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transformation groups for beginners (amer. math. soc 2004 duzhin 192s)

transformation groups for beginners (amer. math. soc 2004 duzhin 192s)

ID：14357197

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时间：2018-07-28

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1、TransformationGroupsforBeginnersS.V.DuzhinB.D.TchebotarevskyContentsPreface5Introduction6Chapter1.Algebraofpoints11x1.Checkeredplane11x2.Pointaddition13x3.Multiplyingpointsbynumbers17x4.Centreofgravity19x5.Coordinates21x6.Pointmultiplication24x7.Complexnumbers28Chapter2.PlaneMovements37x1.Paralleltr

2、anslations37x2.Re ections39x3.Rotations41x4.Functionsofacomplexvariable44x5.Compositionofmovements47x6.Glidere ections52x7.Classi cationofmovements53x8.Orientation56x9.Calculusofinvolutions57Chapter3.TransformationGroups61x1.Arollingtriangle61x2.Transformationgroups6334Contentsx3.Classi cationof nit

3、egroupsofmovements64x4.Conjugatetransformations66x5.Cyclicgroups70x6.Generatorsandrelations73Chapter4.Arbitrarygroups79x1.Thegeneralnotionofagroup79x2.Isomorphism85x3.TheLagrangetheorem94Chapter5.OrbitsandOrnaments101x1.Homomorphism101x2.Quotientgroup104x3.Groupspresentedbygeneratorsandrelations107x

4、4.Groupactionsandorbits108x5.Enumerationoforbits111x6.Invariants117x7.Crystallographicgroups118Chapter6.OtherTypesofTransformations131x1.Anetransformations131x2.Projectivetransformations134x3.Similitudes139x4.Inversions144x5.Circulartransformations147x6.Hyperbolicgeometry150Chapter7.SymmetriesofDi

5、erentialEquations155x1.Ordinarydi erentialequations155x2.Changeofvariables158x3.TheBernoulliequation160x4.Pointtransformations163x5.One-parametergroups168x6.Symmetriesofdi erentialequations170x7.Solvingequationsbysymmetries172Answers,HintsandSolutionstoExercises179Preface5PrefaceThe rstRussianversio

6、nofthisbookwaswrittenin1983-1986byB.D.Tcheb-otarevskyandmyselfandpublishedin1988byVysheishayaShkola"(Minsk)underthetitleFromornamentstodi erentialequations".ThepicturesweredrawnbyVladimirTsesler.Yearswentby,andIwasreceivingpositiveopinionsaboutthebookfromknownandunknownpeople.In1996Idecidedtotrans

7、latethebookintoEnglish.InthecourseofthisworkItriedtomakethebookmoreconsistentandself-contained.Ideletedsomeunimportantfragmentsandaddedseveralnewsections.Also,Icorrectedmanymistakes(IcanonlyhopeIdidno

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