基本數(shù)學術語的英文表達

1、 english expressions on basic mathematical nomenclatures (基本數(shù)學術語的英文表達) chineseenglishchineseenglishchineseenglish整數(shù)分數(shù)小數(shù)實數(shù)虛數(shù)復數(shù)正數(shù)負數(shù)個位數(shù)十位數(shù)百位數(shù)千萬十萬百萬億十億萬億偶數(shù)奇數(shù)（數(shù)的）冪 基數(shù)序數(shù)近似數(shù)百分數(shù)千分數(shù)有效（位)數(shù)integerfractiondecimalreal number（pure）imaginary numbercomplex numberpositive numbernegative numberunits or onestenshundre

2、dsthousandten thousandhundred thousandmillioneven numberodd numberpowercardinal numberordinal numberapproximate numberpercentper-millesignificant digithundred millionbilliontrillion reading skill on numbers:101:200:503: 964:2346:23343:第第3: 第第5: 第第9: 第第12:第第16: 第第20:第第22: 第第56:第第100 : 第第123:第第365:第第2

3、000:四舍五入四舍五入:3.567:0.45:2050.0438:0.01:0.001:one (a) hundred (and/oh) one,two hundred,five hundred and one, nine hundred & sixty-fourtwo thousand (,) three hundred and forty-threetwenty-three thousand (,) three hundred and forty-three.(read: the) third(the) fifth,(the) ninth(the) twelfth(the) si

4、xteenth(the) twentieth,(the) twenty-second(the) fifty-sixthone hundredthone hundred and twenty-thirdthree hundred and sixty-fifthtwo thousandthround(-ing)-offthree point five six sevenzero point four fivetwo thousand and fifty point zero four three eightone hundredth (point zero zero one)one thousan

5、dth (point zero zero one, point two zeroes one)12: a (one) half17: one-seventh, 23: two-thirds: three and six-tenths 3387: thirty-three over eighty-seven (thirty-three divided by eighty-seven)123567: one hundred and twenty-three (,) five hundred and sixty- sevenths (one hundred and twenty-three over

6、 five hundred and sixty-seven)5.7%:6%o:1041: one-hundred oh fourth 361 0 reading skill on numbers (cont.)five point seven percent (or per cent)six permille (or per mille)806543212.564823 0, 3, -4 0.3, -4.5 23170.3i, -4.5i 3-4.5i 1,3, 5,7,9,11, 2, 4, 6, 8, 10, 12, 35.6078: after ? to the ? its ? =35.

7、61 4. read:1. whatre the following groups of numbers?2. read the digits name and tell how much of them?73= 0.428571428571= 0.4285713. read:1.3： identifying & reading skill on numbers百分位：百分位：percentiletenth, hundredth, thousandth, ten thousandth, hundred thousandth, millionth 中文中文英文英文中文中文英文英文中文中文

8、英文英文(數(shù)數(shù))運算運算加加減減乘乘除除比例比例比率比率圓括號圓括號（）（）方括號方括號 花括號花括號 等于等于恒等于恒等于不等于不等于正比于正比于近似等近似等于于大于大于小于小于絕對值絕對值 x階乘階乘(n!)(累加累加)和和(乘積乘積)積積(相除相除)商商最大值最大值最小值最小值乘方乘方(xn)開方開方 ( ) 指數(shù)指數(shù)nx2.1： words of operations (i)operationplus, addminustimes, multiplied bydivided by, overproportionratio of (a to b),a is to bround brack

9、ets,parenthesi(e)ssquare bracketsbracesbe equal to, equalsbe identical with/to, be equivalent tobe not equal tobe in direct proportion tobe approximately equal tobe greater thanbe less thanabsolute value of xn factorialthe sum of, the summation ofproductquotient maximum valueminimum valuepower (the

10、nth power of x, x to the nth power)root-extract(-ing),the nth root of xexponent中文中文英文英文中文中文英文英文中文中文英文英文ratio of the circumference of a circle to its diameter趨近于趨近于區(qū)間，區(qū)間，開區(qū)間開區(qū)間,閉區(qū)間閉區(qū)間,半開區(qū)間半開區(qū)間e=2.7183base of natural logarithm(自然對數(shù)自然對數(shù))xy,y”i=-1多元函多元函數(shù)數(shù)對數(shù)，對數(shù)，常用對數(shù)常用對數(shù)logarithm，common logarithm以以20為為底的對

11、底的對數(shù)數(shù)lnx三角函數(shù)三角函數(shù)反三角反三角函數(shù)函數(shù)雙曲函雙曲函數(shù)數(shù)雙曲正切雙曲正切集集(合）合）set子集子集空集空集交集交集并集并集補集補集complements定律定律law因式因式factor因式分解因式分解定理定理theorem法則法則 rule理論理論theory2.1： words of operations (i-cont.)approaches to,interval，symbol of imaginary number(復數(shù)符號復數(shù)符號)tends toopen interval，closed intervaldelta x,increment xhalf-open int

