分析（第1卷）

图书标准信息

• 作者 [德]阿莫恩（Amann H.） 著
• 出版社 世界图书出版公司
• 出版时间 2012-09
• 版次 1
• ISBN 9787510048005
• 定价 89.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 426页
• 正文语种 英语

【内容简介】

　　Thepresentbookstrivesforclarityandtransparency.Rightfromthebegin-ning，itrequiresfromthereaderawillingnesstodealwithabstractconcepts，aswellasaconsiderablemeasureofself-initiative.Forthesee&，rts，thereaderwillberichlyrewardedinhisorhermathematicalthinkingabilities，andwillpossessthefoundationneededforadeeperpenetrationintomathematicsanditsapplications.
　　Thisbookisthefirstvolumeofathreevolumeintroductiontoanalysis.Itde-velopedfrom.coursesthattheauthorshavetaughtoverthelasttwentysixyearsattheUniversitiesofBochum，Kiel，Zurich，BaselandKassel.Sincewehopethatthisbookwillbeusedalsoforself-studyandsupplementaryreading，wehaveincludedfarmorematerialthancanbecoveredinathreesemestersequence.Thisallowsustoprovideawideoverviewofthesubjectandtopresentthemanybeautifulandimportantapplicationsofthetheory.Wealsodemonstratethatmathematicspossesses，notonlyeleganceandinnerbeauty，butalsoprovidesefficientmethodsforthesolutionofconcreteproblems.

【目录】

Preface
ChapterⅠFoundations
1FundamentalsofLogic
2Sets
ElementaryFacts
ThePowerSet
Complement,IntersectionandUnion
Products
FamiliesofSets
3Functions，
SimpleExamples
CompositionofFunctions
CommutativeDiagrams
Injections,SurjectionsandBijections
InverseFunctions
SetValuedFunctions
4RelationsandOperations
EquivalenceRelations
OrderRelations
Operations
5TheNaturalNumbers
ThePeanoAxioms
TheArithmeticofNaturalNumbers
TheDivisionAlgorithm
TheInductionPrinciple
RecursiveDefinitions
6Countability
Permutations
EquinumerousSets
CountableSets
InfiniteProducts
7GroupsandHomomorphisms
Groups
Subgroups
Cosets
Homomorphisms
Isomorphisms
8R.ings,FieldsandPolynomials
Rings
TheBinomialTheorem
TheMultinomialTheorem
Fields
OrderedFields
FormalPowerSeries
Polynomials
PolynomialFunctions
DivisionofPolynomiajs
LinearFactors
PolynomialsinSeveralIndeterminates
9TheRationalNumbers
TheIntegers
TheRationalNumbers
RationalZerosofPolynomials
SquareRoots
10TheRealNumbers
OrderCompleteness
Dedekind'sConstructionoftheRealNumbers
TheNaturalOrderonR
TheExtendedNumberLine
ACharacterizationofSupremumandInfimum
TheArchimedeanProperty
TheDensityoftheRationalNumbersinR
nthRoots
TheDensityoftheIrrationalNumbersinR
Intervals
ChapterⅡConvergence
ChapterⅢContinuousFunctions
ChapterⅣDifferentiationinOneVariable
ChapterⅤSequencesofFunctions
AppendixIntroductiontoMathematicalLogic
Bibliography
Index