高等学校教材：高等数学基础2英文版

图书标准信息

• 作者 布劳尔、马知恩、王绵林 著
• 出版社 高等教育出版社
• 出版时间 2006-01
• 版次 1
• ISBN 9787040177947
• 定价 36.20元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 453页
• 字数 520千字
• 正文语种 英语
• 丛书 高等学校教材

【内容简介】

　　Thisisthesecondvolumeofthetextbook"FundamentalsofAdvancedMath-ematics"writtenbythesameauthors.Itincludesvectoralgebraandanalyticgeometryinspace,multivariablecalculus,andlinearordinarydifferentiale-quations.Theintentionsandfeaturesareasintroducedintheprefacetothefirstvolume.Werepeatheretheimportantadvicetostudentsinthefirstvol-ume,asitisequallyimportantforthissecondvolume.Inordertolearncalculus,itisnotenoughtoreadthetextbookasifitwereanewspaper.Learningrequirescarefulreading,workingthroughexam-plesstepbystep,andsolvingproblems.Solvingproblemsrequiresmorethanimitationofexamples.Itisnecessarytothinkaboutwhattheproblemreallyasksandtodevelopamethodforthatparticularproblem.Ifsomethingisstillnotclearafteryouhavetriedtounderstandit,youshouldaskaclassmate,amoreadvancedstudent,oryourteacher.Ifaclassmateasksyouaquestion,youmaylearnagreatdealfromexplainingtheanswer.

Thefollowingtwoadditionalremarksmightbehelpfultoreadersinu-singthesecondvolume.

（1）Thematerialonlinearsystemsofordinarydifferentialequations（Section9.2）isnotincludedinthefundamentalrequirements.Beforestudy-ingit,readerswillneedsomebasicknowledgeoflinearalgebra.

（2）Someofthematerialinthisvolumehasbeenstatedintermsofma-tricesanddeterminants.ForreaderswhoarenotyetfamiliarwiththebasicconceptsandoperationsformatricesanddeterminantswehaveincludedabriefoutlineinAppendixA.

【目录】

Chapter5VectorAlgebraandAnalyticGeometryinSpace

5.1VectorsandTheirLinearOperations

5.1.1Theconceptofvector

5.1.2LinearoperationSonvectorS

5.1.3Projectionofvectors

5.1.4RectangularcoordinatesystemsinspaceandcomponentsofVectors

Exercises5.1

5.2MultiplicativeOperationsonVectors

5.2.1Thescalarproduct(dotproduct，innerproduct)oftwovectorS

5.2.2Thevectorproduct(crossproduct，outerproduct)oftwovectors

5.2.3Themixedproductofthreevectors

Exercises5.2

5.3PlanesandLinesinSpace

5.3.1Equationsofplanes

5.3.2Positionrelationshipsbetweentwoplanes

5.3.3Equationsofstraightlinesinspace

5.3.4Positionrelationshipsbetweentwolines

5.3.5Positionrelationshipsbetweenalineandaplane

5.3.6Distancefromapointtoaplane(1ine)

Exercises5.3

5.4SurfacesandSpaceCurves

5.4.1Equationsofsurfaces

5.4.2Quadricsurfaces

5.4.3Equationsofspacecurves

Chapter6TheMultivariableDifferentialCalculusanditsApplications

6.1LimitsandContinuityofMultivariableFunctions

6.1.1PrimaryknowledgeofpointsetsinthespaceRn

6.1.2Theconceptofamultivariablefunction

6.1.3Limitandcontinuityofmultivariablefunctions

Exercises6.1

6.2PartialDerivativesandTotalDifferentialsofMultivariableFunctions

6.2.1Partialderivatives

6.2.2Totaldifferentials

6.2.3Higher-orderpartialderivatives

6.2.4Directionalderivativesandthegradient

Exercises6.2

6.3DifferentiationofMultivariableCompositeFunctionsandImplicitFunctions

6.3.1Partialderivativesandtotaldifferentialsofmultivariablecompositefunctions

6.3.2Differentiationofimplicitfunctionsdefinedbyoneequation

6.3.3Differentiationofimplicitfunctionsdeterminedbymorethanoneequation

Exercises6.3

6.4ExtremeValueProblemsforMultivariableFunctions

6.4.1Unrestrictedextremevalues

6.4.2Globalmaximaandminima

6.4.3Extremevalueswithconstraints;ThemethodofLagrangemultipliers

Exercises6.4

*6.5TaylorsFormulaforFunctionsofTwoVariables

6.5.1Taylorsformulaforfunctionsoftwovariables

……

Chapter7TheIntegralCalculusofMultivariableScalarFunctionsandItsApplications

Chapter8TheIntegralCalculusofMultivariableVectorvaluedFunctionsanditsApplecationsintheTheoryofFields

Chapter9LinearOrdinaryDifferentialEquations

AppendixABasicPropertiesofMatricesandDeterminants

AppendixBAnswersandHintsforExercises