tom apostol - calculus volume 1

《tom apostol - calculus volume 1》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、TomM.ApostolCALCULUSVOLUME1One-VariableCalculus,withanIntroductiontoLinearAlgebraSECONDEDITIONJohnWiley&Sons,Inc.NewYorklSantaBarbaralLondonlSydneylTorontoCONSULTINGEDITORGeorgeSpringer,IndianaUniversityXEROX@isatrademarkofXeroxCorporation.SecondEditionCopyright01967byJohnWiJey&Sons,

2、Inc.FirstEditioncopyright01961byXeroxCorporation.Al1rightsreserved.Permissioninwritingmustbeobtainedfromthepublisherbeforeanypartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopy,recording,oranyinformationstorageorretrievalsy

3、stem.ISBN0471000051LibraryofCongressCatalogCardNumber:67-14605PrintedintheUnitedStatesofAmerica.1098765432TOJaneandStephenPREFACEExcerptsfromthePrefacetotheFirstEditionThereseemstobenogeneralagreementastowhatshouldconstituteafirstcourseincalculusandanalyticgeometry.Somepeopleinsistth

4、attheonlywaytoreallyunderstandcalculusistostartoffwithathoroughtreatmentofthereal-numbersystemanddevelopthesubjectstepbystepinalogicalandrigorousfashion.Othersarguethatcalculusisprimarilyatoolforengineersandphysicists;theybelievethecourseshouldstressapplica-tionsofthecalculusbyappeal

5、tointuitionandbyextensivedrillonproblemswhichdevelopmanipulativeskills.Thereismuchthatissoundinboththesepointsofview.Calculusisadeductivescienceandabranchofpuremathematics.Atthesametime,itisveryimpor-tanttorememberthatcalculushasstrongrootsinphysicalproblemsandthatitderivesmuchofitsp

6、owerandbeautyfromthevarietyofitsapplications.Itispossibletocombineastrongtheoreticaldevelopmentwithsoundtrainingintechnique;thisbookrepresentsanattempttostrikeasensiblebalancebetweenthetwo.Whiletreatingthecalculusasadeductivescience,thebookdoesnotneglectapplicationstophysicalproblems

7、.Proofsofa11theimportanttheoremsarepresentedasanessentialpartofthegrowthofmathematicalideas;theproofsareoftenprecededbyageometricorintuitivediscussiontogivethestudentsomeinsightintowhytheytakeaparticularform.Althoughtheseintuitivedis-cussionsWillsatisfyreaderswhoarenotinterestedindet

8、ailedproofs,