12、ervalmultivariatefunctiony prime,y double primelogarithm with base20ell en xtrigonometricfunctioninverse trigonometricfunctionhyperbolicfunctionhyperbolictangentsubsetsempty setintersectionsunionsfactorize混合運算混合運算mixed operation函數(shù)函數(shù)極限極限無窮大無窮大微分微分導數(shù)導數(shù)偏導數(shù)偏導數(shù)全微分全微分積分積分不定積分不定積分定積分定積分二重積二重積分分三重積分三重積分正弦正弦

13、（sin）余弦余弦（cos）正切正切（tan）余切余切(cot)正割正割(sec)余割余割 (csc)反正弦反正弦（sin1）(數(shù)數(shù))集集（合）（合）2.1： words of operations (i) (cont.)閉環(huán)積分閉環(huán)積分中文中文英文英文中文中文英文英文中文中文英文英文functionlimitinfinitydifferentialderivativepartial derivativecomplete differentialintegralindefinite integraldefinite integraldouble integraltriple integrals

14、inecosinetangentcotangentsecantcosecantinverse sine function (arcsine function)setclosed linearintegral交換律交換律commutative property函數(shù)函數(shù)極限極限結合律結合律微分微分導數(shù)導數(shù)分配律分配律約分約分積分積分分式分式根式根式單項式單項式多項式多項式figure次數(shù)次數(shù),階數(shù)階數(shù)通分通分公分母公分母平方差平方差化簡化簡提取公提取公因式因式分組分組grouping2.1： words of operations (i) (cont.)中文中文英文英文中文中文英文英文中文中文英文

15、英文functionlimitassociativepropertydifferentialderivativedistributivepropertycancellationintegralfractionradical(expression)monomialpolynomial數(shù)字、圖數(shù)字、圖degree，orderreduction of fractions to a common denominatorcommondenominatordifferenceof squaresabstractingcommonfactorssimplify分數(shù)指數(shù)冪分數(shù)指數(shù)冪power offactio

16、nal exponent代數(shù)方代數(shù)方程程algebraicequation未知未知數(shù)數(shù)unknown已知數(shù)已知數(shù)known線性方線性方程程linearequation二次二次方程方程quadraticequation方程組方程組system ofequations二元方二元方程程equation with2 variables一次一次方程方程first-degree eq.配方法配方法completingthe square判別式判別式discriminant代入代入法法substitution method不等式不等式inequality矩陣矩陣matrix逆矩逆矩陣陣inversematr

17、ix合并合并同類項同類項combiningsimilar terms同底冪同底冪powerswith same base2階行階行列式列式determinant of order 2余子式余子式cofactor圖形圖形graph示意示意圖圖diagram2.1： words of operations (i) (cont.)中文中文英文英文中文中文英文英文中文中文英文英文2.2： reading skill on signsx to the third power plus two times a times y to the fourth power plus twosix plus x o

18、ver (divided by) the quantity x squared times the quantity x to the fifth power minus four to the third power.six-tenths open brace, a open square bracket b plus left round bracket c minus d right round bracket close square bracket, close brace.: the first derivative of y with respect to x equals dy

19、 over dx.the second partial derivative of y with respect to x is equal to delta squared y over delta x squared.dxdy(一階導數(shù)一階導數(shù)) y(x)=352)4(6xxx: a b + (c - d) :10622xy(二階偏導數(shù)二階偏導數(shù)) y”(x，z)=:x3+2ay4+2 : 二階混合偏導數(shù)二階混合偏導數(shù): the second mixed partial derivative of f with respect to x and y函數(shù)份函數(shù)份f(x)從從a到到b的定積分的

20、定積分: the definite integral of f of x with limits a and b (from a to b)g(x) 積分函數(shù)積分函數(shù)function of integral(a,b) 積分區(qū)間積分區(qū)間integral intervalthe difference of g of x evaluated at b and adefinite integral of f, a to b, equals g, a to bf(x,y)的二重積分的二重積分: the double integral of f over (region) r w.r.t. x and y

21、( , )rf x y dxdy( , )dbcaf x y dxdy f(x,y)的二重積分的二重積分: integrating from a to b of f of x, y w.r.t. x and from c to d w.r.t. y( ) ( )bbaaf x dxg xmbab根底數(shù)根底數(shù)radicand（base），），m根指數(shù)根指數(shù)index（root），），a是是b的的m次根次根principal mth root of b連連(乘乘)積：積：product of all ak from k equals 1 to n1nkka累加累加(求和求和)：capital si

22、gma ak from k equals 1 to n1nkks1. a b, a+ b c, f a, x 4.53. 4!=4321, e2x=2x+1, 4. sin1(0.5)=30o, tan( 45o) =1, log10(10)=1 )(422mdxdyxyscxxdx221)( 3)2(32mdvzyxn5.2. x=4, =8, 6xx-3lim(y )=2.2：practice on reading skill of signsc)ydxxdy(the closed linear integral of (xdy-ydx) in the integral region wi

