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1、10.80.60.40.2z0-0.2-10-0.4-5-100x-505y51010VectorCalculusMichaelCorralVectorCalculusMichaelCorralSchoolcraftCollegeAbouttheauthor:MichaelCorralisanAdjunctFacultymemberoftheDepartmentofMathematicsatSchoolcraftCollege.HereceivedaB.A.inMathematicsfromtheUniversityofCaliforniaatBe
2、rkeley,andreceivedanM.A.inMathematicsandanM.S.inIndustrial&OperationsEngineeringfromtheUniversityofMichigan.ThistextwastypesetinLATEX2εwiththeKOMA-Scriptbundle,usingtheGNUEmacstexteditoronaFedoraLinuxsystem.ThegraphicswerecreatedusingMetaPost,PGF,andGnuplot.Copyright©2008Micha
3、elCorral.Permissionisgrantedtocopy,distributeand/ormodifythisdocumentunderthetermsoftheGNUFreeDocumentationLicense,Version1.2oranylaterversionpublishedbytheFreeSoftwareFoundation;withnoInvariantSections,noFront-CoverTexts,andnoBack-CoverTexts.Acopyofthelicenseisincludedinthese
4、ctionentitledGNUFreeDocumentationLicense.PrefaceThisbookcoverscalculusintwoandthreevariables.Itissuitableforaone-semestercourse,normallyknownasVectorCalculus,MultivariableCalculus,orsimplyCalculusIII.Theprerequisitesarethestandardcoursesinsingle-variablecalculus(a.k.a.Calculus
5、IandII).Ihavetriedtobesomewhatrigorousaboutprovingresults.Butwhileitisimportantforstudentstoseefull-blownproofs-sincethatishowmathematicsworks-toomuchrigorandemphasisonproofscanimpedetheflowoflearningforthevastmajorityoftheaudienceatthislevel.IfIweretoratethelevelofrigorinthebo
6、okonascaleof1to10,with1beingcompletelyinformaland10beingcompletelyrigorous,Iwouldrateitasa5.Thereare420exercisesthroughoutthetext,whichinmyexperiencearemorethanenoughforasemestercourseinthissubject.Thereareexercisesattheendofeachsec-tion,dividedintothreecategories:A,BandC.TheA
7、exercisesaremostlyofaroutinecomputationalnature,theBexercisesareslightlymoreinvolved,andtheCexercisesusu-allyrequiresomeeffortorinsighttosolve.AcrudewayofdescribingA,BandCwouldbeEasy,ModerateandChallenging,respectively.However,manyoftheBexercisesareeasyandnotalltheCexercisesar
8、edifficult.Thereareafewexercisesthatrequirethestudenttowritehi
