常用数学符号英文对照

数学术语英文对照表在学习数学时，不可避免地需要掌握一些数学术语。

下面是一些常见的数学术语的中英文对照表：1. 数学 Mathematics2. 数学符号 Mathematical symbol3. 数字 Digit4. 字符 Character5. 算术 Arithmetic6. 代数 Algebra7. 几何 Geometry8. 统计学 Statistics9. 概率 Probability10. 三角学 Trigonometry11. 微积分 Calculus12. 矩阵 Matrix13. 向量 Vector14. 线性代数 Linear algebra15. 数学模型 Mathematical model16. 方程 Equation17. 垂直 Perpendicular18. 平行 Parallel19. 正比例 Direct proportion20. 反比例 Inverse proportion21. 旋转 Rotation22. 缩放 Scaling23. 变形 Deformation24. 函数 Function25. 极限 Limit26. 微分 Differential27. 积分 Integral28. 中心 Central29. 对称 Symmetry30. 相似 Similarity31. 等式 Equality32. 不等式 Inequality33. 方形 Rectangle34. 正方形 Square35. 圆 Circle36. 椭圆 Ellipse37. 球球体 Sphere38. 三角形 Triangle39. 直角三角形 Right triangle40. 等腰三角形 Isosceles triangle41. 等边三角形 Equilateral triangle42. 直线 Line43. 射线 Ray44. 线段 Line segment45. 弧 Arc46. 正弦 Sine47. 余弦 Cosine48. 正切 Tangent49. 余切 Cotangent50. 弦 Chord总之，数学术语是数学学习的基础，掌握数学术语对于提高数学能力以及学好数学至关重要。

数系词汇中英文对照表本文是针对湘教版选修2-2教案中涉及到的数系词汇进行中英文对照的整理和总结。

以便同学们更好地理解数学概念和术语。

数系词汇对照表中文名称英文名称整数Integer正整数Positive Integer负整数Negative Integer非负整数Non-negative Integer非正整数Non-positive Integer真分数Proper Fraction假分数Improper Fraction约分Simplification余数Remainder分数Fraction百分数Percentage小数Decimal循环小数Repeating Decimal非循环小数Non-repeating Decimal有理数Rational Number无理数Irrational Number实数Real Number虚数Imaginary Number复数Complex Number绝对值Absolute Value整除Divisible互质Relatively Prime质数Prime Number合数Composite Number素数Prime Number最大公因数Greatest Common Divisor 最小公倍数Least Common Multiple 对数Logarithm运算Operation开方Square Root数词名称的英文表达数词英文一One二Two三Three四Four五Five六Six七Seven八Eight九Nine十Ten百Hundred千Thousand万Ten Thousand亿Hundred Million数学符号的英文表达数学符号英文+ Plus- Minus× Multiply÷ Divide≈Approximately Equal to≠Not Equal to< Less than> Greater than≤Less than or Equal to≥Greater than or Equal to以上数系词汇的对照表和数学符号的英文表达可以帮助同学们更好地掌握数学知识，理解数学概念和术语。

常用数学符号英文对照Basic math symbolsSymbol Symbol Name Meaning / definition Example= equals sign equality 5 = 2+35 is equal to 2+3≠not equal sign inequality 5 ≠ 45 is not equal to 4≈approximatelyequal approximationsin(0.01) ≈ 0.01,x≈y means x is approximatelyequal to y> strict inequality greater than 5 > 45 is greater than 4< strict inequality less than 4 < 54 is less than 5≥inequality greater than or equal to 5 ≥ 4,x≥y means x is greater than or equal to y≤inequality less than or equal to 4 ≤ 5,x ≤ y means x is greater than or equal to y( ) parentheses calculate expression insidefirst2 × (3+5) = 16[ ] brackets calculate expression insidefirst[(1+2)×(1+5)] = 18 + plus sign addition 1 + 1 = 2−minus sign subtraction 2 − 1 = 1±plus - minus both plus and minusoperations3 ± 5 = 8 and -2±minus - plus both minus and plusoperations3 ± 5 = -2 and 8 * asterisk multiplication 2 * 3 = 6×times sign multiplication 2 × 3 = 6 ·multiplication dot multiplication 2 · 3 = 6÷division sign /division 6 ÷ 2 = 3obelus/ division slash division 6 / 2 = 3–horizontal line division / fractionmod modulo remainder calculation 7 mod 2 = 1. period decimal point, decimal2.56 = 