23、th boundary curve c6.chineseenglishchineseenglishchineseenglish加法加法(的的)減法減法(的的)乘法乘法除法除法乘數(shù)乘數(shù)被乘數(shù)被乘數(shù)分子分子分母分母除數(shù)除數(shù)被除數(shù)被除數(shù)余數(shù)余數(shù)因子因子定理定理法則法則定律定律/規(guī)則規(guī)則代數(shù)代數(shù)單項式單項式多項式多項式3.1： words of operations (ii)addition(additive)subtraction(subtractive)multiplicationdivisionmultipliermultiplicandnumeratordenominatordivisordi

24、videndremainderfactortheoremrulelawalgebramonomialpolynomial chineseenglishchineseenglishchineseenglish方程方程(方程的方程的) 解解已知數(shù)已知數(shù)未知數(shù)未知數(shù)方程組方程組變量變量線性方程線性方程不等式不等式常數(shù)常數(shù)標量標量矢（向）量矢（向）量(方程等的方程等的)根根3.1： words of operations (ii) (cont.)equationsolutionknownunknowna system of equationsvariablelinear equationinequal

25、ityconstantscalarvectorrootcoefficientgive the names of the following operations:2 + 3 = 5, 5 - 4 = 1, 5 3 = 15, 20 8 = 2.5 tell the names of the numbers in the above operations71ais a? b=5 is 3.2： reading skill on the expressionssolution:x2-2x=15 place the constant term on the right side.x2-2x+1=1+

26、15 complete the square of (x+1) by adding the square of half the coefficient of x (12) to both sides.(x+1)2=16 complete the square.x-1=4 use the square root property.x=14 solve for xx1=1+4, x2=1-4 x sub 1 equals 1 plus 4, and x sub 2 is equal to 1 minus 4.x1=5, x2= -3 at last, x sub one equals 5 , a

27、nd x sub 2 equals minus 3.3.2： a practice on solving an equationexplain the steps to solve: x2-2x-15=0chineseenglishchineseenglishchineseenglish線線角角點點線段線段射線射線端點端點直線直線曲線曲線折線折線垂直的垂直的水平的水平的傾斜的傾斜的相交相交垂直于垂直于平行于平行于直角直角銳角銳角鈍角鈍角平角平角補角補角余角余角對頂角對頂角對角線對角線三角形三角形四邊形四邊形多邊形多邊形平行平行四邊形四邊形矩形矩形菱形菱形正方形正方形4.1： vocabular

28、y of geometrylineanglepointline segmentrayendpointstraight linecurve (line)broken linevertical (to)horizontalslant (declined)intersect(-ing)perpendicular(to)parallel (to)right angleacute angleobtuse anglestraight anglesupplementary anglecomplementary anglevertex anglediagonaltrianglequadrilateralpol

29、ygonparallelogramrectanglelozenge, rhombusessquare梯形梯形周長周長面積面積圓圓(形形)弦弦弧弧同心的同心的圓周圓周(向向)的的內接的內接的切線切線割線割線內切內切扇形扇形半徑半徑直徑直徑(圓圓)弓形弓形長度長度體積體積寬度寬度高度高度厚度厚度棱柱棱柱多面體多面體底面底面?zhèn)让鎮(zhèn)让骈L方體長方體六面體六面體正方體正方體棱錐棱錐圓柱圓柱圓錐圓錐圓臺圓臺球球(體體)4.1： vocabulary of geometry (cont.)chineseenglishchineseenglishchineseenglish表面積表面積 | | 球冠球冠 | |

30、 旋轉體旋轉體 | trapezoidperimeterareacirclechordarcconcentriccircumferentialinscribedtangent linesecant lineinner tangencysectorradii（radius）diametersegmentlengthvolumewidthaltitude、heightthicknessprismpolyhedronbaselateral facerectangular solidhexahedrontetragonal solid /cubepyramidcylinderconetruncated

31、 conespheresurface areaspherical crownrotational solid4.2： practice on plane/space graphsthe length of line segment ad is computed by: ad=5 times cotangent(50 degrees) metersthe length of dc is: dc=5 times cotangent(30 degrees) metersthe base line of the triangle ac is then the sum of ad and dc, i.e

32、., ac=ad+dc=5 times left square bracket cotangent(50 degrees) plus cotangent(30 degrees) right square bracket. unit is metersthus, according to the formula of triangle area, we can get the area to be found as follow: s=(ac*5)=xxx (m2).)(50cotan30cotan5)50cotan(5)30cotan(5oooomac）（）（50o30oa d cb5 m21

33、the area of the triangle, denoted by s, is equal to one half times left round bracket ac times the height 5 right round bracket. the unit is meter squared.5.1： practice on geometrical computationcondition: mass of the car: no friction on the way, start at the top b with vo =0 m/s。 to find: the speed

34、 of the car at the point a (the end) of the slope.solution: we can have two different ways to find out the results.(1)firstly, according to law of energy conservation, potential energy of the car at the top of the slope is equal to the kinetic energy of the car at the endpoint of the slope. i.e., th

35、e potential energy at the top of the slope: mgh=(equals) m vt t 2/2 (the kinetic energy at the endpoint of the slope, a). gh2vt =20*8 . 9*2= 20(m/s) 5.2： practice on solving a physics problem 30omh=20 mvwf2af1 bc(2) secondly, resolute the gravity force w into two components, f1 and f2 parallel to the motion of the car and perpendicular t