Advanced Mathematics（高等数学）

图书标准信息

• 作者 陈明明 编
• 出版社 化学工业出版社
• 出版时间 2010-10
• 版次 1
• ISBN 9787122094599
• 定价 28.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 222页
• 字数 374千字
• 正文语种 英语
• 丛书 高等学校规划教材；高等数学

【内容简介】

TheaimofthisbookistomeettherequirementofbilingualteachingofadvancedmathematicsTheselectionofthecontentsisinaccordancewiththefundamentalrequirementsofteachingissuedbytheMinistryofEducationofChinaAndbaseonthepropertyofouruniversity,weselectsomeexamplesaboutpetrochemicalindustryTheseexamplesmayhelpreaderstounderstandtheapplicationofadvancedmathematicsinpetrochemicalindustry
ThisbookisdividedintotwovolumesThefirstvolumecontainscalculusoffunctionsofasinglevariableanddifferentialequationThesecondvolumecontainsvectoralgebraandanalyticgeometryinspace,multivariablecalculusandinfiniteseries
Thisbookmaybeusedasatextbookforundergraduatestudentsinthescienceandengineeringschoolswhosemajorsarenotmathematics,andmayalsobesuitabletothereadersatthesamelevel.

【目录】

Chapter1Functionsandlimits11.1Mappingsandfunctions
1.1.1Sets
1.1.2Mappings
1.1.3Functions
Exercise11141.2Limitsofsequences
1.2.1Conceptoflimitsofsequences
1.2.2Propertiesofconvergentsequences
Exercise12211.3Limitsoffunctions
1.3.1Definitionsoflimitsoffunctions
1.3.2Thepropertiesoffunctionallimits
Exercise13261.4Infinitesimalandinfinityquantity
1.4.1Infinitesimalquantity
1.4.2Infinityquantity
Exercise14291.5Rulesoflimitoperations
Exercises15341.6Principleoflimitexistencetwoimportantlimits
Exercise16391.7Comparingwithtwoinfinitesimals
Exercise17421.8Continuityoffunctionsanddiscontinuouspoints
1.8.1Continuityoffunctions
1.8.2Discontinuouspointsoffunctions
Exercise18461.9Operationsoncontinuousfunctionsandthecontinuityof
elementaryfunctions
1.9.1Continuityofthesum，difference，productandquotientofcontinuousfunctions
1.9.2Continuityofinversefunctionsandcompositefunctions
1.9.3Continuityofelementaryfunctions
Exercise19491.10Propertiesofcontinuousfunctionsonaclosedinterval
1.10.1Boundednessandmaximumminimumtheorem
1.10.2Zeropointtheoremandintermediatevaluetheorem
*1.10.3Uniformcontinuity
Exercise1
Exercise

Chapter2Derivativesanddifferential552.1Conceptofderivatives
2.1.1Examples
2.1.2Definitionofderivatives
2.1.3Geometricinterpretationofderivative
2.1.4Relationshipbetweenderivabilityandcontinuity
Exercise21622.2FundamentalDerivationRules
2.2.1Derivationrulesforsum，difference，productandquotientoffunctions
2.2.2Therulesofderivativeofinversefunctions
2.2.3Therulesofderivativeofcompositefunctions（TheChainRule）
2.2.4Basicderivationrulesandderivativeformulas
Exercise22692.3Higherorderderivatives
Exercise23732.4Derivationofimplicitfunctionsandfunctionsdefined
byparametricequations
2.4.1Derivationofimplicitfunctions
2.4.2Derivationofafunctiondefinedbyparametricequations
2.4.3Relatedratesofchange
Exercise24782.5TheDifferentialsoffunctions
2.5.1Conceptofthedifferential
2.5.2Geometricmeaningofthedifferential
2.5.3Formulasandrulesondifferentials
2.5.4Applicationofthedifferentialinapproximatecomputation
Exercise2
Exercise