2+56/100separatora b power exponent 23= 8a^b caret exponent 2 ^ 3= 8√a square root √a ·√a = a√9 = ±33√a cube root 3√a ·3√a ·3√a = a3√8 = 24√a fourth root 4√a ·4√a ·4√a ·4√a = a4√16 = ±2n√a n-th root (radical) for n=3, n√8 = 2% percent1% = 1/100 10% × 30 = 3‰per-mille1‰ = 1/1000 = 0.1%10‰ × 30 = 0.3ppm per-million1ppm = 1/1000000 10ppm × 30 = 0.0003ppb per-billion 1ppb = 1/1000000000 10ppb × 30 = 3×10-7ppt per-trillion 1ppt = 10-1210ppt × 30 = 3×10-10ABC = 30°AOB = 30°°degree 1 turn = 360°α = 60°deg degree 1 turn = 360deg α = 60deg′prime arcminute, 1° = 60′α = 60°59′″double prime arcsecond, 1′ = 60″α = 60°59′59″line infinite lineAB line segment line from point A to point Bray line that start from point Aarc arc from point A to point B= 60°⊥perpendicular perpendicular lines (90° angle) AC ⊥ BC| | parallel parallel lines AB | | CD≅congruent to equivalence of geometric shapes and size ∆ABC≅∆XYZ ~ similarity same shapes, not same size ∆ABC~ ∆XYZ Δtriangle triangle shape ΔABC≅ΔBCD |x-y| distance distance between points x and y | x-y | = 5πpi constant π = 3.141592654...is the ratio between the circumference and diameter of acirclec = π·d = 2·π·rrad radians radians angle unit 360° = 2π rad c radians radians angle unit 360° = 2πcgrad gradians / gons grads angle unit 360° = 400 gradg gradians / gons grads angle unit 360° = 400 gx x variableto findwhen 2x = 4, then x = 2≡equivalence identical to≜equal by definition equal bydefinition:= equal by definition equal bydefinition~ approximately equal weakapproximation11 ~ 10≈approximately equal approximation sin(0.01) ≈ 0.01∝proportional to proportional to y∝x when y = kx, k constant ∞lemniscate infinity symbol≪much less than much less than 1 ≪1000000≫much greater than much greaterthan1000000 ≫1( ) parentheses calculateexpressioninside first2 * (3+5) = 16[ ] brackets calculateexpressioninside first[(1+2)*(1+5)] = 18{ } braces set⌊x⌋floor brackets rounds numberto lower integer⌊4.3⌋ = 4⌈x⌉ceiling brackets rounds numberto upper integer⌈4.3⌉ = 5x! exclamation mark factorial4! = 1*2*3*4 = 24 | x | single vertical bar absolute value | -5 | = 5f (x) function of x maps values ofx to f(x)f (x) = 3x+5(f∘g) function composition (f∘g) (x)= f (g(x))f (x)=3x,g(x)=x-1 ⇒(f∘g)(x)=3(x-1)(a,b) open interval (a,b) = x∈(2,6)[a ,b ] closed interval[a ,b ] = {x | a ≤ x ≤ b }x ∈ [2,6]∆ delta change / difference∆t = t 1 - t 0∆ discriminantΔ = b 2 - 4ac∑sigmasummation -sum of all values in range of series ∑ x i = x 1+x 2+...+x n∑∑sigmadouble summation∏capital piproduct -product of all values in range of series∏ x i =x 1∙x 2∙...∙x ne e constant / Euler's numbere =2.718281828... e = lim (1+1/x )x , x →∞γ Euler-Mascheroni constant γ =0.527721566...