向量微积分

图书标准信息

• 作者 [英]马修斯 著
• 出版社 世界图书出版公司
• 出版时间 2008-05
• 版次 1
• ISBN 9787506292269
• 定价 35.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 179页
• 正文语种 英语

【内容简介】

Vectorcalculusisthefundamentallanguageofmathematicalphysics.Itprovidesawaytodescribephysicalquantitiesinthree-dimensionalspaceandthewayinwhichthesequantitiesvary.Manytopicsinthephysicalsciencescanbeanalysedmathematicallyusingthetechniquesofvectorcalculus.Thesetopicsincludefluiddynamics，solidmechanicsandelectromagnetism，allofwhichinvolveadescriptionofvectorandscalarquantitiesinthreedimensions.
Thisbookassumesnopreviousknowledgeofvectors.However，itisassumedthatthereaderhasaknowledgeofbasiccalculus，includingdifferentiation，integrationandpartialdifferentiation.Someknowledgeoflinearalgebraisalsorequired，particularlytheconceptsofmatricesanddeterminants.

【目录】

1.VectorAlgebra
1.1Vectorsandscalars
1.1.1Definitionofavectorandascalar
1.1.2Additionofvectors
1.1.3Componentsofavector

1.2Dotproduct
1.2.1Applicationsofthedotproduct
1.3Crossproduct
1.3.1Applicationsofthecrossproduct
1.4Scalartripleproduct
1.5Vectortripleproduct
1.6Scalarfieldsandvectorfields

2.Line，SurfaceandVolumeIntegrals
2.1Applicationsandmethodsofintegration
2.1.1Examplesoftheuseofintegration
2.1.2Integrationbysubstitution
2.1.3Integrationbyparts

2.2Lineintegrals
2.2.1Introductoryexample：workdoneagainstaforce
2.2.2Evaluationoflineintegrals
2.2.3Conservativevectorfields
2.2.4Otherformsoflineintegrals

2.3Surfaceintegrals
2.3.1Introductoryexample：flowthroughapipe
2.3.2Evaluationofsurfaceintegrals
2.3.30ltherformsofsurfaceintegrals

2.4volumeintegrals
2.4.1Introductoryexample：massofanobjectwithvariabledensity
2.4.2Evaluationofvolumeintegrals

3.Gradient，DivergenceandCurl
3.1PartialdifierentiationandTaylorseries
3.1.1Partialdifierentiation
3.1.2Taylorseriesinmorethanonevariable

3.2Gradientofascalarfield
3.2.1Gradientsconservativefieldsandpotentials
3.2.2Physicalapplicationsofthegradient

3.3Divergenceofavectorfield
3.3.1Physicalinterpretationofdivergence
3.3.2Laplacianofascalarfield

3.4Cllrlofavectorfield
3.4.1Physicalinterpretationofcurl
3.4.2Relationbetweencurlandrotation
3.4.3Curlandconservativevectorfields

4.SuffixNotationanditsApplications
4.1Introductiontosuffixnotation
4.2TheKroneckerdelta
4.3Thealternatingtensor
4.4Relationbetweenijkandij
4.5Grad，divandcurlinsuffixnotation
4.6Combinationsofgrad，divandcurl
4.7Grad，divandcurlappliedtoproductsoffunctions

5.IntegralTheorems
5.1Divergencetheorem
5.1.1C：onservationofmassforafluid
5.1.2Applicationsofthedivergencetheorem
5.1.3Relatedtheoremslinkingsurfaceandvolumeintegrals

5.2Stokes’Stheorem
5.2.1ApplicationsofStokes’Stheorem
5.2.2Relatedtheoremslinkinglineandsurfaceintegrals

6.CurvilinearCoordinates
6.1Orthogonalcurvilinearcoordinates
6.2Grad，divandcurlinorthogonalcurvilinearcoordinatesystems
6.2.1Gradient
6.2.2Divergence
……
7.CartesianTensors
8.ApplicationsofVectorCalculus
Solutions
Index