advanced calculus fifth edition - wilfred kaplan

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1、(SZilt6i)(SX156i).''L.'''AdvancedCalculus0.,...L:FifthEdition*:q!fl&-I~3[#]WilfredKaplan8it*iPrefacetotheFifthEditionAsIfecall,itwasin1948thatMarkMorkovin,acolleagueinengineering,ap-proachedmetosuggestthatIwriteatextforengineeringstudentsneedingtoproceedbeyondelement

2、arycalculustohandlethenewapplicationsofmathematics.WorldWarI1hadindeedcreatedmanynewdemandsformathematicalskillsinavarietyoffields.MarkwaspersuasiveandIpreparedabookof265pages,whichappearedinlithoprintedform,anditwasusedasthetextforanewcourseforthird-yearstudents.Thet

3、ypesettingwasdoneusinga"varityper,"anewtypewriterthathadkeysformathematicalsymbols.Inthesummerof1949IleftAnnArborforasabbaticalyearabroad,andwerentedourhometoafriendandcolleagueEricReissner,whohadavisitingappointmentattheUniversityofMichigan.Ericwasanadvisertoanewpubl

4、isher,Addison-Wesley,andlearnedaboutmylithoprintedbookwhenhewasaskedtoteachacourseusingit.Hewrotetome,askingthatIconsiderhavingitpublishedbyAddison-Wesley.Thusbeganthecourseofthisbook.ForthefirsteditionthetypesettingwascarriedoutwithleadtypeandIwasinvitedtowatchthepro

5、cess.Itwasimpressivetoseehowthetyperepresentingthesquarerootofafunctionwascreatedbyphysicallycuttingawayatanappropriatetypeshowingthesquarerootsignandsqueezingtypeforthefunctionintoit.Howtheskilledpersoncarryingthisoutwouldhavemarveledatthecomputermethodsforprintingsu

6、chsymbols!ThiseditiondiffersfromthepreviousoneinthatthechapteronordinarydifferentialequationsincludedinthethirdeditionbutomittedinthefourtheditionhasbeenrestoredasChapter9.Thusthepresentbookincludesallthematerialpresentinthepreviouseditions,withtheexceptionoftheintrod

7、uctoryreviewchapterofthefirstedition.Anumberofminorchangeshavebeenmadethroughout,especiallysomeup-datingofthereferences.Thepurposeofincludingallthetopicsistomakethebookmoreusefulforreference.Thusitcanservebothastextforoneormorecoursesandasasourceofinformationafterthec

8、ourseshavebeencompleted.ABOUTTHEBOOKThebackgroundassumedisthatusuallyobtainedinthefreshman-sophomorecalcu-lussequence.Linear