【考研数学】143分牛人的重点及难点归纳辅导笔记

【考研数学】143分牛人的重点及难点归纳辅导笔记([PubMed]143

pointsofthefocusanddifficultiesofcattleinduction

coachingnotes)

Mathematicsemphasisanddifficultyinductionguidance

Partone

Chapter1setsandmappings

Section1.sets

Section2.mappingandfunction

Theteachingrequirementofthischapteristounderstandthe

conceptofsetandtheconceptofmapping,tograspthe

representationofrealnumberset,therepresentationand

functionoffunction

Somebasicpropertiesof.

Thecontinuityoftherealnumbersystem,1.

Section2.ofsequencelimit

Section3.infinity

Section4.convergencecriteria

Theteachingrequirementsofthischapter:grasptheconcept

anddefinitionofthelimitofsequence,graspandapplythe

convergencecriterionofseries,andunderstandtherealnumber

system

Themeaningofcontinuity,andaseriesoffundamentaltheorems

forrealnumbersystems.

Thethirdchapter,functionlimitandcontinuousfunction

Section1.functionlimit

Section2.continuousfunction

Section3.infinitesimalandinfinity

Section4.continuousfunctiononaclosedinterval

Theteachingrequirementofthischapteristograsptheconcept

offunctionlimit,therelationbetweenthelimitoffunction

andthelimitofsequence,theorderofinfinitesimaland

infinity

Thebasicpropertiesofcontinuousfunctionsonclosed

intervalsareestimated.

Thefourthchapterisdifferentiation

Section1.differentialandderivative

Themeaningandnatureofsection2.ofthederivative

Section3.derivativefouroperationsandinversefunction

derivationrule

Spoundfunctionderivationruleandits

application

Section5.highorderderivativeandhighorderdifferential

Theteachingrequirementsofthischapteraretounderstandthe

conceptsofdifferentialandderivative,higherorder

differentialandhigherorderderivatives,theirproperties

andtheirrelations,andmasterthem

Derivativeanddifferentialmethods.

Thefifthchapteristhedifferentialmeanvaluetheoremand

itsapplication

Section1.differentialmeanvaluetheorem

The2.L,Hospitallaw

Section3.polynomialinterpolationandTaylorformula

TheformulaofTaylorfunctionanditsapplicationinsection

4.

Forexample,5.application

Theapproximatesolutionof6.functionequation

Thischapterteachingrequirements:graspthedifferential

meantheoremandfunctionoftheTaylorformula,andapplied

tothefunctionofthenatureoftheresearch,skilled

transportation

ThelimitiscalculatedbyusingtheL,Hospitalrule,andthe

extremumproblemandthefunctionmappingproblemaresolved

byapplyingdifferentiationtosolvingthefunction.

Thesixthchapterisindefiniteintegral

Section1.indefiniteintegralconceptsandoperationalrules

Section2.elementintegralmethodandintegralmethod

Theindefiniteintegralofrationalfunctionandits

applicationinsection3.

Theteachingrequirementsofthischapter:grasptheconcepts

andalgorithmsofindefiniteintegral,andapplythe

substitutionmethodandtheintegralmethodskillfullytosolve

indefiniteintegral,

Graspthemethodoffindingindefiniteintegralofrational

functionandpartialirrationalfunction.

Theseventhchapterintegral(Section1,section3)

Section1.theconceptofdefiniteintegralandIntegrability

Conditions

Thebasicpropertiesofsection2.ofthedefiniteintegral

Thefundamentaltheoremofcalculus3..

Theseventhchapterintegral(Section4,section6)

Aegralingeometry

Section5.applicationexamplesofcalculus

Numericalcalculationofsection6.ofthedefiniteintegral

Thischapterteaching:understandingtheconceptofdefinite

integral,firmlygraspthefundamentaltheoremofcalculus:

NewtonLeibnizformula,skilledset

Integralcalculation,skilleduseofinfinitesimalmethodto

solvegeometry,physicsandpracticalapplicationofthe

problem,theinitialgraspofdefiniteintegralnumerical

Count.

Theeighthchapterisimproperintegral

Theconceptandcalculationsection1.abnormalintegral

Convergencecriteriaofsection2.abnormalintegral

Theteachingrequirementsofthischapter:grasptheconcept

ofimproperintegral,mastertheconvergencejudgmentmethod

ofabnormalintegralandthecalculationofabnormalintegral

Count.

