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1、10.80.60.40.2z0-0.2-10-5-0.4-100-5x055y1010VectorCalculusMichaelCorralVectorCalculusMichaelCorralSchoolcraftCollegeAbouttheauthor:MichaelCorralisanAdjunctFacultymemberoftheDepartmentofMathematicsatSchoolcraftCollege.HereceivedaB.A.inMathematicsfromtheUniversityofCaliforniaatBerk
2、eley,andreceivedanM.A.inMathematicsandanM.S.inIndustrial&OperationsEngineeringfromtheUniversityofMichigan.ThistextwastypesetinLATEX2εwiththeKOMA-Scriptbundle,usingtheGNUEmacstexteditoronaFedoraLinuxsystem.ThegraphicswerecreatedusingMetaPost,PGF,andGnuplot.Copyrightc2008MichaelCo
3、rral.Permissionisgrantedtocopy,distributeand/ormodifythisdocumentunderthetermsoftheGNUFreeDocumentationLicense,Version1.2oranylaterversionpublishedbytheFreeSoftwareFoundation;withnoInvariantSections,noFront-CoverTexts,andnoBack-CoverTexts.Acopyofthelicenseisincludedinthesectione
4、ntitledGNUFreeDocumentationLicense.PrefaceThisbookcoverscalculusintwoandthreevariables.Itissuitableforaone-semestercourse,normallyknownasVectorCalculus,MultivariableCalculus,orsimplyCalculusIII.Theprerequisitesarethestandardcoursesinsingle-variablecalculus(a.k.a.CalculusIandII).
5、Ihavetriedtobesomewhatrigorousaboutprovingresults.Butwhileitisimpor-tantforstudentstoseefull-blownproofs-sincethatishowmathematicsworks-toomuchrigorandemphasisonproofscanimpedetheflowoflearningforthevastma-jorityoftheaudienceatthislevel.IfIweretoratethelevelofrigorinthebookonasc
6、aleof1to10,with1beingcompletelyinformaland10beingcompletelyrigorous,Iwouldrateitasa5.Thereare420exercisesthroughoutthetext,whichinmyexperiencearemorethanenoughforasemestercourseinthissubject.Thereareexercisesattheendofeachsection,dividedintothreecategories:A,BandC.TheAexercisesa
7、remostlyofaroutinecomputationalnature,theBexercisesareslightlymoreinvolved,andtheCexercisesusuallyrequiresomeeffortorinsighttosolve.AcrudewayofdescribingA,BandCwouldbeEasy,ModerateandChallenging,respectively.However,manyoftheBexercisesareeasyandnotalltheCexercisesaredifficult.Th
8、ereareafewexercisesthatrequirethestudenttowrite
