analysis-analysis i (h. amann and j. escher)

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1、HerbertAmannJoachimEscherAnalysisITranslatedfromtheGermanbyGaryBrookfieldBirkhäuserVerlagBasel•Boston•BerlinAuthors:HerbertAmannJoachimEscherInstitutfürMathematikInstitutfürAngewandteMathematikUniversitätZürichUniversitätHannoverWinterthurerstr.190Welfengarten1CH-8057ZürichD-30167Hannovere-mail

2、:amann@math.unizh.che-mail:escher@ifam.uni-hannover.deOriginallypublishedinGermanunderthesametitlebyBirkhäuserVerlag,Switzerland©1998byBirkhäuserVerlag2000MathematicalSubjectClassification26-01,26Axx;03-01,30-01,40-01,54-01ACIPcataloguerecordforthisbookisavailablefromtheLibraryofCongress,Washin

3、gtonD.C.,USABibliografischeInformationDerDeutschenBibliothekDieDeutscheBibliothekverzeichnetdiesePublikationinderDeutschenNationalbibliografie;detailliertebibliografischeDatensindimInternetüberabrufbar.ISBN3-7643-7153-6BirkhäuserVerlag,Basel–Boston–BerlinThisworkissubjecttoco

4、pyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broad-casting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Foranykindofusepermissionofthecopyrightownermustbeobtained.©2005Bir

5、khäuserVerlag,P.O.Box133,CH-4010Basel,SwitzerlandPartofSpringerScience+BusinessMediaCoverdesign:MichaLotrovsky,4106Therwil,SwitzerlandPrintedonacid-freepaperproducedfromchlorine-freepulp.TCFDPrintedinGermanyISBN3-7643-7153-6987654321www.birkhauser.chPrefaceLogicalthinking,theanalysisofcomplexre

6、lationships,therecognitionofunder-lyingsimplestructureswhicharecommontoamultitudeofproblems—thesearetheskillswhichareneededtodomathematics,andtheirdevelopmentisthemaingoalofmathematicseducation.Ofcourse,theseskillscannotbelearned‘inavacuum’.Onlyacontinuousstrugglewithconcreteproblemsandastrivin

7、gfordeepunderstandingleadstosuccess.Agoodmeasureofabstractionisneededtoallowonetoconcentrateontheessential,withoutbeingdistractedbyappearancesandirrelevancies.Thepresentbookstrivesforclarityandtransparency.Rightfromthebegin-ning,i