Theninthchapter,numberseries

Theconvergenceofthe1.numberseries

Section2.superiorlimitandlower1imit

Section3.positiveseries

Section4.arbitrarytermprogression

Section5.infiniteproduct

Theteachingrequirementsofthischapter:grasptheconcept

ofconvergenceanddivergenceofseveralseries,understandthe

conceptsofsequence,upperlimitandlowerlimit,and

skillfullyuseallkindsof

Thecriterionisusedtodistinguishthepositiveseries,the

convergenceanddivergenceofanyseriesandinfiniteproduct.

Thetenthchapteristheseriesoffunctionterms

Theuniformconvergenceoffunctionseriesofsection1.

Section2.andrecognizingthepropertiesofuniform

convergenceofaseries

Section3.powerseries

Section4.powerseriesexpansionofafunction

Section5.polynomialapproximationofcontinuousfunctions

Theteachingrequirementsofthischapterare:tograspthe

conceptofuniformconvergenceoffunctionseries(function

sequence),andtojudgetheconsistencyofconvergence

Thepropertiesofuniformconvergentseriesandtheproperties

ofpowerseriescanbeskillfullyexpandedaspowerseries,and

thepowerseriesexpansionoffunctionsisunderstood

Importantapplications.

TheeleventhchapteristhelimitandcontinuityinEuclid

spaces

Thebasictheoremon1.Euclidspace.

Section2.multivariatecontinuousfunction

Spertiesofcontinuousfunction

Theteachingrequirementsofthischapter:understandthe

topologicalpropertiesofEuclidspace,grasptheconceptof

the1imitandcontinuityofmultivariatefunction,distinguish

it

Thedifferencebetweentheconceptofafunctionandtheunary

function,andthepropertiesofthecontinuousfunctionon

compactset.

Thetwelfthchapterstudiesthemultivariatefunction

differential(1-5)

Section1.partialderivativeanddifferential

Section2.derivationruleofcompoundfunction

The3.Taylorformula

Section4.implicitfunction

Applicationof5.partialderivativesingeometry

Thetwelfthchapterstudiesthemultivariatefunction

differential(6-7)

Section6.unconditionalextremum

Section7.conditionalextremumproblemandLagrange

multipliermethod

Theteachingrequirementsofthischapteraretograspthe

conceptsofpartialderivativesanddifferentialfunctionsof

multivariatefunctionsanddistinguishtheregionsbetween

themandthecorrespondingconceptsofunaryfunctions

Donotgraspthederivationofmultivariatefunctionsand

implicitfunctions,grasptheapplicationofpartial

derivativesingeometry,andgraspthefunctionofmultivariate

functions

Themethodofconditionalextremumandconditionalextremum.

Thethirteenthchapteristhemultipleintegral

Section1.boundedclosedregiononthetripleintegral

Spertiesandcalculationofdoubleintegral

Segralvariablesubstitution

Section4.abnormalintegral

Section5.differentialform

Theteachingrequirementofthischapteristounderstandthe

conceptofmultipleintegral,masterthemethodsofcalculating

themultipleintegralandtheabnormalmultipleintegral,and

applythevariablegenerationskillfully

Changethemethodtocalculatethemultipleintegral,and

understandtheintroductionofdifferentialformintheformula

ofthevariablesubstitutionofthemultipleintegral.

Thefourteenthchapteriscurvilinearintegralandsurface

integral

Section1.firstclasslineintegralsandsurfaceintegralsof

thefirsttype

Section2.ofsecondkindofcurvilinearintegralandsurface

integralsofthesecondtype

The3.Greenformula,GaussformulaandStokesformula

Section4.differentialdifferentialform

Section5.preliminaryfieldtheory

Theteachingrequirementsofthischapter:graspthetwokinds

ofcurveintegralandtwokindsofsurfaceintegralconceptand

calculationmethod,mastertheGreenformula,Gauss

ThemeaningandapplicationofformulaandStokesformula,and

theintroductionofexteriordifferential,wegiveGreen

formula,GaussformulaandStokes

Themeaningoftheformulainunifiedform,andapreliminary

understandingofthetheoryoffieldknowledge.

Thefifteenthchapteristheintegralofparametricvariables

Section1.containsthecommonmeaningintegralvariable

Improperintegralwithvariablesection2.

