高等数学（英文版 下册）[北京邮电大学高等数学双语教学组 编] 2012年版

高等数学（英文版 下册）
作者：北京邮电大学高等数学双语教学组 编
出版时间：2012年版
内容简介
《高等数学.下(英文版)》为《高等数学》双语教材的第二部分，主要内容包括微分方程及其简单应用、解析几何、多元函数的微分及其应用、多元函数的积分及其应用，以及曲线、曲面积分。
　　《高等数学.下(英文版)》的每一个部分都经过了精细的筛选，力求做到重点突出、层次分明、叙述清楚、深入浅出、简明易懂。全书例题较为丰富，并且每一节之后均配有一定数量的习题。习题分为两个部分，第一部分主要是对基本知识和基本方法的训练，第二部分则主要强调对基本知识和方法的灵活运用能力。本书适用于高等学校理工科各专业学生的双语教学，同时也可作为其他专业的教材和参考教材。
目录
《高等数学.下(英文版)》
chapter7differentialequations
7.1basicconceptsofdifferentialequations
7.1.1examplesofdifferentialequations
7.1.2basicconcepts
7.1.3geometricinterpretationofthefirst-orderdifferentialequation
exercises7.1
7.2first-orderdifferentialequations
7.e.1first-orderseparabledifferentialequation
7.2.2homogeneousfirst-orderequations
7.2.3linearfirst-orderequations
7.2.4bernoulli"sequation
7.2.5someotherexamplesthatcanb
ereducedtolinearfirst-orderequations
exercises7.2
7.3reduciblesecond-orderdifferentialequations
exercises7.3
7.4higher-orderlineardifferentialequations
7.4.1someexamplesoflineardifferentialequationofhigher-order
7.4.2structureofsolutionsoflineardifferentialequations
exercises7.4
.7.5higher-orderlinearequationswithconstantcoefficients
7.5.1higher-orderhomogeneouslinearequationswithconstantcoefficients
7.5.2higher-ordernonhomogeneouslinearequationswithconstantcoefficients
exercises7.5
7.6"euler"sdifferentialequation
exercises7.6
7.7applicationsofdifferentialequations
exercises7.7
chapter8vectorsandsolidanalyticgeometry
8.1vectorsinplaneandinspace
8.1.1vectors
8.1.2operationsonvectors
8.1.3vectorsinplane
8.1.4rectangularcoordinatesystem
8.1.5vectorsinspace
exercises8.1
parta
partb
8.2productsofvectors
8.2.1scalarproductoftwovectors
8.2.2vectorproductoftwovectors
8.2.3triplescalarproductofthreevectors
8.2.4applicationsofproductsofvectors
exercises8.2
parta
partb
8.3planesandlinesinspace
8.3.1equationsofplanes
8.3.2equationsoflinesinspace
exercises8.3
parta
partb
8.4surfacesandspacecurves
8.4.1cylinders
8.4.2cones
8.4.3surfacesofrevolution
8.4.4quadricsurfaces
8.4.5spacecurves
8.4.6cylindricalcoordinatesystem
8.4.7sphericalcoordinatesystem
exercises8.4
parta
partb
chapter9thedifferentialcalculusformulti-variablefunctions
9.1definitionofmulti-variablefunctionsandtheirbasicproperties
9.1.1spacer2andrn
9.1.2multi-variablefunctions
9.1.3visualizationofmulti-variablefunctions
9.1.4limitsandcontinuityofmulti-variablefunctions
exercises9.1
parta
partb
9.2partialderivativesandtotaldifferentialsofmulti-variablefunctior
9.2.1partialderivatives
9.2.2totaldifferentials
9.2.3higher-orderpartialderivatives
9.2.4directionalderivativesandthegradient
exercises9.2
parta
partb
9.3differentiationofmulti-variablecompositeandimplicit
functions
9.3.1partialderivativesandtotaldifferentialsofmulti-variablecomposit
functions
9.3.2differentiationofimplicitfunctions
9.3.3differentiationofimplicitfunctionsdeterminedbyequationsystems
exercises9.3
parta
partb
chapter10applicationsofmulti-variablefunctions
10.1approximatefunctionvaluesbytotaldifferential
10.2extremevaluesofmulti-variablefunctions
10.2.iunrestrictedextremevalues
10.2.2globalmaximaandminima
10.2.3themethodofleastsquares
10.2.4constrainedextremevalues
10.2.5themethodoflagrangemultipliers
exercises10.2
parta
partb
10.3applicationsingeometry
10.3.1arclengthalongacurve
10.3.2tangentlineandnormalplaneofaspacecurve
10.3.3tangentplanesandnormallinestoasurface
10.3.4"curvatureforplanecurves
exercises10.3
parta
partb
syntheticexercises
chapter11multipleintegrals
11.1conceptandpropertiesofdoubleintegrals
11.1.1conceptofdoubleintegrals
11.1.2propertiesofdoubleintegrals
exercises11.1
11.2evaluationofdoubleintegrals
11.2.1geometricmeaningofdoubleintegrals
11.2.2doubleintegralsinrectangularcoordinates
11.2.3doubleintegralsinpolarcoordinates
11.2.4*integrationbysubstitutionfordoubleintegralsingeneral
exercises11.2
parta
partb
11.3tripleintegrals
11.3.1conceptandpropertiesoftripleintegrals
11.3.2tripleintegralsinrectangularcoordinates
11.3.3tripleintegralsincylindricalandsphericalcoordinates
11.3.4"integrationbysubstitutionfortripleintegralsingeneral
exercises11.3
parta
partb
11.4applicationsofmultipleintegrals
11.4.1surfacearea
11.4.2thecenterofgravity
11.4.3themomentofinertia
exercises11.4
parta
partb
chapter12lineintegralsandsurfaceintegrals
12.1lineintegrals
12.1.1lineintegralswithrespecttoarclength
12.1.2lineintegralswithrespecttocoordinates
12.1.3relationsbetweentwotypesoflineintegrals
exercises12.1
parta
partb
12.2green"sformulaanditsapplications
12.2.1green"sformula
12.2.2conditionsforpathindependenceoflineintegrals
exercises12.2
parta
partb
12.3surfaceintegrals
12.3.1surfaceintegralswithrespecttosurfacearea
12.3.2surfaceintegralswithrespecttocoordinates
exercises12.3
parta
partb
12.4gauss"formula
exercises12.4
parta
partb
12.5stokes"formula
12.5.1stokes"formula
12.5.2conditionsforpathindependenceofspacelineintegrals
exercises12.5
bibliography