φgolden ratio golden ratio constantπpi constant π =3.141592654...is the ratiobetween the circumference and diameter of a circlec = π·d = 2·π·rA ⊗Btensor product tensor product of A and BA ⊗ Binner product[ ] brackets matrix of numbers ( ) parentheses matrix of numbers| A | determinant determinant of matrix A det(A ) determinant determinant of matrix A|| x || double vertical bars normA T transpose matrix transpose(A T )ij = (A )ji A † Hermitian matrix matrix conjugate transpose (A †)ij = (A )ji A * Hermitian matrix matrix conjugate transpose(A *)ij = (A )jiA -1inverse matrixA A -1 = Irank(A ) matrix rank rank of matrix A rank(A ) = 3 dim(U )dimensiondimension of matrix Arank(U ) = 3Probability and statistics symbolsSymbolSymbol Name Meaning / definitionExampleP (A )probability function probability of event A P (A ) = 0.5P (A ∩ B ) probability ofeventsintersection probability that of events A and BP (A ∩B ) = 0.5P (A ∪B ) probability ofevents unionprobability that of events A or B P (A ∪B ) = 0.5P (A | B )conditionalprobability function probability of event A given event B occuredP (A | B ) = 0.3f (x ) probabilitydensity function (pdf) P (a ≤ x ≤ b ) = ∫ f (x ) dxF (x )cumulativeF (x ) = P (X ≤ x )distribution function (cdf)μ population mean mean of population valuesμ = 10E (X )expectation valueexpected value of random variable X E (X ) = 10E (X | Y )conditional expectationexpected value of random variable X given YE (X | Y=2) = 5var (X ) variance variance of random variable X var (X ) = 4σ2variancevariance of population values σ2 = 4std (X ) standard deviationstandard deviation of random variable X std (X ) = 2σXstandard deviationstandard deviation value of random variable X σX = 2medianmiddle value of random variable xcov (X ,Y )covariance covariance ofrandom variables X and Y cov (X,Y ) = 4corr (X ,Y ) correlationcorrelation ofrandom variables X and Y corr (X,Y ) = 0.6ρX ,Ycorrelation correlation ofrandom variables X and YρX ,Y = 0.6∑summation summation - sum ofall values in range of series∑∑double summationdouble summationMo mode value that occurs most frequently in populationMR mid-range MR = (x max+x min)/2 Md sample median half the population isbelow this valueQ1lower / firstquartile 25% of population are below this valueQ2median /second quartile 50% of population are below this value = median of samplesQ3upper / thirdquartile 75% of population are below this valuex sample mean average / arithmeticmeanx = (2+5+9) / 3 = 5.333s2samplevariance population samples variance estimators2 = 4s samplestandarddeviationpopulation samplesstandard deviationestimators = 2z x standard score z x = (x-x) / s xX ~ distribution of X distribution ofrandom variable XX ~ N(0,3)N(μ,σ2) normaldistributiongaussian distribution X ~ N(0,3)U(a,b) uniformdistributionequal probability inrange a,bX ~ U(0,3)exp(λ)exponentialdistributionf (x) = λe-λx , x≥0gamma(c, λ)gammadistributionf (x) = λ c x c-1e-λx /Γ(c), x≥0χ 2(k) chi-squaredistributionf (x) = x k/2-1e-x/2 /( 2k/2 Γ(k/2) )F (k1, k2) F distributionBin (n ,p )binomial distribution f (k ) = n C k p k (1-p )n-kPoisson (λ)Poisson distribution f (k ) = λk e -λ / k !Geom (p )geometric distribution f (k ) = p (1-p ) kHG (N ,K ,n ) hyper-geometric distributionBern (p ) Bernoulli distributionsubset the set {9,14,28} A ⊄ B not subset left set not a subset of right set{9,66} ⊄{9,14,28} A ⊇B supersetset A has more elements or equalto the set B{9,14,28} ⊇{9,14,28} A ⊃Bproper superset / strictsupersetset A has more elements than setB{9,14,28} ⊃{9,14}A ⊅B not superset set A is not a superset of set B{9,14,28} ⊅{9,66} 2A power set all subsets of Apower set all subsets of AA =B equalityboth sets have the samemembersA={3,9,14},B={3,9,14},A=BA c complementall the objects that do not belongto set AA \B relative complementobjects that belong to A and notto BA = {3,9,14},B = {1,2,3},A-B = {9,14} A - B relative complementobjects that belong to A and notto BA = {3,9,14},B = {1,2,3},A-B = {9,14} A ∆ B symmetric differenceobjects that belong to A or B butnot to their intersectionA = {3,9,14},B = {1,2,3},A ∆B ={1,2,9,14} A ⊖ B symmetric differenceobjects that belong to A or B butnot to their intersectionA = {3,9,14},B = {1,2,3},A ⊖B ={1,2,9,14}a∈A element of set membership A={3,9,14}, 3 ∈Ax∉A not element of no set membership A={3,9,14}, 1 ∉A(a ,b ) ordered pair collection of 2 elementsA×B cartesian product set of all ordered pairs from Aand B|A| cardinality the number of elements of set AA={3,9,14}, |A|=3 #A cardinality the number of elements of set AA={3,9,14}, #A=3aleph-nullinfinite cardinality of naturalnumbers setaleph-one cardinality of countable ordinalnumbers setØ empty set Ø = { }C = {Ø}universal set set of all possible valuesnatural numbers / whole numbers set (with zero) 0 = {0,1,2,3,4,...}0 ∈ 01natural numbers / wholenumbers set (withoutzero)1 = {1,2,3,4,5,...}6 ∈ 1integer numbers set= {...-3,-2,-1,0,1,2,3,...} -6 ∈rational numbers set= {x | x =a /b , a ,b ∈}2/6 ∈real numbers set= {x | -∞ < x <∞} 6.343434∈complex numbers set= {z | z=a +bi ,-∞<a <∞, -∞<b <∞}6+2i ∈∨reversed caret or x∨y | vertical line or x | y x' single quote not - negation x'x bar not - negation x¬not not - negation ¬x ! exclamation mark not - negation ! x ⊕circled plus / oplus exclusive or - xor x⊕y ~ tilde negation ~ x ⇒implies⇔equivalent if and only if (iff)↔equivalent if and only if (iff)∀for all∃there exists∄there does not exists∴therefore∵because / sincee e constant / Euler'snumber e = 2.718281828...e = lim(1+1/x)x ,x→∞y ' derivative derivative - Lagrange's notation (3x3)' = 9x2y '' second derivative derivative of derivative (3x3)'' = 18xy(n)nth derivative n times derivation (3x3)(3) = 18derivative derivative - Leibniz's notation d(3x3)/dx = 9x2second derivative derivative of derivative d2(3x3)/dx2 = 18xnth derivative n times derivationtime derivative derivative by time - Newton's notationtime secondderivativederivative of derivativeD x y derivative derivative - Euler's notationD x2y second derivative derivative of derivativepartial derivative ∂(x2+y2)/∂x = 2x ∫integral opposite to derivation ∫f(x)dx∫∫double integral integration of function of 2variables∫∫f(x,y)dxdy∫∫∫triple integral integration of function of 3variables∫∫∫f(x,y,z)dxdydz∮closed contour / lineintegral∯closed