the calculus_a genetic approach_2007

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1、THECALCULUSTHECALCULUSAGeneticApproachOTTOTOEPLITZNewForewordbyDavidBressoudPublishedinAssociationwiththeMathematicalAssociationofAmericaTheUniversityofChicagoPressChicago·LondonThepresentbookisatranslation,editedaftertheauthor'sdeathbyGottfriedKotheandtranslatedintoEnglishbyLuiseLange.The

2、Germanedition,DieEntwicklungderInfinitesimalrechnung,waspublishedbySpringer-Verlag.TheUniversityofChicagoPress,Chicago60637TheUniversityofChicagoPress,ltd.,London©1963byTheUniversityofChicagoForeword©2007byTheUniversityofChicagoAllrightsreserved.Published2007PrintedintheUnitedStatesofAmeri

3、ca161514131211100908072345ISBN-13:978-0-226-80668-6(paper)ISBN-10:0-226-80668-5(paper)LibraryofCongressCataloging-in-PublicationDataToeplitz,Otto,1881-1940.[EntwicklungderInfinitesimalrechnung.English]Thecalculus:ageneticapproach/OttoToeplitz;withanewforewordbyDavidM.Bressoud.p.cm.Includes

4、bibliographicalreferencesandindex.ISBN-13:978-0-226-80668-6(pbk.:alk.paper)ISBN-10:0-226-80668-5(pbk.:alk.paper)1.Calculus.2.Processes,Infinite.I.Title.QA303.T64152007515-dc222006034201§ThepaperusedinthispublicationmeetstheminimumrequirementsoftheAmericanNationalStandardforInformationScien

5、ces-PermanenceofPaperforPrintedLibraryMaterials,ANSIZ39.48-1992.FOREWORDTOTHECALCULUS:AGENETICAPPROACHBYOTTOTOEPLITZSeptember30,2006OttoToeplitzisbestknownforhiscontributionstomathematics,buthewasalsoanavidstudentofitshistory.Heunderstoodhowusefulthishistorycouldbeinin•formingandshapingthe

6、pedagogyofmathematics.Thisbook,thefirstpartofanuncompletedmanuscript,presentshisvisionofanhistoricallyinformedpedagogyfortheteachingofcalculus.Thoughwritteninthe1930s,ithasmuchtotellusto•dayabouthowwemight-evenhowweshould-teachcalculus.Weliveinanageofagreatdemocratizationofcalculus.Acourse

7、oncereservedforanelitefewisnowmovingintothestandardcollegepreparatorycurriculum.Thisbeganinthe1950s,butthemovementhasacceleratedinthepastfewdecadesasknowledgeofcalculushascometobeviewedasaprerequisiteforadmissiontothebestcollegesanduniversities,almostirrespect