经典英文数学教材系列:代数曲线几何初步
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八五品
仅1件
作者[英]菌吉布森(Gibson C.G) 著
出版社世界图书出版公司
出版时间2009-01
版次1
装帧平装
货号d17
上书时间2023-12-23
商品详情
- 品相描述:八五品
图书标准信息
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作者
[英]菌吉布森(Gibson C.G) 著
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出版社
世界图书出版公司
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出版时间
2009-01
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版次
1
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ISBN
9787506292641
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定价
35.00元
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装帧
平装
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开本
32开
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纸张
胶版纸
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页数
250页
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正文语种
简体中文,英语
- 【内容简介】
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GeneralBackgroundIfirstbecameinvolvedintheteachingofgeometryabouttwentyyearsago,whenmydepartmentintroducedanoptionalsecondyearcourseonthegeometryofplanecurves,partlytoredresstheimbalanceintheteachingofthesubject。ItWasmildlyrevolutionary,sinceitwentbacktoanearliersctofpreceptswherethedifferentialandalgebraicgeometryofcuweswerepursuedsimultaneously,totheirmutua!advantage.
- 【目录】
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ListofIllustrations
ListofTables
Preface
1RealAlgebraicCurves
1.1ParametrizedandImplicitCurves
1.2IntroductoryExamples
1.3CurvesinPlanarKinematics
2GeneralGroundFields
2.1TwoMotivatingExamples
2.2Groups,RingsandFields
2.3GeneralAffinePlanesandCurves
2.4ZeroSetsofAlgebraicCurves
3PolynomialAlgebra
3.1FactorizationinDomains
3.2PolynomialsinOneVariable
3.3PolynomialsinSeveralVariables
3.4HomogeneousPolynomials
3.5FormalDifferentiation
4AtfineEquivalence
4.1AffineMaps
4.2AfflineEquivalentCurves
4.3DegreeasanAffineInvariant
4.4CentresasAffineInvariants
5AfflineConics
5.1AfflineClassification
5.2TheDeltaInvariants
5.3UniquenessofEquations
6SingularitiesofAflineCurves
6.1IntersectionNumbers
6.2MultiplicityofaPointonaCurve
6.3SingularPoints
7TangentstoAflineCurves
7.1GeneralitiesaboutTangents
7.2TangentsatSimplePoints
7.3TangentsatDoublePoints
7.4TangentsatPointsofHigherMultiplicity
8RationalAflineCurves
8.1RationalCurves
8.2DiophantineEquations
8.3ConicsandIntegrals
9ProjectiveAlgebraicCurves
9.1TheProjectivePlane
9.2ProjectiveLines
9.3AtfinePlanesintheProjectivePlane
9.4ProjectiveCurves
9.5AffineViewsofProjectiveCurves
10SingularitiesofProjectiveCurves
10.1IntersectionNumbers
10.2MultiplicityofaPointonaCurve
10.3SingularPoints
10.4DeltaInvariantsviewedProjectively
11ProjectiveEquivalence
11.1ProjectiveMaps
11.2ProjectiveEquivalence
11.3ProjectiveConics
11.4AflineandProjectiveEquivalence
12ProjectiveTangents
12.1TangentstoProjectiveCurves
12.2TangentsatSimplePoints
12.3CentresviewedProjectively
12.4FociviewedProjectively
12.5TangentsatSingularPoints
12.6Asymptotes
13Flexes
13.1HessianCurves
13.2ConfigurationsofFlexes
14IntersectionsofProiectiveCurves
14.1TheGeometricIdea
14.2ResultantsinOneVariable
14.3ResultantsinSevera!Variables
14.4B6zout’STheorem
14.5ThcMultiplicityInequality
14.6InvarianceoftheIntersectionNumber
15ProiectiveCubics
15.1GeometricTypes0fCubics
15.2CubicsofGeneralType
15.3SingularIrreducibleCubics
15.4ReducibleCubics
16LinearSystems
16.1ProjectiveSpacesofCurves
16.2PcncilsofCuiNes
16.3SolvingQuarticEquations
16.4SubspacesorProjectiveSpaces
16.5LinearSystemsofCulwes
16.6DualCulNes
17TheGroupStructureonaCubic
17.1TheNineAssociatedPoints
17.2TheStarOperation
17.3CubicsasGroups
17.4GroupComputations
17.5DeterminationoftheGroups
18RationalProjectiveCurves
18.1ThcProjectiveConcept
18.2QuarticswithThreeDoublePoints
18.3ThcDeficiencyofaCHIve
18.4SomeRationalCurves
18.5SomeNon-RationalCurves
Index
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