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1、ADVANCEDCALCULUS1996–1997GilbertWeinsteinOffice:CH493BTel:(205)934-3724(205)934-2154FAX:(205)934-9025Email:weinstei@math.uab.eduOfficehours:Monday1:00pm–2:30pmWednesday8:30am–10:00am3AbouttheCourseWelcometoAdvancedCalculus!Inthiscourse,youwilllearnAnalysis,thatisthetheoryo
2、fdifferentiationandintegrationoffunctions.However,youwillalsolearnsomethingmorefundamentalthanAnalysis.Youwilllearnwhatisamathematicalproof.Youmayhaveseensomeproofsearlier,buthere,youwilllearnhowtowriteyourownproofs.Youwillalsolearnhowtounderstandsomeoneelse’sproof,finda
3、flawinaproof,fixadeficientproofifpossibleanddiscarditifnot.Inotherwordsyouwilllearnthetradeofmathematicalexploration.Mathematicalreasoningtakestime.InCalculus,youexpectedtoreadaprob-lemandimmediatelyknowhowtoproceed.Hereyoumayexpectsomefrustrationandyoushouldplantospendal
4、otoftimethinkingbeforeyouwritedownanything.Analysiswasnotdiscoveredovernight.Ittookcenturiesforthecorrectapproachtoemerge.Youwillhavetogothroughanacceleratedprocessofrediscovery.Twentyhoursofworkaweekoutsideclassisnotanunusualaverageforthiscourse.Thecourseisruninthefol
5、lowingway.Inthesenotes,youwillfindDefinitions,Theorems,andExamples.Iwillexplainthedefinitions.Athome,onyourown,youwilltrytoprovethetheoremsandthestatementsintheexamples.Youwillusenobooksandnohelpfromanyone.Itwillbejustyou,thepencilandthepaper.Everystatementyoumakemustbeju
6、stified.Inyourarguments,youmayuseanyresultwhichprecedesinthenotestheitemyouareproving.Youmayusetheseresultseveniftheyhavenotyetbeenproven.However,youmaynotuseresultsfromothersources.Then,inclass,Iwillcallforvolunteerstopresenttheirsolutionsattheboard.Everycorrectproofis
7、worthonepoint.Ifmorethanonepersonvolunteerforanitem,theonewiththefewestpointsiscalledtotheboard,tiestobebrokenbylot.Yourgradewillbedeterminedbythenumberofpointsyouhaveaccumulatedduringtheterm.Youhavetounderstandtheproofspresentedbyothers.Someoftheideasmaybeusefultoyoul
8、ater.Youmustquestionyourpeerswhenyouthinkafaultyargumentisgivenorsomethingisnotentirelycleartoyou.Ifyoudon’t,Imostpro
