《高等數(shù)學》課件-1.1 高等數(shù)學-英語

ChineseLanguageEnglishClassicalChineseMathematicsThefatherofmodernscience,Galileo,saidthatmathematicsisthelanguageinwhichtheuniversecommunicates.Pythagoras'philosophyof'Allthingsarenumbers'conveystheideathateverythingintheuniversecanbedescribedthroughthelanguageofmathematics,withnumbersbeingthefundamentalessenceofallthings.AdvancedMathematicsCoursePart1:Introduction-TheBeautyofMathematicsPart2:DeepeningUnderstanding-ClassroomImplementationPart3:Exploration-PresentationofResultsTableofContentsIntroduction:TheBeautyofMathematicsBeautyofMathematicsPart

1TheBeautyofMathematicsThePrinceofMathematics,Gauss,oncesaid—Mathematicsisthequeenofthesciences.TheFatherofModernChineseMathematics,HuaLuogeng,oncesaid:Thevastnessoftheuniverse,theminutenessofparticles,Thespeedofrockets,theingenuityofchemicalengineering,ThechangesoftheEarth,themysteriesofbiology,Thecomplexityofdailylife,allrelyonmathematics.Lookingback,Mathematicshasalwaysbeenwithus.QiuChengdong,thefirstChineserecipientoftheFieldsMedal,believesthatmathematicsisthemotherofboththeoreticalandappliedsciences.TheAmericanmathematicianKleinbelieved:“Mathematicsisthehighestintellectualachievementofhumanityandthemostuniquecreationofthehumanmind.”

IntelligentizationDigitalizationInFebruary2023,theCentralCommitteeoftheCommunistPartyofChinaandtheStateCouncilissuedthe"OverallLayoutPlanfortheConstructionofDigitalChina,"whichproposedthatbuildingDigitalChinaisanimportantengineforadvancingChinese-stylemodernizationinthedigitalera.Itisastrongsupportforestablishingnewcompetitiveadvantagesforthecountryandaimstofullyempowereconomicandsocialdevelopment.Thecurrenttrendinautomationfocusesmoreonlarge-scaleunmannedproduction,coveringindustriessuchasunmannedworkshops,unmannedfactories,unmannedkitchens,unmannedagriculturalbases,andunmannedlogisticstransportation.Theautomationiterationintheseareaswillbedrivenatahigherspeedandonalargerscale.Thefuturewillbeaneraofhighinterconnectionandintegration.Primaryschool(),Middleschool(),Highschool(),Advancedmathematics

Addition,subtraction,multiplication,divisionAlgebraicgeometry

Moreabstractandmoredimensional？

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⑧ThePythagoreanidearepresentedbythe"MathematicsSchool"of"1-0.999...>0"Zeno'sideaof"1-0.999...=0,but1-0.999...>0"Parmenides'ideaof"1-0.999...=0,or1-0.999...>0"

Multiplybothsidesoftheequationby3

Solution:

ElementaryMathematicsAdvancedMathematicsResearchobject:ConstantsElementarymethods:FinitemethodsElementarymathematicsisthestudyofconstantsusing

finitemethods.Researchobject:Variables(Functions)）

Researchmethod:ThemethodoflimitsAdvancedmathematicsisthestudyofvariablesusingthemethodoflimits.Everythingcanbeunderstoodthroughnumbers;thefundamentalprinciplesaresimple."AdvancedMathematics"usesmicroscopicmethodstosolvemacroscopicproblems.Animportantconceptistheideaofinfinitesimalelements,wheremacroscopicquantitiessuchasarea,volume,andworkaredividedintoinfinitesimalparts,approachingzero.infinitesimal[ConceptofInfinity]SpringandAutumnPeriodandWarringStatesPeriod

Mozi,MoJingSpaceandtimearebothfiniteandinfinite.Itimplicitlysuggeststheideaofinfinitemotion.[GerminationofLimits]WarringStatesPeriodZhuangZhou,Zhuangzi–TheWorldThegreatesthasnooutside,thisiscalledthegreatestone;thesmallesthasnoinside,thisiscalledthesmallestone.“Theproblemofdividingastick":"Aone-foot-longstick,ifhalvedeachtime,wouldneverbeexhaustedthroughcountlessgenerations."[ExhaustionMethod]WeiandJinDynastiesLiuHui,MethodofCircle-Splitting,NineChaptersontheMathematicalArtBydividingitfinerandfiner,thelossbecomessmaller.Dividingitfurtherandfurther,untilitisnolongerdivisible,willmakeitexactlymatchtheentirecircumferenceofthecircle.ZuChongzhi,PiCalculationHewasthefirsttocalculateπtosevendecimalplaces.[ExhaustionMethod]AncientGreeceArchimedesusedmetalplateswithinfinitesimalwidthtomeasureareasandvolumes.Zeno’sParadoxes[IndivisibleQuantities]Early17thCentury

Cavalieri,GeometriaIndivisibilibus(GeometryofIndivisibleQuantities)[FlawedCalculus]Late17thCentury