The3.Eulerintegral

Theteachingrequirementofthischapteristomasterthe

propertyandcalculationoftheintegraloftheconstantofthe

parametricvariable,andtograsptheuniformconvergenceof

theimproperintegraloftheparametricvariable

Theconceptofuniformlyconvergentdiscrimination,the

propertiesofuniformlyconvergentimproperintegralandits

applicationinintegralcomputation,masteringEuler

Calculationofintegral.

Thesixteenthchapter,Fourierseries

Section1.Fourierseriesexpansionofafunction

Convergencecriteriaofsection2.oftheFourierseries

SpertiesofFourierseries

4.FourierandFourierintegraltransform

Section5.fastFouriertransform

TheteachingrequirementofthischapteristograsptheFourier

seriesexpansionmethodofperiodicfunctionandmasterthe

convergencejudgmentmethodofFourierseries

ThepropertiesofFourierserieshaveapreliminary

understandingoftheFouriertransformandtheFourier

integral.

testquestions

First,answerthefollowingquestions

1,

LimitLim,Tan,Tan

Sin,In()

X

X

ToX

9

2?

Two

One

2,

(ex1)3Exdx.+formula

3,

Limitlim.

X

XX

Xxx

++

+++

100101

010010001

Two

32

4,

YxTDT,fory.x=formula'3

Zero

2sin2

5,

setup

FXbeg,amongthem

Xxx

Xxx

0=f(a)f(a)a

+=?

>?

???

??

++?

Two

Two

11

21

110

6,

Seekthelimit

Lim

XLN

X

ToX

9

One

21

7,lety=(3x+1)In(3x+1),y

8,

Seekdx.

X

Xformula?

21

02

Three

One

9,setY,x,x,e,x,dy.

X()=?

32

One

10,

Theimplicitfunctiondeterminedbytheconstantofthe

equation

Differential

Xyaa

YYxdy

Two

Three

Two

Three

Two

+=3>0

0

0

H,

SetbyandbyOK

Trytofind

Y,y,x,x,s,y,s

Dy

DX

=0=(1+2)1=(1),

221

Two

12,setY,y,x,determinedbyequationye,y

Xy

==，X，

+

0,

13,ifx>0,provex+,1+,x>2x,2In()2

14,

ForFormula1

Sixteen

14xx

DX

15,

Forthemainpurpose.?

Two

1x4x2

DX

16,

(1)(1)

D

Formula2+X+X

X

Two.Answerthefollowingquestions

1,todoaconefunnel,itsbuslength20cm,tomakeitthe

largestvolume,askhowhighitshouldbe?

2,thecurvey=2,x2andy=xsurroundedbytheplanefigure

ofthearea

3,thecurvey=x2andy=x3onthesurfaceofthe[0,1]

surroundedbytheareaoftheplane

Three.Answerthefollowingquestions

Itisprovedthattheequationx5,7x=4,hasatleastone

realrootintheinterval(1,2)

Four.Answerthefollowingquestions

Determinetheconcavityandconvexityofthecurvey=(x+3)

xon[0++)

Secondpart

(1)CourseName:differentialgeometry

(2)basiccontent:theclassicaltheoryofcurvesandsurfaces

inthree-dimensionalspace.Themaincontentsare:

Thecurvetheory,including:thetangentvectorandthearc

lengthofcurve;andfromtheprincipalnormalvectormethod

vector;curvatureandtorsion;Frenet

TheframeandtheFrenetformula,thelocalstructureofthe

curve,thebasictheoremofthecurvetheory,andsomeintegral

propertiesoftheplanecurve,

Suchastangentrotationindextheorem,geometricpropertyof

convexcurve,IsoperimetricInequality,fourvertextheorem

and

Cauchy-Croftonformula.Someglobalpropertiesofspacecurves,

suchastheCroftonformulaofsphericalsurface,Fenchel

Fary-Milnorandtheorem.

Thelocaltheoryofsurfacesincludes:representationof

surfaces,tangentvectors,normalvectors,rotationsurfaces,

ruledsurfaces,andsurfaces

Developthesurface;thefirstfundamentalformandthe

intrinsicquantityofthesurface;thesecondfundamentalform

ofthesurface;theactiveframeonthesurface

Thebasicformula;asymptoteandWeingartentransformandthe

conjugatecurvedline;curvature;principalcurvatureand

principaldirection,.

