微分方程用的对称和积分方法

图书标准信息

• 作者 George W.Bluman Stephen C.Anco 著
• 出版社 世界图书出版公司
• 出版时间 2004-11
• 版次 1
• ISBN 9787506271899
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 419页
• 正文语种 英语

【内容简介】

　　Thepresentbookincludesacomprehensivetreatmentofdimensionalanalysis.rhereisafulldiscussionofaspectsofLiegroupsofpointtransformations（pointsymmetries），contactsymmetries，andhigher-ordersymmetriesthatareessentialforfilingsolutionsofdifferentialequations.Noknowledgeofgrouptheoryisassumed.Emphasisisplacedonexplicitalgorithmstodiscoversymmetriesandintegratingfactorsadmittedbyagivendifferentialequationandtoconstructsolutionsandfirstintegralsresultingfromsuchsymmetriesandintegratingfactors.Thisbookshouldbeparticularlysuitableforappliedmathematicians，engineers，andscientistsinterestedinhowtofindsystematicallyexplicitsolutionsofdifferentialequations.Almostallexamplesaretakenfromphysicalandengineeringproblemsincludingthoseconcernedwithheatconduction，wavepropagation，andfluidflow.

【目录】

Preface
Introduction

1DimensionalAnalysis,Modeling,andInvariance
1.1Introduction
1.2DimensionalAnalysis:BuckinghamPi-Theorem
1.2.1AssumptionsBehindDimensionalAnalysis
1.2.2ConclusionsfromDimensionalAnalysis
1.2.3ProofoftheBuckinghamPi-Theorem
1.2.4Examples
1.3ApplicationofDimensionalAnalysistoPDEs
1.3.1Examples
1.4GeneralizationofDimensionalAnalysis:InvarianceofPDEsUnderScalingsofVariables
1.5Discussion

2LieGroupsofTransformationsandInfinitesimalTransformations
2.1Introduction
2.2LieGroupsofTransformations
2.2.1Groups
2.2.2ExamplesofGroups
2.2.3GroupofTransformations
2.2.4One-ParameterLieGroupofTransformations
2.2.5ExamplesofOne-ParameterLieGroupsofTransformations
2.3InfinitesimalTransformations
2.3.1FirstFundamentalTheoremofLie
2.3.2ExamplesIllustrating'Lie'sFirstFundamentalTheorem
2.3.3InfinitesimalGenerators
2.3.4InvariantFunctions
2.3.5CanonicaICoordinates
2,3.6ExamplesofSetsofCanonicalCoordinates
2.4PointTransformationsandExtendedTransformations（Prolongations）
2.4.1ExtendedGroupofPointTransformations:OneDependentandOneIndependentVariable
2.4.2ExtendedInfinitesimalTransformations:OneDependentandOneIndependentVariable
2.4.3ExtendedTransformations:OneDependentandnIndependentVariables
2.4.4ExtendedInfinitesimalTransformations:OneDependentandnIndependentVariables
2.4.5ExtendedTransformationsandExtendedInfinitesimalTransformations:mDependentandnIndependentVariables
2.5MultiparameterLieGroupsofTransformationsandLieAlgebras
2.5.1r-ParameterLieGroupsofTransformations
2.5.2LieAlgebras
2.5.3ExamplesofLieAlgebras
2.5.4SolvableLieAlgebras
2.6MappingsofCurvesandSurfaces
2.6.1InvariantSurfaces,InvariantCurves,InvariantPoints
2.6.2MappingsofCurves
2.6.3ExamplesofMappingsofCurves
2.6.4MappingsofSurfaces
2.7LocalTransformations
2.7.1PointTransformations
2.7.2ContactandHigher-OrderTransformations
2.7.3ExamplesofLocalTransformations
2.8Discussion

3OrdinaryDifferentialEquations（ODEs）
3.1Introduction
3.1.1ElementaryExamples
3.2First-OrderODEs
3.2.1CanonicaICoordinates
3.2.2IntegratingFactors
3.2.3MappingsofSolutionCurves
3.2.4DeterminingEquationforSymmetriesofaFirst-OrderODE
3.2.5DeterminationofFirst-OrderODEsInvariantUnderaGivenGroup
3.3InvarianceofSecond-andHigher-OrderODEsUnderPointSymmetries
3.3.1ReductionofOrderThroughCanonicaICoordinates
3.3.2ReductionofOrderThroughDifferentiallnvariants
3.3.3ExamplesofReductionofOrder
3.3.4DeterminingEquationsforPointSymmetriesofannth-OrderODE
3.3.5Determinationofnth-OrderODEsInvariantUnderaGivenGroup
……

4PartialDifferentialEquations（PDEs）