Chapter3Meanvaluetheoremsindifferentialcalculusand
applicationsofderivatives873.1Meanvaluetheoremsindifferentialcalculus
Exercise31923.2L'Hospital'srule
Exercise32963.3Taylorformula
Exercise331003.4Monotonicityoffunctionsandconvexityofcurves
3.4.1Monotonicityoffunctions
3.4.2Convexityofcurvesandinflectionpoints
Exercise341053.5Extremevaluesoffunctions，maximumandminimum
3.5.1Extremevaluesoffunctions
3.5.2Maximumandminimumoffunction
Exercise351123.6Differentiationofarcandcurvature
3.6.1Differentiationofanarc
3.6.2Curvature
Exercise3
Exercise

Chapter4Indefiniteintegral1204.1Conceptandpropertyofindefiniteintegral
4.1.1Conceptofantiderivativeandindefiniteintegral
4.1.2Tableoffundamentalindefiniteintegrals
4.1.3Propertiesoftheindefiniteintegral
Exercise411254.2Integrationbysubstitutions
4.2.1Integrationbysubstitutionofthefirstkind
4.2.2Integrationbysubstitutionofthesecondkind
Exercise421334.3Integrationbyparts
Exercise431374.4Integrationofrationalfunction
4.4.1Integrationofrationalfunction
4.4.2Integrationwhichcanbetransformedintotheintegrationofrationalfunction
Exercise4
Exercise

Chapter5Definiteintegrals1435.1Conceptandpropertiesofdefiniteintegrals
5.1.1Examplesofdefiniteintegralproblems
5.1.2Thedefinitionofdefineintegral
5.1.3Propertiesofdefiniteintegrals
Exercise511485.2Fundamentalformulaofcalculus
5.2.1Therelationshipbetweenthedisplacementandthevelocity
5.2.2Afunctionofupperlimitofintegral
5.2.3NewtonLeibnizformula
Exercise521545.3Integrationbysubstitutionandpartsfordefiniteintegrals
5.3.1Integrationbysubstitutionfordefiniteintegrals
5.3.2Integrationbypartsfordefiniteintegral
Exercise531605.4Improperintegrals
5.4.1Improperintegralsonaninfiniteinterval
5.4.2Improperintegralsofunboundedfunctions
Exercise541655.5TestsforConvergenceofimproperintegralsΓfunction
5.5.1Testforconvergenceofinfiniteintegral
5.5.2Testforconvergenceofimproperintegralsofunboundedfunctions
5.5.3Γfunction
Exercise5
Exercise

Chapter6Applicationsofdefiniteintegrals1736.1Methodofelementsfordefiniteintegrals1736.2Theapplicationsofthedefiniteintegralingeometry
6.2.1Areasofplanefigures
6.2.2Thevolumesofsolid
6.2.3Lengthofplanecurves
Exercise621826.3TheapplicationsofthedefiniteIntegralinphysics
6.3.1Workdonebyvariableforce
6.3.2Forcebyaliquid
6.3.3Gravity
Exercise6
Exercise

Chapter7Differentialequations1897.1Differentialequationsandtheirsolutions
Exercise711917.2Separableequations
Exercise721947.3Homogeneousequations
7.3.1Homogeneousequations
7.3.2Reductiontohomogeneousequation
Exercise731987.4Afirstorderlineardifferentialequations
7.4.1Linearequations
7.4.2Bernoulli'sequation
Exercise742017.5Reduciblesecondorderequations
7.5.1y（n）=f（x）
7.5.2y″=f（x，y′）
7.5.3y″=f（y，y′）
Exercise752067.6secondorderlinearequations
7.6.1Constructionofsolutionsofsecondorderlinearequation
7.6.2Themethodofvariationofparameters
Exercise762107.7Homogeneouslineardifferentialequationwith
constantcoefficients
Exercise772147.8Nonhomogeneouslineardifferentialequationwith
constantcoefficients
7.8.1f（x）=eλxPm（x）
7.8.2f（x）=eλxP（1）l（x）cosωx+P（2）n（x）sinωx
Exercise782197.9Euler'sdifferentialequation
Exercise7
Exercise
Reference