surfaceintegral∰closed volumeintegral[a,b] closed interval [a,b] = {x | a ≤ x ≤ b}(a,b) open interval (a,b) = {x | a < x < b}i imaginary unit i≡ √-1 z = 3 + 2i z* complex conjugate z = a+bi→z*=a-bi z* = 3 - 2i z complex conjugate z = a+bi→z = a-bi z = 3 - 2i ∇nabla / del gradient / divergence operator ∇f (x,y,z)vectorunit vectorx * y convolution y(t) = x(t) * h(t)Laplace transform F(s) = {f (t)}Fourier transform X(ω) = {f (t)}δdelta function∞lemniscate infinity symbol。

字母符号中英文，罗马数字对照一、键盘符号释义：` backquote 反引号~ tilde 波浪符! Exclam 感叹号@ at 单价# numbersign井号英语是hash，美语是pound,音乐里是sharp$ dollar 美元币值符号% percent 百分号^ caret 弧形号& ampersand 和，与，引用* asterisk,star 星号,数学公式读作multiply( parenleft,opening parentheses 左扩符号) parenright,closing paretheses 右扩符号- minus;hyphen连字符,不读_ underscore 减号+ plus 加号= equal 等号[ bracketleft,opening bracket 左方括号] bracketright,closing bracket 右方括号{ braceleft 左花括号} braceright 右花括号; semicolon 分号: colon 冒号' quote 逗号" doublequote 引号/ slash 斜线，除号backslash 反斜杠| bar 分竖线, comma 分隔符号< less 小于号> greater 大于号. Period 句号，点? Question 问号space 空格二、数学符号释义：+ plus 加号；正号- minus 减号；负号± plus or minus 正负号× is multiplied by 乘号÷ is divided by 除号＝ is equal to 等于号≠ is not equal to 不等于号≡ is equivalent to 全等于号≌ is equal to or approximately equal to 等于或约等于号≈ is approximately equal to 约等于号＜ is less than 小于号＞ is more than 大于号≮ is not less than 不小于号≯ is not more than 不大于号≤ is less than or equal to 小于或等于号≥ is more than or equal to 大于或等于号% per cent 百分号‰ per mill 千分号∞ infinity 无限大号∝ varies as 与…成比例号√ (square) root 平方根∵ since; because 因为∴ hence 所以∷ equals, as (proportion) 等于，成比例∠ angle 角⌒ semicircle 半圆⊙ circle 圆○ circumference 圆周π pi 圆周率△ triangle 三角形⊥ perpendicular to 垂直于∪ union of 并，合集∩ intersection of 交，通集∫ the integral of …的积分∑ (sigma) summation of 总和° degree 度′ minute 分〃 second 秒℃ Celsius system 摄氏度{ open brace, open curly 左花括号} close brace, close curly 右花括号( open parenthesis, open paren 左圆括号) close parenthesis, close paren 右圆括号() brakets/ parentheses 括号[ open bracket 左方括号] close bracket 右方括号[] square brackets 方括号. period, dot 句号，点| vertical bar, vertical virgule 竖线& ampersand, and, reference, ref 和，于，引用/ slash, divide, oblique 斜线，斜杠，除号// slash-slash, comment 双斜线，注释符# pound 井号backslash, sometimes escape 反斜线，转义符或续行符~ tilde 波浪符. full stop 句号, comma 逗号: colon 冒号; semicolon 分号? question mark 问号! exclamation mark 叹号' apostrophe 撇号- hyphen 连字号-- dash 破折号... dots/ ellipsis 省略号" single quotation marks 引号"" double quotation marks 双引号‖ parallel 双线号，分隔号～ swung dash 代字号§ section; division 分节号→ arrow 箭号；参见号_ underscore 下划线三、罗马、阿拉伯数字、英语对照释义：I 1 one 1st the firstII 2 two 2nd the secondIII 3 three 3rd the thirdIV 4 four 4th the fourthV 5 five 5th the fifthVI 6 six 6th the sixthVII 7 seven 7th the seventhVIII 8 eight 8th the eighthIX 9 nine 9th the ninthX 10 ten 10th the tenthXI 11 eleven 11th the eleventhXII 12 twelve 12th the twelfthXIII 13 thirteen 13th the thirteenth XIV 14 fourteen 14th the fourteenth XV 15 fifteen 15th the fifteenth XVI 16 sixteen 16th the sixteenth XVII 17 