資源描述：
《advanced calculus - gilbert weinstein》由會員上傳分享，免費(fèi)在線閱讀，更多相關(guān)內(nèi)容在學(xué)術(shù)論文-天天文庫。
1、ADVANCEDCALCULUS1996–1997GilbertWeinsteinO?ce:CH493BTel:(205)934-3724(205)934-2154FAX:(205)934-9025Email:weinstei@math.uab.eduO?cehours:Monday1:00pm–2:30pmWednesday8:30am–10:00am3AbouttheCourseWelcometoAdvancedCalculus!Inthiscourse,youwilllearnAnalysis,thatisthetheoryofdi?eren
2、tiationandintegrationoffunctions.However,youwillalsolearnsomethingmorefundamentalthanAnalysis.Youwilllearnwhatisamathematicalproof.Youmayhaveseensomeproofsearlier,buthere,youwilllearnhowtowriteyourownproofs.Youwillalsolearnhowtounderstandsomeoneelse’sproof,?nda?awinaproof,?xad
3、e?cientproofifpossibleanddiscarditifnot.Inotherwordsyouwilllearnthetradeofmathematicalexploration.Mathematicalreasoningtakestime.InCalculus,youexpectedtoreadaprob-lemandimmediatelyknowhowtoproceed.Hereyoumayexpectsomefrustrationandyoushouldplantospendalotoftimethinkingbeforeyo
4、uwritedownanything.Analysiswasnotdiscoveredovernight.Ittookcenturiesforthecorrectapproachtoemerge.Youwillhavetogothroughanacceleratedprocessofrediscovery.Twentyhoursofworkaweekoutsideclassisnotanunusualaverageforthiscourse.Thecourseisruninthefollowingway.Inthesenotes,youwill?n
5、dDe?nitions,Theorems,andExamples.Iwillexplainthede?nitions.Athome,onyourown,youwilltrytoprovethetheoremsandthestatementsintheexamples.Youwillusenobooksandnohelpfromanyone.Itwillbejustyou,thepencilandthepaper.Everystatementyoumakemustbejusti?ed.Inyourarguments,youmayuseanyresul
6、twhichprecedesinthenotestheitemyouareproving.Youmayusetheseresultseveniftheyhavenotyetbeenproven.However,youmaynotuseresultsfromothersources.Then,inclass,Iwillcallforvolunteerstopresenttheirsolutionsattheboard.Everycorrectproofisworthonepoint.Ifmorethanonepersonvolunteerforani
7、tem,theonewiththefewestpointsiscalledtotheboard,tiestobebrokenbylot.Yourgradewillbedeterminedbythenumberofpointsyouhaveaccumulatedduringtheterm.Youhavetounderstandtheproofspresentedbyothers.Someoftheideasmaybeusefultoyoulater.Youmustquestionyourpeerswhenyouthinkafaultyargument
8、isgivenorsomethingisnotentirelycleartoyou.Ifyoudon’t,Imostpro
