《数学专业英语》常用英文表达

MATHEMATICALENGLISHMathematicalEnglish，SchoolofAppl.Math.AimoftheCourse:Expectedprogressinthefollowingaspects:.Readingskillsoftheoriginalmathematicalarticlesandbooks.Writingskillsofmathematicalandotherscientificarticles.Translatingskillsofmathematicalarticles:bothtranslationfromChinesetoEnglishandEnglishtoChinese*Reading,writingandtranslationofmathematicalmaterialsshouldbebrife,simple,exactandeasytobeunderstood2SomeEnglishexpressionsofnumbers:ThesetofnumbersconsistsofrealnumbersandpureimaginarynumbersshownasfollowsComplexnumbers(C)Pureimaginarynumbers(I)Realnumbers(R)Rationalnumbers(Q)Irrationalnumbers(Q´)Integers(Z)Fractions(F)Naturalnumbers(N),Zero,NegativesofNaturalNumbersNotice:ReadingofIntegersone,ten,hundred,thousand,tenthousand,hundredthousand,million.Tenmillion,hundredmillion,billion···3Expressionsofsomebasicmathematicalsigns:1.Generalsignsofoperation+Plus,positive-Minus,negativeExample:2+3readastwoplusthreeExample:6-2readassixminustwo±Plusorminus,PositiveornegativeExample:readasequalsplusorminus3Multipliedby,timesExample:56readas5times6or5multipliedby6,Overoristoordividedby34Example:readas3over4,threequarters,3dividedby43,x4xProportion:Example::12readastheratioof1to200Percent,PercentExample:020readas2Percent‰Permille,permilleExample:5‰readas5permille2.BasicsignsofrelationshipsBeequalto,equalsBeidenticalwith/to,beequivalentto5cExample:readascisidenticalwith(to)5,cisequivalentto55BenotequaltoExample:0cdacplusdtimesaisnotequalsto0Beapproximatelyequalto30.42973dividedby7isapproximatelyEqualtozeropointfourtwonineExample:,Belessthan,begreaterthanExample:,abcdaislessthanb,cisgreaterthand,Belessthanorequalto,begreaterthanorequaltoExample:38xxisgreaterthanorequaltominus3andlessthanorequalto8,Befarlessthan,befargreaterthanExample:6ccisfargreaterthanminus66xAxbelongstoAxisanelement(oramember)ofAxdoesnotbelongtoAxisnotanelement(oramember)ofAABAiscontainedinBorAisasubsetofBAcontainsBorBisasubsetofAAcapBorAmeetBorAintersectionBAcupBorAjoinBorAunionBAminusBorthedifferencebetweenAandB6xAABABAB\ABSignsofelementaryalgebraAbsolutevalueExample:217xTheabsolutevalueof2timesxplus1equals7!nFactorialnExample:!554321Factorial5equals5times4times3times2times1ΣThesumofthetermsindicated,summationofExample:5nn=1sThesumofsnfromnequals1to5TheproductofthetermsindicatedExample:1nnaProductofallanfromnequals1toinfinity7max,minmaximumvalue,minimumvalueEample:fxmax()Maximumvalueoff(x)1naamax(,)Maximumvalueoftheseriesa1toanPowersandrootsExample:2xxsquared3xxcubed4xxtothefourth,orxtothepowerfournxxtothenth,orxtothepowernnxxtothepowerminusn1xxinverseExample:x(square)rootx,thesquarerootofx3xcuberoot(of)x8Imaginarynumberandtwocommonirrationalnumbers,1i,1lim(1)xxexratioofthecircumferenceofacircletoitsdiameter,approximatevalue3.14159269Example:4216Twotothefourthpowerissixteen4xfourthroot(of)xnxnthroot(of)x2()xyxplusyallsquared2()xyxoveryallsquaredSomesignsinelemetaryanalysisIntervalsOpeninterval(,)abTheopeninterval(,)abreferstothesetofallrealnumbersxbetweenleftendpointatotherightendpointb(excludingaandb)withaxb.Closedinterval[,]abTheclosedinterval[,]abreferstothesetofallrealnumbersxbetweenleftendpointatotherightendpointb(includingaandb)withaxbHalfopen(closed)interval[,)(,]aborabThehalfopenintervalrefersrealnumbersxbetweenleftendpointatotherightendpointb(includingabutnotb)withaxb[,)abtothesetofall10FunctionfExample:20(),.fxaxbxcaThefunctionofxequalsatimesthesquareofxplusbtimesxplusc,whereaisnotequaltozero.Approach,tendtoExample:nanaapproaches(tendsto)infinitylimlimitExample:0lim()xxfxAThelimitoff(x)asxtendstox0isA11infinityExample:limnnxaThelimitofxnasnapproachesinfinityisa.Example:0limxThelimitasxapproacheszero0limxThelimitasxapproacheszerofromabove0limxThelimitasxapproacheszerofrombelow0theintegralfromzerotoinfinityExample:()bafxdxintegralfromatoboff(x)dxDdoubleintegraloverthedomainDDtripleintegraloverthedomainD12()fxfprimex,fdashedxExample:()fxfdouble-primex,fdouble-dashedx()fxftriple-primex,ftriple-dashedx(4)()fxffourxddxdbydxExample:,dffdxxdfbydx1fxthepartial(derivative)offwithrespectto1x221fxthesecondpartial(derivative)offwithrespectto1x13