seventeen 17th the seventeenth XVIII 18 eighteen 18th the eighteenth XIX 19 nineteen 19th the nineteenthXX 20 twenty 20th the twentiethXXI 21 twenty-one 21st the twenty-firstXXV 25 twenty-five 25th the twenty-fifthXXX 30 thirty 30th the thirtiethXL 40 forty 40th the fortiethL 50 fifty 50th the fiftiethLX 60 sixty 60th the sixtiethLXX 70 seventy 70th the seventiethLXXX 80 eighty 80th the eightiethXC 90 ninety 90th the ninetiethIC 99 ninety-nine 99th the ninety-ninthC 100 one hundred 100th the hundredth罗马数字记数方法和规则：I（1） V (5) X (10) L (50) C (100) D (500) M (1000) 组数规则：左减右加。

1．Professional Basics Knowledge1/21/32/31/41/1001/1000 113/3244320.25＋－±×÷＝≈( ) [ ] { }≢≣∞∵∴→x＋y (a + b ) a = ba ≠b a ±b a ≈b a ＞b a ＞＞b a ≣b a ＜b a ＜＜b a ≢b a ⊥b x →∞a ≡b ∟a a half, one halfa third, one thirdtwo thirdsa quarter, one quarter , a fourth, one fourtha (one) hundredtha (one) thousandthone hundred and thirteen over three hundred and twenty four four and two thirdszero (0, naught) point two fiveplus, positiveminus, negativeplus or minusmultiplied by, timesdivided bybe equal to, equalsbe approximately equal to, approximately equalsround brackets; parenthesessquare (angular) bracketsbracesless than or equal tomore than or equal toinfinitybecausethereforemaps intox plus ybracket a plus b bracket closeda equals b, a is equal to b, a is ba is not equal to b, a is not ba plus or minus ba is approximately equal to ba is greater than ba is much [far] greater than ba is greater than or equal to ba is less than ba is much less than ba is less than or equal to ba is perpendicular to bx approaches infinitya is identically equal to b, a is of identity to bangle aa ～ba ∠ba ∝ bx 2x 3x3x %2%‰5‰㏒n x㏒10x㏒e x,㏑xe x ,exp(x)x nx1/n or n xsincostg, tanctg, cotsc, seccsc, cosecsin -1 arcsincos -1 ,arcossinhcosh∑∑=ni ix 1∏∏=ni ix 1∣x ∣xb ’b ’’ the difference between a and b a is parallel to b a varies directly as b x square; x squared; the square of x~, the second power of x, x to second power x cube; x cubed; the cube of x; the third power of x, x to the third power the square root of x the cube root of x percent two percent per mill five per mill log x to the base n log x to the base 10; common logarithm log x to the base e , natural logarithm, Napierian logarithm exponential function of x; e to the power x the nth power of x; x to the power n the nth root of x, x to the power one over n sine cosine tangent cotangent secont cosecant arc sine arc cosine the hyperbolic sine the hyperbolic cosine the summation of the summation of x sub i ,where i goes from 1 to n the product of the product of x sub i , where i goes from 1to n the absolute value of x the mean value of x, x bar b primeb double prime; b second primeb ’’’ f(x) △ x, δx dx dx dy 22dx y d n n dx y d u y ∂∂ ⎰ ⎰⎰ ⎰…⎰ ⎰b aF a 22007’13’’00C1000C320Fb triple primefunction f of xfinite difference or incrementthe increment of xdee x; dee of x; differential xthe differential coefficient of y with respect to x, the first derivative of