Gausscurvatureandmeancurvature;thelocalstructureofthe

surface;theGaussmappingandthethirdfundamentalform;the

wholeumbilicalcurve

Surface,minimalsurfaceandconstantGausscurvaturesurface;

thebasictheoremofsurfacetheory;geodesiccurvatureand

geodesic;vector

Parallelmovement.

Basicrequirements:throughthestudyofthiscourse,students

shouldmastersomebasicgeometricconceptsandresearchin

curvetheoryandsurfacetheory

Somecommonmethodsoffractalgeometry.Inordertofurther

studyandstudymoderngeometrytolaythefoundation;onthe

otherhand,culture

Abilitytocombinetheorywithpracticeandanalyzeproblems

andsolveproblems.

Two,teachingoutline

Chapter1curvetheoryofthree-dimensionalEuclideanspace

Section1arctangentvectorcurvelength

Teachingrequirements:understandthebasicconceptsofcurves,

findthetangentvectorandarclengthofcurves,andusearc

lengthparameterstorepresentthecurve

Line。

Section2mainvectorandnormalvectorfromthecurvatureand

torsion

Teachingrequirements:understandingthecurvatureandtorsion

andnormalvectorandnormalvector,fromcloseplaneandthe

tangentplanefromthebasicconcept

Accounting,curvature,andtorsion.

Section3FrenetframeFrenetformula

Teachingrequirements:MasterFrenetformula,canuseFrenet

formulatosolvepracticalproblems.

Section4inaneighboringpropertycurve

Teachingrequirements:expressingthelocalcanonicalformof

acurveinafield,andunderstandingthesetsenseofthe

interferencesign.

Thebasictheoremofsection5curvetheory

Teachingrequirements:graspthebasictheoremofcurvetheory,

andcanfindsomesimplecurvesofknowncurvatureand

disturbance.

Someofthenatureofthewholesection6planecurve

6.1someconceptsaboutclosedcurves

6.2rotationindextheoremoftangents

6.3convexcurve*

6.4IsoperimetricInequality*

6.5,fourvertextheorem*

6.6Cauchy-Croftonformula*

Teachingrequirements:understandsomebasicconceptsofplane

curve:closedcurve,simplecurve,tangentimage,relative

wholecurve

Rotationindexandconvexcurve.Mastersomegeneralproperties

ofplanecurve:simpleclosedcurvecut

Theindextheoremofrotation,thegeometricpropertyofconvex

curve,IsoperimetricInequality,fourvertextheoremand

Cauchy-Croftonformula.

Thenatureofthewholesection7spacecurve

Croftonformulaof7.1sphere*

7.2Fencheltheorem*

7.3Fary-MiInortheorem*

Teachingrequirements:understandingtheconceptoftotal

curvature.Graspsomeoftheglobalpropertiesofthespace

curve:theCroftonofthesphere

Formula,FencheltheoremandFary-MiInortheorem.

Thesecondchapteristhelocalgeometryofthecurvedsurface

in3DEuclideanspace

Said1surfacetangentvectorvectormethod

1.1definitionofsurface

Tangentplaneof1.2tangentvectors

1.3normalvector

1.4parametricrepresentationofsurfaces

1.5cases

1.6,parametricsurfacefamily,planefamily,enveloping

surface,developablesurface

Teachingrequirements:graspthreelocalanalytic

representationsofthesurface,findthetangentplaneand

normalofthesurface,andunderstandtherotationalsurface

Andruledsurface;graspthefeatureofdevelopablesurface.

First,secondbasicforms,2surface

2.1thefirstfundamentalformofasurface

Orthogonalparametriccurvenetworkof2.2surfaces

Intrinsicgeometryof2.3equidistantcorrespondingsurfaces

2.4conformalcorrespondence

2.5thesecondfundamentalformofasurface

Teachingrequirements:graspthefirstbasicformofthe

surfaceandrelatedquantities-thearclengthofthecurve

onthesurfaceandthecurveofthetwointersection

Thecalculationofintersectionangleandarea,andunderstand

itsgeometricmeaning;understandingisometryandconformal

mapping;master

Secondbasicform.