Newton

Leibniz19thCenturyCauchyEuler

Lagrange[SystematicCalculus]1870sWeierstrass,thefamousε–Nandε–δdefinitionsPracticalityThecoretechnologiesofthethreemajorindustrialrevolutionsinhumanhistoryareallcloselyrelatedtomathematics.FirstIndustrialRevolution(1760s–mid-19thcentury):Thecoretechnology,thesteamengine,requiredcalculationsrelatedtomotionandchange.Thesecalculationscouldonlybeachievedthroughtheapplicationofcalculus.Calculus→Mechanics→ModernScienceandTechnologySecondIndustrialRevolution(1870s–early20thcentury):Thedevelopmentofelectricalcommunicationtechnologyreliedontheadvancementofelectromagnetictheory,anditwascalculusthatlaidthemathematicalfoundationforthistheory.Maxwell’sEquations→ElectromagneticWaveTheory→CommunicationTechnologyThirdIndustrialRevolution(1940s–1950stopresent):Therelationshipbetweenelectroniccomputersandmathematicsbecameevenmoreprofound.Everystageofcomputerdevelopmenthasbeeninseparablefrommathematiciansandmathematics.StokesEquations→FluidMechanicsTheory→AeronauticsTheFourthIndustrialRevolution……ClassApplicationPart

2DeepeningUnderstanding-ClassroomImplementationFirstYearofUniversity80instructionalHoursMoldDesignandManufacturingMajorPublicBasicCoursesforHigherVocationalEducationinScienceandEngineeringModule1:LimitsandContinuityTableofContentsModule2:DerivativesandDifferentialsModule3:ApplicationsofDerivativesModule4:IndefiniteIntegralsModule5:DefiniteIntegralsandTheirApplicationsFollowtheprincipleof“modelingthinkingastheguidingprinciple,withapplicationasthepurpose”高等數(shù)學Emphasizethedevelopmentofstudents'fundamentalcomputationalabilities,aswellastheirskillsinproblemanalysisandproblem-solving.Providethenecessarymathematicalconcepts,theories,methods,computationalskills,andabilitiesforfuturestudyofspecializedcourses.The“AdvancedMathematics”coursewasrecognizedasamodelcourseforideologicaleducationinTianjin.Thecasestudyofthe“AdvancedMathematics”courseonideologicaleducationwasawardedasanoutstandingcaseinTianjin'scourseideologicaleducation.Thecourseparticipatedinthe2020and2021TianjinVocationalCollegeSkillsCompetitionintheteachingabilitycategoryandwonthecity'ssecondprize.Severalmicro-lessonswereawardedprizes.Onemunicipal-levelresearchproject,fourbureau-levelprojects,andtwocollege-levelprojectswerecompleted.“AdvancedMathematics,”“ProbabilityTheoryandMathematicalStatistics,”and“AppliedMathematics”wererecognizedaspartofthe100coursesforideologicaleducationconstructioninthecollege‘s“Double-High”initiative.CourseDevelopmentOutstandingCaseStudyTeachingCompetence/TeachingAbilityMicro-lessonProductionAward-winningPapersResearchProjectsBasedontheclassroomrevolution,thiscoursehasachievedsomeresultsinareassuchaseducationandteaching,ideologicaleducationwithinthecurriculum,andresearchtopics.ConceptUnderstandingTheoremDerivationModelingComputationCharacteristicsoftheMathematicsCourseAdvancedmathematicsischaracterizedbyits“highlevelofabstraction,rigorouslogicalstructure,andwideapplicability.”Weorganizethecorecompetenciesfromthreeaspects:conceptunderstanding,theoremderivation,andmodelingcomputation.ExperimentalNatureIdeologicalNatureProfessionalismApplicabilityMathematicalExperiment

MathematicalThinkingProfessionalKnowledge

ModelingApplicationrestructuringtheknowledgeframeworkcontentandextensionRedesigningtheteachingmodelFive-dimensionalimmersiveteachingmodelreconstructingtheassessmentandevaluationsystemprocess-basedvalue-addedquality-focusedreshapingtheclassroomstructurescenariocreation,modelderivation,groupinquiry,intensivepractice,inductiveexpansionrebuildingtheresourceplatformMOOCplatformanimationresourcesothercoursesreorganizingtheideologicalandpoliticalframework44663ideologicalandpoliticalcoursestructureAdoptingamultidimensionalteachingapproachtocollaborativelyorganizeclassroominstruction,thiscourseintegratesmathematicswiththemolddesignandmanufacturingmajor.Itaimstocultivatestudents'awarenessofapplyingmathematics,fosterinnovation,andguidestudentstodevelopmethodsofthinkingsuchasassociation,induction,andsubstitution.Thegoalistonurtureaspiritofactiveexplorationandindependentlearninginstudents.Strengtheningthought

emphasizingapplicationcultivatingabilities

improvingqualityCompositionofGradesAchievementdisplayPart

3Exploration–PresentationofResultsFour-DimensionalSpace–IndependentThinkingandExploringtheUnknownFromtwo-dimensionalanalyticgeometrytothree-dimensionalanalyticgeometry,thepropertiesandequationsofcurvesandplanesundergotransformations.Basedonthis,weinferandconjectureaboutfour-dimensionalspace.Zhuangzi:Thegreatesthasnooutside;itiscalledtheGreatOne.Thesmallesthasnoinside;itiscalledtheSmallOne.LiuHui:Oneofthefoundersofclassicalmathematicaltheory,knownforhismethodofcircle-squaring.Leibniz:Thefounderofcalculus,amasterofsymbolism.AcademicianYuanYaxiang:Thebeautyofmathematics.MathematicianQiuChengdong:

Fallingflowersareindependent,andtheswallowsflytogethe