y with respect of xthe second derivative of y with respect of xthe nth derivative of y with respect of xThe partial derivative of y with respect of u, where y is a function of u and another variable (or variables)integral ofdouble integral ofn-fold integral ofintegral between limits a and b (…from a to b)vector F a sub two twenty degreesseven minutes; seven feetthirteen seconds; thirteen inches zero degree Centigrade [Celsius]one [a] hundred degrees Centigrade thirty-two degrees Fahrenheit。

目录第一部分英汉微积分词汇Part 1 English-Chinese Calculus Vocabulary第一章函数与极限Chapter 1 function and Limit (1)第二章导数与微分Chapter 2 Derivative and Differential (2)第三章微分中值定理Chapter 3 Mean Value theorem of differentials and theApplicati on of Derivatives (3)第四章不定积分Chapter 4 Indefinite Intergrals (3)第五章定积分Chapter 5 Definite Integral (3)第六章定积分的应用Chapter 6 Application of the Definite Integrals (4)第七章空间解析几何与向量代数Chapter 7 Space Ana lytic Geomertry and Vector Algebra (4)第八章多元函数微分法及其应用Chapter 8 Differentiation of functions Several variablesand Its Application (5)第九章重积分Multiple Integrals (6)第十章曲线积分与曲面积分Chapter 10 Line(Curve ) Integrals and Sur face Integrals……………………6 第十一章无穷级数Chapter 11 Infinite Series……………………………………………………6 第十二章微分方程Chapter 12 Differential Equation (7)第二部分定理定义公式的英文表达 Part 2 English Expression for Theorem, Definition and Formula第一章函数与极限Chapter 1 Function and L imit (19)1.1 映射与函数(Mapping and Function ) (19)1.2 数列的极限(Limit of the Sequence of Number) (20)1.3 函数的极限(Limit of Function) (21)1.4 无穷小与无穷大(Infinitesimal and Inifinity) (23)1.5 极限运算法则(Operation Rule of L imit) (24)1.6 极限存在准则两个重要的极限(Rule for theExistence of Limits Two Important Limits) (25)1.7 无穷小的比较(The Comparison of infinitesimal) (26)1.8 函数的连续性与间断点(Continuity of FunctionAnd Discontinuity Points) (28)1.9 连续函数的运酸与初等函数的连续性(OperationOf Continuous Functions and Continuity ofElementary Functions) (28)1.10 闭区间上联系汗水的性质(Properties ofContinuous Functions on a Closed Interval) (30)第二章导数与数分Chapter2 Derivative and Differential (31)2.1 导数的概念(The Concept of Derivative) (31)2.2 函数的求导法则(Rules for Finding Derivatives) (33)2.3 高阶导数(Higher-order Derivatives) (34)2.4 隐函数及由参数方程所确定的函数的导数相关变化率(Derivatives of Implicit Functions and Functions Determined by Parametric Equation and Correlative Change Rate) (34)2.5 函数的微分(Differential of a Function) (35)第三章微分中值定理与导数的应用Chapter 3 Mean Value Theorem of Differentials and theApplication of Derivatives (36)3.1 微分中值定理(The Mean Value Theorem) (36)3.2 洛必达法则(L’Hopital’s Rule) (38)3.3 泰勒公式(Taylor’s Formula) (41)3.4 函数的单调性和曲线的凹凸性(Monotonicityof Functions and Concavity of Curves) (43)3.5 函数的极值与最大最小值(Extrema, Maximaand Minima of Functions) (46)3.6 函数图形的描绘(Graphing Functions) (49)3.7 曲率(Curvature) (50)3.8 方程的近似解(Solving Equation Numerically) (53)第四章不定积分Chapter 4 Indefinite Integrals (54)4.1 不定积分的概念与性质(The Concept andProperties of Indefinite Integrals) (54)4.2 换元积分法(Substitution Rule for Indefinite Integrals) (56)4.3 分部积分法(Integration by Parts) (57)4.4 有理函数的积分(Integration of Rational Functions) (58)第五章定积分Chapter 