Thebasicformulaofsection3onthesurfaceoftheframe

surface

3.1theConventionofomittingandtypingmarks

Thebasicformulaofthemovableframesurfaceon3.2surfaces

3.3WeingartentransformW

Conjugatedirectionasymptoteasymptoticdirectionof3.4

surfaces

Teachingrequirements:graspthebasicformulaofthemovable

frameandsurfaceonthesurface,andcanfindtheconnection

systemoftheorthogonalparametriccurvenet

Number;understandtheWeingartentransformandconjugate

directionsandasymptoticdirections,andfindsomesimple

curves

Asymptoticcurve.

Section4surfacecurvature

Thenormalcurvatureofacurveona4.1surface

4.2principalprincipalcurvatures

4.3Dupinreticle

4.4curvature

4.5principalcurvatureandcurvaturelinecalculation,total

curvature,meancurvature

4.6curvaturenetwork

Theshapeof4.7surfacesadjacenttoonepoint

The4.8Gaussmappingandthethreefundamentalform

4.9thetotalcurvatureandmeancurvaturesatisfysome

propertiesofthesurface

Teachingrequirements:understanding,curvature,principal

directionandprincipalcurvature,curvatureline,total

curvatureandmeancurvature,conceptsandgeometricmeanings

Yi,andwillcalculatethem;grasptheGaussmappingandthe

threebasicform;beabletotunethewholenavel

Surfacesareclassifiedwiththetotalcurvatureofthesurface

aszero.Graspthegeometricmeaningoftheminimalsurfaceand

askforsomesimplicity

Singleminimalsurface.

Thebasictheoremofthebasicequationsandthe5surfaceon

thesurface

5.1basicequationsofsurface

5.2fundamentaltheoremofsurfacetheory

Teachingrequirements:masteringandunderstandingthebasic

equationsofsurfaceandthebasictheoremofsurfacetheory.

Section6geodesicgeodesiccurvature

6.1geodesiccurvaturevectorgeodesiccurvature

6.2Liouvilleformulaforgeodesiccurvature

6.3geodesic

Geodesiccoordinatesystemofgeodesiccoordinatesystemin6.4

coordinatesystem

6.5applications

6.6grounddisturbancerate

6.7Gauss-Bonnetformula

Teachingrequirements:understandingandmasteringthe

geodesiccurvatureandgeodesic,grounddisturbance,normal

coordinatesystem,geodesiccoordinatesystemandmeasurement

Thedefinitionandgeometricmeaningoftheearthcoordinate

system.Thegeodesiccurvatureandgeodesiccanbecalculated

byusingtheLiouvilleformula

Line;canusethepolarcoordinatesystemtostudythecurved

surfacewhosetotalcurvatureisconstant;understand(part)

Gauss-Bonnetformula.

Parallelmotionvectoronthesurfaceofthesection7

7.1vectorsmovingalongasurfaceofacurve;absolutemotion;

absolutedifferentiation

7.2thenatureofabsolutedifferential

7.3selfparallelcurve

Seven

?

?

???

?

???

?

?

?

???

9

9

???

9

9

Arightsideis2

123

12242

62,R,h,h,H

HH??

???

?

++?

SoTisin(1,2,-)

1)theFderivativeatthatpointisthtransformationof

123,h,h,andhto(62,242),12123,h,h,H+H+H.

[Note1:thisanswermaintainsthewaytheoriginalquestion

isrepresentedbythelinevector..

[Note2:whenT:R3=R2means23

Two

Two

2,

32R

Z

Y

X

YXZR

Xy

Z

Y

T

??

?

?

??

?

9

A???

9

???

+

二？

???

?

??

9

9

CanwegetTin?

?

?

?

??

?

?

Z

Y

X

TheF-derivativeat..:

???

?

???

??

=?

?

?

9

??

9

?

??

?

9

??

9

?

ZYX

X

z

Y

X

T

222

620

Thatis,3

Three

Two

One

Three

Two

One

Three

Two

1,

222

620

R

Hhh

Hhh

ZYx

X

Hhh

Z

Y

X

T

??

9

9

??

9

?

?

??

9

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9

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?

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?

9

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9

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?

9

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?

9

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?

So二

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?

?

??

?

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??

?

?

??

9

9

??

?

?

??

9

?

?

Three

Two

One

One

Two

One

H

HH

T3

Three

Two

One

123

21422,

62R

Hhh

Hhh

HandH

??

?

?

??

9

?

???

????

++?

9

Or?

??

?

???

?

?

?

