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首页 Calculus Syllabus(下册)

Calculus Syllabus(下册).doc

Calculus Syllabus(下册)

甜丝丝田思思
2019-06-14 0人阅读 举报 0 0 暂无简介

简介:本文档为《Calculus Syllabus(下册)doc》,可适用于综合领域

高等数学()(全英语)教学大纲Calculus():CourseOutlineBusinessCollegeofBeijingUnionUniversityCourseCode:Semester:ClassTimes:  minuteclassesCredits:Prerequisite: DepartmentsDivisions: DivisionofBasicCoursesRequiredText:               Thomas’Calculus(TenthEdition)originallybyGeorgeBThomas,JrMassachusettsInstituteofTechnologyRecommendedText:Introduction:Thepurposeofthiscourseistoprovideanintroductiontocalculus,abranchofmathematicsdealingwithchangeandmotionWherethereismotionorgrowth,wherevariableforcesareatworkproducingacceleration,calculusisthemathematicstoapplyCalculuswasfirstinventedtomeetthemathematicalneedsofthescientistsofthesixteenthandseventeenthcenturies,needsthatweremainlymechanicalinnatureToday,calculusanditsextensionsinmathematicalanalysisarefarreachingindeed,andthephysicists,mathematicians,andastronomersArangeoffieldsnowuseitinthemathematicalmodelsthatbringunderstandingabouttheuniverseandtheworldaroundusAims: Toreallyunderstandhowtousetheconceptsincalculustodescribemotionandchangeofamaterialintheworld Touseagraphingutility(software:Mathematica)asatooltoinvestigatemathematicalideas,tosupporttheanalyticalwork,andtosolveproblemswithnumericalandgraphicalmethodsObjectives:Attheendofthecourseastudentshouldbeableto understandtheapplicationofintegration gettoknowthecomputationofthedifferentialequations illustratetheimportantrepresentationoffunctionbyseriesotherthanpowerseries understandvectorsandprojectilemotionintheplane treatthepartialderivativeswithconstrainedvariablesanddirectionalderivatives calculatemasses,momentsandcentersofmasswithmultipleintegralsSyllabus(LectureSchedule):Chapter:ApplicationsofIntegrals,(lectures)SectionsfromtowillbeincludedThevolumesofsolidscanbecalculatedwithintegralsaslimitsofRiemannsumsofcontinuousfunctionsonclosedintervalsArclengthformulasaredevelopedforbothexplicitfunctionandparametriccurvesintheplaneThelengthsofcurvescanalsobecalculatedwithintegralsTheapplicationstocalculatethevolumesofsolidsandthelengthsofcurvesareveryimportanttounderstandthissubjectCalculusChapter:DifferentialEquations(lectures)Sectionsfrom,,andwillbeincludedThedefinitionofdifferentialequationsasthelinkbetweenderivativeandintegralSolvethefirstorderseparabledifferentialequationsSolvethelinearfirstorderdifferentialequationsDifferentialequationsaresoimportanttosolvetherealworldproblemslikethepopulationissueChapter:InfiniteSeries(lectures)SectionsfromtowillbeincludedThebasicideasconcerningsequencesofnumbersandtheirlimitsarecoveredMostoftheimportantseriesconvergencetestsarepresentedtogetherTorepresentsomefunctionsastheTaylorseriesThischaptercontainstheelementaryintroductionofseriesandisusefulinintegrationChapter:Vectorsintheplaneandpolarfunctions(lectures)SectionsfromtowillbeincludedPermitsanearlierselfcontainedtreatmentofplanarvectorsVectorideasaremotivatedbytheirapplicationtostudyingpaths,velocities,accelerations,andforcesassociatedwithbodiesmovingalongplanarpaths ThisisthelastchaptertotreattheideasofsinglevariablecalculusandthetransitionalchaptertonextthreedimensionalcalculusChapter:Multivariablefunctionsandtheirderivatives(lectures)SectionsfromtowillbeincludedLimitsandcontinuityforfunctionsofseveralvariablesPartialderivativesandthechainrule(similartochapter),directionalderivativesandgradientvectorsFindtheextremevaluesbytwoways,oneofwhichisLagrangeMultipliersThischaptercanbecontrastedwithchapterthroughFromlimitstoExtremevaluesallthecontentsaretheexpansionofxyplanecalculusChapter:Multipleintegrals(lectures)SectionsfromtowillbeincludedTheintroductionofthegeometricalmeansofdoubleintegralsUsedoubleintegralstofindtheareas,moments,andcentersofmassExceptdoubleintegralinxyplane,thepolarformdoubleintegralisalso

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Calculus Syllabus(下册)

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