单变量微积分
出版时间:
2015-05
版次:
1
ISBN:
9787510094903
定价:
80.00
装帧:
平装
开本:
16开
纸张:
胶版纸
页数:
350页
字数:
430千字
正文语种:
简体中文
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Inrecentlyyears,moreandmoreChinesestudentsaregoingoverseas,eitherasexchangestudents,ortopursuedegrees.Atthesametime,moreandmorestudentsarecomingfromothercountriestoChineseuniversitiestofurthertheirstudies.We'venoticedthatintermsofbothknowledgetransferandinterculturalcommunication,theEnglishlanguagehasplayedanindispensablerole.Furthermore,itistheinterestofthesestudentstohaveasmoothtransitionfromonesystemtoanother,fortheircreditstotransfer,andforthemtoimmersethemselvesinthenewenvironmentasquicklyaspossible.Tothisend,moreandmoreChineseschoolsareofferingcoursesdeliveredbilinguallyorinEnglishtoenhancestudents'internationaloutlook.
OneofthegreatestchallengesinofferingChinesestudentsacourseinEnglishisfindingasuitabletextbook:thetextbookmustseriouslyconsiderwhatstudentshavedoneintheirhighschools;itmustmeetthenationalandlocalofficialcoursestandards;anditshouldresonatewithsignificantinternationalflavorssoastobenefitstudents. CHAPTER1PrereqrusitesforCalculus
1.1OverviewofCalculus
1.2SetsandNumbers
1.2.1Sets
1.2.2Numbers
1.2.3TheLeastUpperBoundProperty
1.2.4TheExtendedRealNumberSystem
1.2.51ntervals
1.3Functions
1.3.1DefinitionofaFunction
1.3.2GraphofaFunction
1.3.3SomeBasicFunctionsandTheirGraphs
1.3.4BuildingNewFunctions
1.3.5FundamentalElementaryFunctions
1.3.6PropertiesofFunctions
1.4Exercises
CHAPTER2LimitsandContinruty
2.1RatesofChangeandDerivatives
2.2LimitsofaFunction
2.2.1DefinitionofaLimit
2.2.2PropertiesofLimitsofFunctions
2.2.3LimitLaws
2.2.4One-sidedLiruits
2.2.5LimitsInvolvingInfinityandAsymptotes
2.3LimitsofSequences
2.3.1DefinitionsandProperties
2.3.2Subsequences
2.4SqueezeTheoremandCauchy'sTheorem
2.5InfinitesimalFunctionsandAsymptoticFunctions
2.6ContinuousandDiscontinuousFunctions
2.6.1ContinuityandDiscontinuity
2.6.2ContinuousFunctions
2.6.3TheoremsonContinuousFunctions
2.6.4UniformContinuity
2.7SomeProofsinChapter
2.8Exercises
CHAPTER3I'heDerivative
3.1DerivativeofaFunctionataPoint
3.1.1InstantaneousRatesofChangeandDerivativesRevisited
3.1.2One-sidedDerivatives
3.1.3AFunctionMayFailtoHaveaDerivativeataPoint
3.2DerivativeasaFunction
3.2.1GraphingtheDerivativeofaFunction
3.2.2DerivativesofSomeBasicFunctions
3.3DerivativeLaws
3.4DerivativeofanJnverseFunction
3.5DifferentiatingaCompositeFunction-TheChainRule
3.6DerivativesofHigherOrders
3.7ImplicitDifferentiation
3.8FunctionsDefinedbyParametricandPolarEquations
3.8.1FunctionsDefinedbyParametricEquations
3.8.2PolarCurves
3.9RelatedRatesofChange
3.10TheTangentLineApproximationandtheDifferentia
3.10.1Linearization
3.10.2Differentials
3.11DerivativeRules-Summary
3.12Exercises
CHAPTER4ApplicationsoftheDerivative
4.1ExtremeValuesandTheCandidateTheorem
4.2TheMeanValueTheore
4.3MonotonicFunctionsandTheFirstDerivativeTest
4.3.1MonotonicFunctions
4.3.2TheFirstDerivativeTest
4.4ExtendedMeanValueTheoremandtheL'Hopital'sRules
4.4.1ExtendedMeanValueTheorem
……
CHAPTER5TheDefiniteIntegral
CHAPTER6TechniquesforIntegrationandImproperIntegrals
CHAPTER7ApplicationsoftheDefiniteIntegral
CHAPTER8InfiniteSeries,Sequences,andApproximations
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内容简介:
Inrecentlyyears,moreandmoreChinesestudentsaregoingoverseas,eitherasexchangestudents,ortopursuedegrees.Atthesametime,moreandmorestudentsarecomingfromothercountriestoChineseuniversitiestofurthertheirstudies.We'venoticedthatintermsofbothknowledgetransferandinterculturalcommunication,theEnglishlanguagehasplayedanindispensablerole.Furthermore,itistheinterestofthesestudentstohaveasmoothtransitionfromonesystemtoanother,fortheircreditstotransfer,andforthemtoimmersethemselvesinthenewenvironmentasquicklyaspossible.Tothisend,moreandmoreChineseschoolsareofferingcoursesdeliveredbilinguallyorinEnglishtoenhancestudents'internationaloutlook.
