江苏省高等教育自学考试大纲Jiangsu higher education self study examination program.docx

江苏省高等教育自学考试大纲Jiangsu higher education self study examination program.docx

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江苏省高等教育自学考试大纲Jiangsuhighereducationselfstudyexaminationprogram

江苏省高等教育自学考试大纲（Jiangsuhighereducationselfstudyexaminationprogram）

Documentsfromthenetwork,Icollected,finishing,andifthereareomissions,errors,butalsopleasecorrectme!

GaoGang1132

Jiangsuhighereducationselfstudyexaminationprogram

27707AppliedMathematicsinEconomics

NanjingAgriculturalUniversityseries

JiangsuhighereducationselftaughtExaminationCommitteeOffice

First,thenatureofthecourseanditssettings,purposesandrequirements

（1）thenature,statusandtasksofthecourse

Theapplicationofeconomicmathematicsisanimportantbasiccourseineconomicsandmanagementmajors,whosemaintaskistocultivatethebasicconcept,sincescholarssystematicallystudycalculusineconomicsandmanagementspecialtybasictheoryandbasicprinciple,tocultivatestudents'abilityofabstractthinkingbasedonthecalculuslearningability,logicalreasoninganddiscoverytheproblemandtheabilitytoanalyzeandsolveproblems,forthestudentstofollowacourseofstudyforstudentsinthefuturetoengageineconomicmanagementorrelatedbusinessorworktolayagoodfoundation

（two）basicrequirementsandkeypointsofthiscourse;

Thefollowingrequirementsshouldbemetthroughthestudyofthiscourse:

1.toobtainthebasicknowledge,basictheoryandbasicmethodsofthesystemofcalculusofunaryfunctioncalculus,especiallythethinkingandmethodofdealingwithproblemsinCalculusofoneyuan;

2.obtainelementaryknowledgeofmultivariatefunctionaldifferentialcalculus

Theemphasisofthiscourseisonthelimitandcontinuityofaunaryfunction,theconceptsandcalculationsofderivativesanddifferentials,integrals,andtheirapplications

Consideringthecharacteristicsofeconomicmanagementspecialty,thespiritoflayingasolidfoundation,focusesontheapplicationoftheprinciplerequirementsbetweenthebasicconceptinthecurriculumandstudentstounderstandtheirrelationship,graspthecalculationmethodandbasicskills,andtheseconceptsandmethodsinsomesimpleapplications

Therelevanttheoremsinthecoursedonotrequiretheknowledgeoftheconditionsforthetheoremtobeestablished,theconclusionsthatcanbeobtained,theproofofthetheorem,andthecontentthatisnotrelevanttotheeconomy

（three）thelinkbetweenthiscourseandrelatedcourses;

Calculustakesfunctionsastheobjectofstudy.Thiscoursemainlyincludestheconcepts,methods,calculationsandapplicationsofderivatives,differentialandintegralfunctionsofthefunctions,andthelimitisthebasictoolforelucidatingtheseconceptsandmethods

Forthisreason,candidatesshouldhavethebasicknowledgeofhighschoolmathematicswhentheystudythiscourse

Ontheotherhand,thiscourselaysthenecessarymathematicalfoundationforthefollow-upcoursesinthemajorofeconomicsandmanagement

Two,curriculumcontentandassessmentobjectives

Chapter1functionandlimit

I.assessmentofknowledgepoints

1.theconceptoffunction（definitionoffunction,domainofdefinition,methodofexpression）;

2.thebasicpropertiesofafunction（monotonicity,parity,boundedness,periodicity）;

3.compoundfunctionandinversefunction;

4.elementaryfunctionsandpiecewisefunctions;

Theconceptofthelimitof5.seriesandthelimitoffunction,thebasicarithmeticoflimit;

6.theconceptsofinfinityandinfinity,theirrelations,thepropertiesofinfinitesimal,andthecomparisonofinfinitesimalquantities;

7.,twoimportantlimits;

8.continuityanddiscontinuityoffunction

9.commonfunctionsineconomicproblems（demandfunction,supplyfunction,costfunction,incomefunction,profitfunction）;

Two,self-studyrequirements

Functionisoneofthemostbasicconceptsinmathematics.Itreflectsthedependencebetweenquantityandquantityinavarietyofpracticalphenomena.Itisthemainobjectofcalculus

Thelimittheoryisthebasisofcalculus,andthebasicconceptsincalculusareexpoundedbythelimitmethod

Continuousfunctionsarethemostwidelyusedfunctions

Therefore,learningthischapterwilllaythenecessaryfoundationforfuturestudy

Inthischapter,thegeneralrequirementis:

therelationshipbetweenthedefinitionofafunctionandfunctionandgraphics;understandthefunctionofseveralcommonlyusedmethod;severalbasicpropertiesofunderstandingfunction;therelationshipbetweenfunctionandinversefunctiontounderstandtheirimage;graspthefunctionofcompositeandsolution;masteringthebasicelementaryfunctionsandgraphicform;knowwhatistheelementaryfunction;

