English_Expressions_on_Basic_Math.ppt

,LusStudio,吕广庆教育教学工作室LUGuang-qingsEducation&TeachingStudio,For：1stTermofYear2010-2011Students,吕广庆教育与教学工作室,2020年5月22日,课堂教学软件(1),2020年5月22日,UIC吕广庆,数学教学辅助资料,1.1：WordsofNumbers,EnglishExpressionsonBasicMathematicalNomenclatures(基本数学术语的英文表达),1.1：WordsofNumbers,integer,fraction,decimal,realnumber,（pure）imaginarynumber,complexnumber,positivenumber,negativenumber,unitsorones,tens,hundreds,thousand,tenthousand,hundredthousand,million,evennumber,oddnumber,power,cardinalnumber,ordinalnumber,approximatenumber,percent,per-mille,significantdigit,hundredmillion,billion,trillion,1.2：ReadingSkillonNumbers,:,101:200:503:964:2346:23343:第3:第5:第9:第12:第16:第20:第22:第56:第100:第123:第365:第2000:四舍五入:3.567:0.45:2050.0438:0.01:0.001:,One(a)hundred(and/oh)one,twohundred,fivehundredandone,ninehundred&sixty-four,twothousand(,)threehundredandforty-three,twenty-threethousand(,)threehundredandforty-three.,(read:the)third,(the)fifth,(the)ninth,(the)twelfth,(the)sixteenth,(the)twentieth,(the)twenty-second,(the)fifty-sixth,onehundredth,onehundredandtwenty-third,threehundredandsixty-fifth,twothousandth,round(-ing)-off,threepointfivesixseven,zeropointfourfive,twothousandandfiftypointzerofourthreeeight,onehundredth(pointzerozeroone),onethousandth(pointzerozeroone,pointtwozeroesone),:a(one)half,:one-seventh,:two-thirds,:threeandsix-tenths,:thirty-threeovereighty-seven(thirty-threedividedbyeighty-seven),:onehundredandtwenty-three(,)fivehundredandsixty-sevenths(onehundredandtwenty-threeoverfivehundredandsixty-seven),5.7%:6%o:,:one-hundredohfourth,3,1.2：ReadingSkillonNumbers(Cont.),fivepointsevenpercent(orpercent),sixpermille(orpermille),806543212.564823,35.6078:after?Tothe?Its?=35.61,4.Read:,1.Whatrethefollowinggroupsofnumbers?,2.Readthedigitsnameandtellhowmuchofthem?,=0.428571428571=0.428571,3.Read:,1.3：Identifying&ReadingSkillonNumbers,百分位：percentile,tenth,hundredth,thousandth,tenthousandth,hundredthousandth,millionth,2.1：WordsofOperations(I),operation,plus,add,minus,substract,times,multipliedby,dividedby,over,proportion,ratioof(AtoB),AistoB,roundbrackets,Parenthesi(e)s,squarebrackets,braces,beequalto,equals,beidenticalwith/to,beequivalentto,benotequalto,beindirectproportionto,beapproximatelyequalto,begreaterthan,belessthan,absolutevalueofx,nfactorial,thesumof,thesummationof,product,quotient,maximumvalue,minimumvalue,power(thenthpowerofx,xtothenthpower),root-extract(-ing),thenthrootofx,exponent,2.1：WordsofOperations(I-cont.),approachesto,interval，,symbolofimaginarynumber(复数符号),tendsto,openinterval，closedinterval,deltax,incrementx,half-openinterval,multivariatefunction,yprime,ydoubleprime,Logarithmwithbase20,Naturallogarithmofx,Trigonometricfunction,InverseTrigonometricfunction,Hyperbolicfunction,Hyperbolictangent,subsets,Emptyset,intersections,unions,factorize,2.1：WordsofOperations(I)(Cont.),function,limit,infinity,differential,derivative,partialderivative,completedifferential,integral,indefiniteintegral,definiteintegral,doubleintegral,tripleintegral,sine,cosine,tangent,cotangent,secant,cosecant,inversesinefunction(arcsinefunction),ywithrespectto(w.r.t.)x,closedlinearintegral,2.1：WordsofOperations(I)(Cont.),function,limit,Associativeproperty,differential,derivative,Distributiveproperty,cancellation,integral,fraction,radical(expression),monomial,polynomial,数字、图,degree，order,Reductionoffractionstoacommondenominator,CommonDenominator,Differenceofsquares,Abstractingcommonfactors,simplify,2.1：WordsofOperations(I)(Cont.),2.2：ReadingSkillonSigns,xtothethirdpowerplustwotimesatimesytothefourthpowerplustwo,sixplusxover(dividedby)thequantityxsquaredtimesthequantityxtothefifthpowerminusfourtothethirdpower.,six-tenthsopenbrace,aopensquarebracketbplusleftroundbracketcminusdrightroundbracketclosesquarebracket,closebrace.,:thefirstderivativeofywithrespecttoxequalsdyoverdx.,thesecondpartialderivativeofywithrespecttoxisequaltodeltasquaredyoverdeltaxsquared.,(一阶导数)y(x)=,:,ab+(c-d):,x3+2ay4+2:,二阶混合偏导数:thesecondmixedpartialderivativeoffwithrespecttoxandy,函数份f(x)从a到b的定积分:thedefiniteintegraloffofxwithlimitsaandb(fromatob),g(x)积分函数functionofintegral(a,b)积分区间integralinterval,Thedifferenceofgofxevaluatedatbanda,definiteintegraloff,atob,equalsg,atob,f(x,y)的二重积分:thedoubleintegraloffover(region)Rw.r.t.xandy,f(x,y)的二重积分:Integratingfromatoboffofx,yw.r.t.xandfromctodw.r.t.y,b根底数radicand（base），m根指数index（root），a是b的m次根principalmthrootofb,连(乘)积：Productofallakfromkequals1ton,累加(求和)：CumulativeSum(CapitalSigma)ofakfromkequals1ton,1.AB,A+BC,Fa,x4.5,3.4!=4321,e2x=2x+1,4.sin1(0.5)=30o,tan(45o)=1,log10(10)=1,5.,2.2：PracticeonReadingSkillofSigns,theclosedlinearintegralof(xdy-ydx)intheintegralregionwithboundarycurvec,6.,3.1：WordsofOperations(II),addition(additive),subtraction(subtractive),multiplication,division,multiplier,multiplicand,numerator,denominator,divisor,dividend,remainder,factor,theorem,rule,law,algebra,monomial,polynomial,3.1：WordsofOperations(II)(Cont.),equation,solution,known,unknown,asystemofequations,variable,linearequation,inequality,constant,scalar,vector,root,系数：coefficient,上标：superscript（简称super）,下标：subscript（简称sub）,GivethenamesofthefollowingOperations:,2+3=5,5-4=1,53=15,208=2.5,Tellthenamesofthenumbersintheaboveoperations,isa?,b=5is,3.2：ReadingSkillontheExpressions,Solution:x2-2x=15Placetheconstanttermontherightside.x2-2x+1=1+15Completethesquareof(x+1)byaddingthesquareofhalfthecoefficientofx(12)tobothsides.(x+1)2=16Completethesquare.x-1=4Usethesquarerootproperty.x=14Solveforxx1=1+4,x2=1-4xsub1equals1plus4,andxsub2isequalto1minus4.x1=5,x2=-3Atlast,xsuboneequals5,andxsub2equalsminus3.,3.2：Apracticeonsolvinganequation,Explainthestepstosolve:x2-2x-15=0,4.1：VocabularyofGeometry,line,angle,point,linesegment,ray,endpoint,straightline,curve(line),brokenline,vertical(to),horizontal,slant(declined),intersect(-ing),perpendicular(to),parallel(to),rightangle,acuteangle,obtuseangle,straightangle,supplementaryangle,complementaryangle,vertexangle,diagonal,triangle,quadrilateral,polygon,parallelogram,rectangle,lozenge,rhombuses,square,4.1：VocabularyofGeometry(Cont.),表面积|球冠|旋转体|,trapezoid,perimeter,area,circle,chord,arc,concentric,circumferential,inscribed,tangentline,secantline,innertangency,sector,radii（radius）,diameter,segment,length,volume,width,altitude、height,thickness,prism,polyhedron,base,lateralface,rectangularsolid,hexahedron,tetragonalsolid/cube,pyramid,cylinder,cone,truncatedcone,sphere,surfacearea,sphericalcrown,rotationalsolid,4.2：PracticeonPlane/SpaceGraphs,ThelengthoflinesegmentADiscomputedby:AD=5timescotangent(50degrees)metersThelengthofDCis:DC=5timescotangent(30degrees)metersThebaselineofthetriangleACisthenthesumofADandDC,i.e.,AC=AD+DC=5timesleftsquarebracketcotangent(50degrees)pluscotangent(30degrees)rightsquarebracket.UnitismetersThus,accordingtotheformulaoftrianglearea,wecangettheareatobefoundasfollow:S=,(AC*5)=xxx(m2).,Theareaofthetriangle,denotedbyS,isequaltoonehalftimesLeftroundbracketACtimestheheight5rightroundbracket.Theunitismetersquared.,5.1：PracticeonGeometricalComputation,Condition:massofthecar:nofrictionontheway,startatthetopBwithVo=0m/s。ToFind:thespeedofthecaratthepointA(theend)oftheslope.,Solution:Wecanhavetwodifferentwaystofindouttheresults.,Firstly,Accordingtolawofenergyconservation,potentialenergyofthecaratthetopoftheslopeisequaltotheki