高等数学基础1（英文版）

图书标准信息

• 作者 马知恩、王锦森 著
• 出版社 高等教育出版社
• 出版时间 2005-01
• 版次 1
• ISBN 9787040154849
• 定价 32.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 390页
• 字数 470千字
• 正文语种 英语

【内容简介】

TheaimofthisbookistomeettherequirementsofteachingCalculusinEnglishorinbilin．gualeducationaccordingtothecustomsofteachingandthepresentdomesticconditions．Itisdividedintotwovolumes．ThefirstvolumecontainsCalculusofsinglevariable，simpledifferentialequations，infiniteseries，andthesecondvolumecontainstherest．

TheselectionofthecontentsisinaccordancewiththefundamentalrequirementsofteachingissuedbytheMinistryofEducationofChina，andisbasedontheaccOmDlishmentsofreforminteachingduringthepasttenyears．ThearrangementandexplanationofthemaincontentsinthisbookareapproximatelythesameasthepublishedChineseversionwiththesametitleandeditedinchiefbythefirsttwoauthors．ItmayhelpreaderstounderstandthemathematicsandtoimprovetheleveloftheirEnglishbyreadingoneofthemandusingtheotheroneasareference．Thisbookmaybeusedasatextbookforundergraduatestudentsinthescienceandengi．neeringschoolswhosemajorsarenotmathematics，andmayalsobesuitabletothereadersatthesamelevel．

【目录】

~Introduction

ChapterlTheoreticalBasisofCalculus

1．1SetsandFunctions

1．1．1Setsandtheiroperations

1．1．2Conceptsofmappingsandfunctions

1．1．3Compositionofmappingsandcompositionoffunctions

1．1．4Inversemappingsandinversefunctions

1．1．5Elementaryfunctionsandhyperbolicfunctions

1．1．6Someexamplesformodellingoffunctionsinpracticalproblems

Exercises1．1

1．2LimitofSequence

1．2．1Conceptoflimitofasequence

1．2．2Conditionsforconvergenceofasequence

1．2．3Rulesofoperationsonconvergentsequences

Exercises1．2

l-3LimitofFunction

1-3．1Theconceptoflimitofafunction

1．3．2Thepropertiesandoperationrulesoffunctionallimits

1-3-3Twoimportantlimits

Exercises1．3

1．4InfinitesimalandInfiniteQuantities

1．4．1Infinitesimalquantitiesandtheirorder

1．4．2Equivalencetransformationsofinfinitesimals

1．4．3Infinitequantities

ExereIses1．4

1．5ContinUOUSFunctions

1．5．1Theconceptofcontinuousfunctionandclassificationofdiscontinuouspoints

1．5．2OperationsoncontinuousfunctionsandthecontinuAyofelementaryfunct~~ns

1．5．3Propertiesofcontinuousfunct~~nsonaclosedinterval

Exercises1．5

Chapter2TheDiffercmtialCaleuklsandItsApplications

2．1ConceptofDerivatives

2．1．1Definitionofderivatives

2．1．2Relationshipbetweenderivabilityandcontinuity

2．1．3Someexamplesofderivativeprob~~msinsconceandtechnology

Exercises2．1

2．2FundamentalDerivationRules

2．2．1Derivationrulesforsum，difference，productandquotientoffunctions

2．2．2Derivationruleforcompositefunctions

2．2．3Thederivativeofaninversefunction

2．2．4Higher-orderderivatives

Exercises2．2

2．3DerivationofImplicitFunctionsandFunctionsDefinedbyParametricEquations

2．3．1Methodofderivationofimplicitfunctions

2．3．2Methodofderivationofafunctiondefmedbyparametricequations

2．3．3Relatedratesofchange

Exercises2．3

2．4TheDifferential

2．4．1Conceptofthedifferential

2．4．2Geometricmeaningofthedifferential

2．4．3Rulesofoperationsondifferentials

2．4．4Applicationofthedifferentialinapproximatecomputation

Exercises2．4

2．5TheMeanValueTheoreminDifferentialCalculusandL’Hospital’SRules

2．5．1Meanvaluetheoremsindifferentialcalculus

2．5．2L’Hospital’Srules

Exercises2．5

2．6Taylor’STheoremandItsApplications

2．6．1Taylor’Stheorem

2．6．2Maclaurinformulaeforsomeelementaryfunctions

2．6．3SomeapplicationsofTaylor’Stheorem

Exercises2．6

2．7StudyofPropertiesofFunctions

2．7．1Monotonicityoffunctmns

2．7．2Extremevaluesoffunctions

2．7．3Globalmaximaandminima

2．7．4Convexityoffunctmns

Exercises2．7

Syntheticexercises

Chapter3TheIntegralCalculusandItsApplications

3．1ConceptandPropertiesofDefiniteIntegrals

3．1．1Examplesofdefiniteintegralproblems

3．1．2Thedefinitionofdefiniteintegral

3．1．3Propertiesofdefmiteintegrals

Exercises3．1

3．2TheNewton-LeibnizFormulaandtheFundamentalTheoremsofCalculus

3．2．1Newton-Leibnizformula

3．2．2FundamentaltheoremsofCalcUlus

Exercises3．2

3．3IndefiniteIntegralsandIntegration

3．3．1IndeKmiteintegrals

3．3．2Integrationbysubstitutions

3．3．3Integrationbyparts

3．3．4Quadratureproblemsforelementaryfundamentalfunctions

Exercises3．3

3．4ApplicationsofDefiniteIntegrals

3．4．1Methodofelementsforsettingupintegralrepresentations

3．4．2Someexamplesontheapplicationsofthedefmiteintegralingeometry

3．4．3Someexamplesofapplicationsofthedefiniteintegralinphysics

Exercises3．4

3．5SomeTypesofSimpleDifferentialEquations

3．5．1Somefundamentalconcepts

3．5．2Firstorderdifferentialequationswithvariablesseparable

3．5．3Linearequationsoffirstorder

3．5．4Equationsoffirstordersolvablebytransformationsofvariables

3．5．5Differentialequationsofsecondordersolvablebyreducedorder

methods

3．5．6Someexamplesofapplicationofdifferentialequations

Exertises3．5

3．6ImproperIntegrals

3．6．1Integrationonaninfiniteinterval

3．6．2Integralsofunboundedfunctions

Exercises3．6

Chapter4InfinteSeries

4．1SeriesofConstantTerms

4．I．IConceptsandpropertiesofserieswithconstantterms

4．1．2Convergencetestsforseriesofpositiveterms

4．1．3Serieswithvariationofsignsandtestsforconvergence

Exercises4．1

42PowerSeries

4．2．IConceptsofseriesoffunctions

4．2．2Convergenceofpowerseriesandoperationsonpowerseries

4．2．3Expansionoffunctionsinpowerseries

4．2．4Someexamplesofapplicationsofpowerseries

4．2．5Uniformconvergenceofseriesoffunctions

Exercises4．2

4．3FourierSeries

4．3．1Periodicfunctionsandtrigonometricseries

4．3．2OrthogonalityofthesystemoftrigonometricfunctionsandFourierseries

4．3．3Fourierexpansionsofperiodicfunctions

4．3．4Fourierexpansionoffunctionsdefinedontheinterval[O，l]

4．3．5ComplexformofFourierseries

Exercises4．3

Syntheticexercises

AppendixAnswersandHintsforExercises~