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1、HerbertAmannJoachimEscherAnalysisITranslatedfromtheGermanbyGaryBrookfieldBirkhäuserVerlagBasel•Boston•BerlinAuthors:HerbertAmannJoachimEscherInstitutfürMathematikInstitutfürAngewandteMathematikUniversitätZürichUniversitätHannoverWinterthurerstr.190Welfengarten1CH-8057ZürichD-30167Hann
2、overe-mail:amann@math.unizh.che-mail:escher@ifam.uni-hannover.deOriginallypublishedinGermanunderthesametitlebyBirkhäuserVerlag,Switzerland©1998byBirkhäuserVerlag2000MathematicalSubjectClassification26-01,26Axx;03-01,30-01,40-01,54-01ACIPcataloguerecordforthisbookisavailablefromtheLibr
3、aryofCongress,WashingtonD.C.,USABibliografischeInformationDerDeutschenBibliothekDieDeutscheBibliothekverzeichnetdiesePublikationinderDeutschenNationalbibliografie;detailliertebibliografischeDatensindimInternetüberabrufbar.ISBN3-7643-7153-6BirkhäuserVerlag,Basel–Bost
4、on–BerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broad-casting,reproductiononmicrofilmsorinotherways,andstorageindatabanks.Foranykindofusepermissionof
5、thecopyrightownermustbeobtained.©2005BirkhäuserVerlag,P.O.Box133,CH-4010Basel,SwitzerlandPartofSpringerScience+BusinessMediaCoverdesign:MichaLotrovsky,4106Therwil,SwitzerlandPrintedonacid-freepaperproducedfromchlorine-freepulp.TCFDPrintedinGermanyISBN3-7643-7153-6987654321www.birkhaus
6、er.chPrefaceLogicalthinking,theanalysisofcomplexrelationships,therecognitionofunder-lyingsimplestructureswhicharecommontoamultitudeofproblems—thesearetheskillswhichareneededtodomathematics,andtheirdevelopmentisthemaingoalofmathematicseducation.Ofcourse,theseskillscannotbelearned‘inava
7、cuum’.Onlyacontinuousstrugglewithconcreteproblemsandastrivingfordeepunderstandingleadstosuccess.Agoodmeasureofabstractionisneededtoallowonetoconcentrateontheessential,withoutbeingdistractedbyappearancesandirrelevancies.Thepresentbookstrivesforclarityandtransparency.Rightfromthebegin-n
8、ing,i