OneofthegreatestchallengesinofferingChinesestudentsacourseinEnglishisfindingasuitabletextbook:thetextbookmustseriouslyconsiderwhatstudentshavedoneintheirhighschools;itmustmeetthenationalandlocalofficialcoursestandards;anditshouldresonatewithsignificantinternationalflavorssoastobenefitstudents.
-
目录:
CHAPTER1PrereqrusitesforCalculus
1.1OverviewofCalculus
1.2SetsandNumbers
1.2.1Sets
1.2.2Numbers
1.2.3TheLeastUpperBoundProperty
1.2.4TheExtendedRealNumberSystem
1.2.51ntervals
1.3Functions
1.3.1DefinitionofaFunction
1.3.2GraphofaFunction
1.3.3SomeBasicFunctionsandTheirGraphs
1.3.4BuildingNewFunctions
1.3.5FundamentalElementaryFunctions
1.3.6PropertiesofFunctions
1.4Exercises
CHAPTER2LimitsandContinruty
2.1RatesofChangeandDerivatives
2.2LimitsofaFunction
2.2.1DefinitionofaLimit
2.2.2PropertiesofLimitsofFunctions
2.2.3LimitLaws
2.2.4One-sidedLiruits
2.2.5LimitsInvolvingInfinityandAsymptotes
2.3LimitsofSequences
2.3.1DefinitionsandProperties
2.3.2Subsequences
2.4SqueezeTheoremandCauchy'sTheorem
2.5InfinitesimalFunctionsandAsymptoticFunctions
2.6ContinuousandDiscontinuousFunctions
2.6.1ContinuityandDiscontinuity
2.6.2ContinuousFunctions
2.6.3TheoremsonContinuousFunctions
2.6.4UniformContinuity
2.7SomeProofsinChapter
2.8Exercises
CHAPTER3I'heDerivative
3.1DerivativeofaFunctionataPoint
3.1.1InstantaneousRatesofChangeandDerivativesRevisited
3.1.2One-sidedDerivatives
3.1.3AFunctionMayFailtoHaveaDerivativeataPoint
3.2DerivativeasaFunction
3.2.1GraphingtheDerivativeofaFunction
3.2.2DerivativesofSomeBasicFunctions
3.3DerivativeLaws
3.4DerivativeofanJnverseFunction
3.5DifferentiatingaCompositeFunction-TheChainRule
3.6DerivativesofHigherOrders
3.7ImplicitDifferentiation
3.8FunctionsDefinedbyParametricandPolarEquations
3.8.1FunctionsDefinedbyParametricEquations
3.8.2PolarCurves
3.9RelatedRatesofChange
3.10TheTangentLineApproximationandtheDifferentia
3.10.1Linearization
3.10.2Differentials
3.11DerivativeRules-Summary
3.12Exercises
CHAPTER4ApplicationsoftheDerivative
4.1ExtremeValuesandTheCandidateTheorem
4.2TheMeanValueTheore
4.3MonotonicFunctionsandTheFirstDerivativeTest
4.3.1MonotonicFunctions
4.3.2TheFirstDerivativeTest
4.4ExtendedMeanValueTheoremandtheL'Hopital'sRules
4.4.1ExtendedMeanValueTheorem
……
CHAPTER5TheDefiniteIntegral
CHAPTER6TechniquesforIntegrationandImproperIntegrals
CHAPTER7ApplicationsoftheDefiniteIntegral
CHAPTER8InfiniteSeries,Sequences,andApproximations
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