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1、湛江师范学院2012-2013年度第2学期专业英语期中考核课程作业任课教师：栾姝考核要求：1.将下列节选的英文文章翻译成中文；2.要求译文首先要忠于原文，即专业术语要翻译准确，否则会被适当扣分；3.译文在符合原意的基础上要保证通顺，符合中文的语言习惯，否则会被适当扣分。评分标准：1.90-100分：几乎所有专业术语翻译准确，译文语句忠于原文且完全通顺。2.80-89分：大多数专业术语翻译准确，译文语句忠于原文且大多通顺。3.70-79分：部分专业术语翻译基本准确，译文语句基本通顺。4.60-69分：很多
2、专业术语翻译不准确或者漏翻译，译文语句基本通顺。5.0-60分：几乎所有专业术语翻译都不正确，语句不通顺，或者内容有雷同。提交要求：统一用A4纸手写译文，标明姓名、班级、学号，以班级为单位提交。TheExponentialFunctionThisisthemostimportantfunctioninmathematics.Itisdefined,foreverycomplexnumberz,bytheformula.(1)Theseries(1)convergesabsolutely,forevery
3、zandconvergesuniformlyoneveryboundedsubsetofthecomplexplane.Thusexpisacontinuousfunction.Theabsoluteconvergenceof(1)showsthatthecomputationiscorrect.Itgivestheimportantadditionformula(2)validforallcomplexnumbersaandb.Wedefinethenumberetobeexp(1),andshall
4、usuallyreplaceexp(z)bythecustomaryshorterexpressionex.Notethate0=exp(0)=1,by(1).Theorem(a)Foreverycomplexzwehaveex≠0;(b)expisitsownderivative:;(c)Therestrictionofexptotherealaxisisamonotonicallyincreasingpositivefunction,and;(d)Thereexistsapositivenumber
5、suchthatandsuchthatifandonlyifisaninteger;(e)expisaperiodicfunction,withperiod;(f)Themappingmapstherealaxisontotheunitcircle;(g)Ifwisacomplexnumberandw≠0,thenw=ezforsomez.ProofBy(2),.Thisimplies(a).Next,Thefirstoftheaboveequalitiesisamatterofdefinition,t
6、hesecondfollowsfrom(2),andthethirdfrom(1),and(b)isproved.Thatexpismonotonicallyincreasingonthepositiverealaxis,andthat,isclearfrom(1).Theotherassertionsof(c)areconsequencesof.Foranyrealnumbert,(1)showsthatisthecomplexconjugateof.Thus,or(treal).(3)Inother
7、words,iftisreal,liesontheunitcircle.Wedefinecost,sinttobetherealandimaginarypartsof:cost=Re[],sint=Im[](treal).(4)IfwedifferentiatebothsidesofEuler'sidentityeit=cost+isint,(5)whichisequivalentto(4),andifweapply(b),weobtain,sothat.(6)Thepowerseries(1)yiel
8、dstherepresentation(7)Taket=2.Thetermsoftheseries(7)thendecreaseinabsolutevalue(exceptforthefirstone)andtheirsignsalternate.Hencecos2islessthanthesumofthefirstthreetermsof(7),witht=2;thus.Sincecos0=1andcosisacontinuousreal
