physical

quantitiesby derivative, differentiability and continuity of

therelationship between the understanding of the function.

2.grasp the derivation rule of four algorithms and the

derivativeof the composite function derivative formula master

thebasic elementary functions. To understand the four

arithmeticoperations of differential and first-order

differentialform invariance of differential will function.

3.understand the higher derivative concept, higher derivative

willask simple function.

4.,the derivative of the piecewise function is obtained, and

theimplicit function and the derivative of the inverse

functionare determined by the implicit function and the

parameterequation

5.understand and use Rolle (Rolle) theorem, Lagrange (Lagrange)

meanvalue theorem and Taylor (Taylor) theorem, understand and

useCauchy (Cauchy) mean value theorem

6.master the method limits the l'Hopital's rule.

7.understand the extremum concept of function, grasp the

methodof judging the monotonicity of function and the extremum

offunction by derivative, grasp the method of finding the

maximumand minimum of function and its application

8.judge the concavity and convexity of the function graph by

derivative(Note: in the interval, the function has two order

derivative.At that time, the graphics were concave;

Atthat time, the graph is convex), will function graphics and

inflectionpoint level, vertical and oblique asymptote, will

describethe function of the graphics.

9.understand the concept of curvature, curvature circle and

radiusof curvature, and calculate the curvature and radius of

curvature

Three.Integral calculus of one variable function

Examinationcontent

Thebasic properties of the basic concept of the original

functionand integral formula of indefinite integral

indefiniteintegral definite function integral concept and

basicproperties of the integral mean value theorem of integral

upperlimit and its derivative Newton Leibniz (Newton-Leibniz)

anomalousintegral formula of indefinite integral and definite

integralelement integral method and integral method of

rationalfunction, trigonometric function rational and simple

irrationalfunction (generalized) using integral integral

Examinationrequirements

1.understanding of the concept of function, understanding the

conceptof indefinite integral and definite integral.

2.master the basic formula of indefinite integral, master the

propertiesof indefinite integral and definite integral and the

meanvalue theorem of definite integral, and master the method

ofsubstitution integral and partial integration

3.will seek integral rational function, rational formula of

trigonometricfunction and simple irrational function.

4.to understand the function of the upper limit of the integral,

itwill seek its derivative, master the Newton Leibniz formula

5.understand the abnormal integral concept, will calculate the

anomalousintegral.

6.to master some geometrical and physical quantities

calculatedby integral expression and (plane graphics area, the

lengthof plane curve, volume and side area, rotating body

parallelsection area known as three-dimensional volume, power,

grav