Knowsomecommoneconomicfunction;toestablishfunctionwhichcontainsfromtheactualproblemisrelativelysimple;therelationshipbetweenconceptlimitsandinfinitesimalandtheiroperationrules,graspthebasicnatureandthelimitofinfinitesimal,clearinfiniteconceptanditsrelationshipwithinfinitesimals;masterthetwoimportantthelimit;understandingandcomparisonofinfinitesimalandhigherorderinfinitesimal;understandthefunctionofthecontinuityanddiscontinuity,knowthecontinuityofelementaryfunction;clearclosedintervalcontinuousfunctionofthebasicproperties

Thischapterfocusesontheconceptsoffunctionsandelementaryelementaryfunctions,theconceptsandpropertiesoflimitandinfinitesimalquantities,theoperationlawsoflimit,twoimportantlimitsandthecontinuityoffunctions

Difficultiesinthischapter:

thecompositeoffunctions;theconceptoflimit

Three,assessmentrequirements

1.,understandthebasicconceptsoffunctions,willbeskilledindefiningthedomainoffunctionandfindingthefunctionvalueofagivenfunctionatsomepoint;

2.graspthemonotonicity,parity,boundedness,periodicityoffunctions,anddeterminethepropertiesofthegivenfunctions;

3.understandtheconceptofcompositefunctions,analyzethecomplexprocessofcompositefunctions,andunderstandtherelationbetweenfunctionsandtheirinversefunctions,andfindtheinversefunctionsofsimplefunctions;

4.,masterthebasicelementaryfunctionofsimplenatureanditsimage;mastertheconceptofelementaryfunction,willfindthesectionfunctiondefinitiondomainandfunctionvalue;

5.,thefunctionalrelationofthesimpleeconomicapplicationproblemisestablished,includingdemandfunction,supplyfunction,costfunction,incomefunctionandprofitfunction;

6.,understandtheconceptofthelimitofaseries,andusetheobservationmethodtojudgewhetherthelimitofaseriesexists;

7.,understandtheconceptofthelimitoffunction,graspthenatureoflimitandthefourarithmeticoflimit,donotaskforthedescriptionofthelimit""and"";

8.understandtheconceptsofinfinitesimalandinfinity,grasptherelationbetweenthem,andgraspthepropertiesofinfinitesimal,andcomparetheorder（equivalence,higherorder,lowerorderandsameorder）ofinfinitelysmallquantities;

9.mastertwoimportantlimitsandusethemskillfullytofindthelimit;

10.understandtheconceptofcontinuityanddiscontinuityoffunctionsatonepoint,understandthecontinuityofelementaryfunctionsontheirdefinedintervals,andknowthepropertiesofcontinuousfunctionsonclosedintervals;

11.graspthemethodoffindingthelimitofthepiecewisefunctionatthedividingpoint,anddiscussthecontinuityatthesepoints

Thesecondchapterisderivativeanddifferential

I.assessmentofknowledgepoints

1.definitionsofderivativesandtheirgeometricandphysicalmeanings;

2.,therelationbetweendifferentiableandcontinuousfunctions;

3.variousderivationrulesoffunctions;

4.derivativesofbasicelementaryfunctions;

5.higherorderderivatives;

6.differentialdefinitionanddifferentialbasicformulaandoperationlaw;

Two,self-studyrequirements

Thederivativeanddifferentiationoffunctionsaretwoimportantandcloselyrelatedconceptsindifferentialcalculus

Theiremergenceisduetotheextensiveandurgentpracticalneeds（suchasthetangentofcurves,thespeedofmovement,etc.）andtheirwideapplicationsinscienceandEngineering

Inthischapter,thegeneralrequirementis:

thedefinitionofderivativeanddifferential,cleartherelationshipbetweenthem;knowthederivativeofthegeometricmeaningandpracticalsignificance;knowthesolutionmethodoftangentequationofplanecurve;understandtherelationbetweenthecontinuousfunctionandguide;proficientinlawfunctionderivation,especiallythederivationruleofcompoundfunctionmemorize;derivationofbasicelementaryfunction;highorderderivativewillfunction;masterthebasicformulaanddifferentialalgorithm

Thischapterfocusesontheconceptofderivativeanditsgeometricmeaningandthepracticalsignificanceoftherateofchange,thederivationofvariousrulesandthederivativeanddifferentialformulaofbasicelementaryfunctions

Difficultiesinthischapter:

derivationrulesofcompositefunctions

Three,assessmentrequirements

1.,understandthedefinitionofderivativeanditsgeometricmeaning,willfindthetangentequationofplanecurve,understandtherelationbetweenfunctionderivableandcontinuous,anddiscussthesimpleproblemwiththedefinitionofderivative;

2.masterthederivativeformulaofbasicelementaryfunctionandthefouroperationrulesofderivative;

3.,graspthederivationofthecompositefunction,willfindthederivativeofimplicitfunction,willusethelogarithmicderivativemethodtofindthederivativesofsomefunctions;

4.understandtheconceptofhigherorderderivatives,willfindthetwoderivativeoffunction,willcalculatethefirstderivativeofsimplepiecewisefunction;

5.understan