出版社:世界图书出版公司北京公司
年代:2008
定价:35.0
向量微积分不仅为应用数学的各个学科奠定了坚实的基础。而且流体力学、固体力学、电磁学等学科都在很大程度上也依赖于三维向量微积分。
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
5.2StokesStheorem
5.2.1ApplicationsofStokesStheorem
5.2.2Relatedtheoremslinkinglineandsurfaceintegrals
6.CurvilinearCoordinates
6.1Orthogonalcurvilinearcoordinates
6.2Grad,divandcurlinorthogonalcurvilinearcoordinatesystems
6.2.1Gradient
6.2.2Divergence
6.2.3Curl
6.3Cylindricalpolarcoordinates
6.4Sphericalpolarcoordinates
7.CartesianTensors
7.1Coordinatetransformations
7.2Vectorsandscalars
7.3Tensors
7.3.1Thequotientrule
7.3.2Symmetricandanti-symmetrictensors
7.3.3Isotropictensors
7.4Physicalexamplesoftensors
7.4.1Ohmslaw
7.4.2Theinertiatensor
8.ApplicationsofVectorCalculus
8.1Heattransfer
8.2Electromagnetism
8.2.1Electrostatics
8.2.2Electromagneticwavesinavacuum
8.3Continuummechanicsandthestresstensor
8.4Solidmechanics
8.5Fluidmechanics
8.5.1Equationofmotionforafluid
8.5.2Thevorticityequation
8.5.3Bernoullisequation
Solutions
Index
Vectorcalculusisthefundamentallanguageofmathematicalphysics.Itprovidesawaytodescribephysicalquantitiesinthree-dimensionalspaceandthewayinwhichthesequantitiesvary.Manytopicsinthephysicalsciencescanbeanalysedmathematicallyusingthetechniquesofvectorcalculus.Thesetopicsincludefluiddynamics,solidmechanicsandelectromagnetism,allofwhichinvolveadescriptionofvectorandscalarquantitiesinthreedimensions.Thisbookassumesnopreviousknowledgeofvectors.However,itisassumedthatthereaderhasaknowledgeofbasiccalculus,includingdifferentiation,integrationandpartialdifferentiation.Someknowledgeoflinearalgebraisalsorequired,particularlytheconceptsofmatricesanddeterminants.
书籍详细信息 | |||
书名 | 向量微积分站内查询相似图书 | ||
9787506292269 如需购买下载《向量微积分》pdf扫描版电子书或查询更多相关信息,请直接复制isbn,搜索即可全网搜索该ISBN | |||
出版地 | 北京 | 出版单位 | 世界图书出版公司北京公司 |
版次 | 1版 | 印次 | 1 |
定价(元) | 35.0 | 语种 | 英文 |
尺寸 | 14 | 装帧 | 平装 |
页数 | 印数 | 1000 |
向量微积分是世界图书出版公司北京公司于2008.05出版的中图分类号为 O183 的主题关于 微积分-英文 ,向量-英文 的书籍。
(法) 科尔曼 (Coleman,R.) , 著
陈海波, 刘碧玉, 秦宣云, 编著
邹云志, 著
(法) 萨巴蒂尔, 著
邹云志, 著
(美) 浪 (Lang,S.) , 著
(美) 菲茨帕特里克 (Fitzpatrick,P.M.) , 著
(印) 戈培德 (Ghorpade,S.R.) , 著
(美) 安顿 (Anton,H.) , (美) 比文斯 (Bivens,I.) , (美) 戴维斯 (Davis,S.) , 著