二？

9

9

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242

620

One

Two

One

T,theactionofanoperatoronavectorisrepresentedbya

vectoroftheleftmultiplicationofthevectorinthe

correspondingmatrix..

Thirdpart

1.basictheoremofHigherAlgebra

LetKbeanumberfield.TheunityofapolynomialinXwhose

coefficientsarerepresentedbyK[x]onK.If

(...)(0)0

One

01fxx=a+A+X+a=K?Xa=n

NncallsnthenumberofF(x),andisdenotedasDEGF(x).

Theorem(thebasictheoremofhigheralgebra)anyelementof

C[x]musthavezeroinC.

Propositionset()(01)0

One

01fxx=a+A+A+X?A=n=n

N,N,isanpolynomialonC,andais

Apluralnumber.Thereisanwhosefirstfactoris0a,and

the1polynomialQ(x)makesC

F(x)=q(x)(x,a)+F(a)

Mathematicalinductionofnisproved.

Corollary0xf(x)zero,ifandonlyif(0)x?Xf(x)factor

(includingDEGF(x)=1).

Proposition(equivalentpropositionofthebasictheoremof

higheralgebra)n

F(x)=a,x,N+,a,x,N,1+,+A

01

(01)a=0,n=npolynomialC,itcanbedecomposedintoa

productoffactorNcomplex,namely

N,a,a,,a12,make

()())nx=ax=xfalphaxalpha

Itisprovedthatthemathematicalinductionofnismadeby

usingthebasictheoremofHigherAlgebraandproposition1.3.

2.anotherexpressionofthebasictheoremofHigherAlgebra

ThedefinitionofKisanumberfield,andXisanunknown

quantity,thenanequation

…01

One

01++++=?

?

Nn

A,x,N,a,x,N,a,x,a()

(ofwhich,0010a,a...A...A=K=n)iscalledthenumber

fieldKanalgebraicequation;ifx=Alpha,K

Enter(1),andthenmakeitanequation,calledalpha(equation

1),arootinK.

Theorem(anotherformofthefundamentaltheoremofalgebra)

numberfieldKn(1)algebraicequationsinthecomplexdomain

C

Theremustbearootinside.

Thepropositionaln-algebraequationhasandhasexactlyn

roots(repeated)inthecomplexdomainC.

Proposition(anotherformofexpressionofthefundamental

theoremofhigheralgebra)giventwoNandMpolynomialsonC

().....(0)=01+++=n

N

N,F,x,a,a,x,a,x,a,

().....(0)=01+++=m

M

M,G,x,B,B,x,B,x,b,

IfthereisawholenumberL,1=m,1=nandL+1different

complex121,,1...L+betabetabetabeta,so

F()=g()(I,=1,2,...,L+1),I,I,beta,beta,

Thenf(x)=g(x).

1.2.2'stheoremandpropertiesofrootsofalgebraicequations

withrealcoefficients

1

01()nn

Nfx=ax+ax?+L+a,0I,0a,a=K,Letf(x)=0forcomplex

roots

12,nalpha,Lalpha(possiblyrepeated),then

12

01

One

1212

100000

0.

N

In

I

Nn

Nn

F,x,x,x,x,X

A

Xx

Alphaalphaalpha

Alpha,alpha,alpha,alpha

?

===???

=+++++

PIL

LLL

therefore

⑴（）12

One

Zero

One

Na

A=alpha+alpha+L+alpha;

Sigma

<<<

=?

Iin

IIa

A

12

12

Zero

Two

Zero

2(1)alpha;

LLLLLLLL

(1)12

Zero

N

Nn

A

A=alphaalphaLalpha

Weremember

(=,)1012=nsigma,alpha,alpha,L,alpha;

N,N,sigma1,alpha1,alpha2,L,alpha=Alpha1+alpha2,

+L+alpha

LLLLLLLL

PI

Islessthanorlessthanlessthanorequalto

Ilin

R,N,I,I,I

R

R

L

LL

12

12

Zero

12sigma(alpha,alpha,alpha)alphaalpha;

LLLLLLLL

N,N,N,sigma,1,alpha,2,L,alpha,1,alpha,2L,alpha(,,,)

(12,N,sigma,L,sigma,called12,elementarysymmetric

polynomialsofN,alpha,L,alpha).Hence

Theorem2.5(theWeitheorem)sets1

01()nn

Nfx=ax+ax?+L+a,0I,0a