5 Definite Integrals (61)5.1 定积分的概念和性质(Concept of Definite Integraland its Properties) (61)5.2 微积分基本定理(Fundamental Theorem of Calculus) (67)5.3 定积分的换元法和分部积分法(Integration by Substitution andDefinite Integrals by Parts) (69)5.4 反常积分(Improper Integrals) (70)第六章定积分的应用Chapter 6 Applications of the Definite Integrals (75)6.1 定积分的元素法(The Element Method of Definite Integra (75)6.2 定积分在几何学上的应用(Applications of the DefiniteIntegrals to Geometry) (76)6.3 定积分在物理学上的应用(Applications of the DefiniteIntegrals to Physics) (79)第七章空间解析几何与向量代数Chapter 7 Space Analytic Geometry and Vector Algebar (80)7.1 向量及其线性运算(Vector and Its Linear Operation) (80)7.2 数量积向量积(Dot Produc t and Cross Product) (86)7.3 曲面及其方程(Surface and Its Equation) (89)7.4 空间曲线及其方程(The Curve in Three-space and Its Equation (91)7.5 平面及其方程（Plane in Space and Its Equation) (93)7.6 空间直线及其方程（Lines in and Their Equations) (95)第八章多元函数微分法及其应用Chapter 8 Differentiation of Functions of SeveralVariables and Its Application (99)8.1 多元函数的基本概念（The Basic Concepts of Functionsof Several Variables) (99)8.2 偏导数(Partial Derivative) (102)8.3 全微分(Total Differential) (103)8.4 链式法则（The Chain Rule) (104)8.5 隐函数的求导公式(Derivative Formula for Implicit Functions). (104)8.6 多元函数微分学的几何应用(Geometric Applications of Differentiationof Ffunctions of Severalvariables) (106)8.7方向导数与梯度(Directional Derivatives and Gradients) (107)8.8多元函数的极值(Extreme Value of Functions of Several Variables) (108)第九章重积分Chapter 9 Multiple Integrals (111)9.1二重积分的概念与性质(The Concept of Double Integralsand Its Properities) (111)9.2二重积分的计算法(Evaluation of double Integrals) (114)9.3三重积分(Triple Integrals) (115)9.4重积分的应用(Applications of Multiple Itegrals) (120)第十章曲线积分与曲面积分Chapte 10 Line Integrals and Surface Integrals………………………………121 10.1 对弧长的曲线积分(line Intergrals with Respect to Arc Length) ………121 10.2 对坐标的曲线积分(Line Integrals with respect toCoordinate Variables) ……………………………………………………123 10.3 格林公式及其应用(Green's Formula and Its Applications) ………………124 10.4 对面积的曲面积分(Surface Integrals with Respect to Aarea) ……………126 10.5 对坐标的曲面积分(Surface Integrals with Respect toCoordinate Variables) ………………………………………………………128 10.6 高斯公式通量与散度(Gauss's Formula Flux and Divirgence) …… 130 10.7 斯托克斯公式环流量与旋度(Stokes's Formula Circulationand Rotation) (131)第十一章无穷级数Chapter 11 Infinite Series (133)11.1 常数项级数的概念与性质(The concept and Properties ofThe Constant series) ………………………………………………………133 11.2 常数项级数的审敛法(Test for Convergence of the Constant Series) ……137 11.3 幂级数(powe r Series). ……………………………………………………143 11.4 函数展开成幂级数(Represent the Function as Power Series) ……………148 11.5 函数的幂级数展开式的应用(the Appliacation of the Power Seriesrepresentation of a Function) (148)11.6 函数项级数的一致收敛性及一致收敛级数的基本性质(The Unanimous Convergence of the Ser ies of Functions and Its properties) (149)11.7 傅立叶级数（Fourier Series）.............................................152 11.8 一般周期函数的傅立叶级数(Fourier Series of Periodic Functions) (153)第十二章微分方程Chapter 12 Differential Equation……………………………………………155 12.1 微分方程的基本概念（The Concept of DifferentialEqu ation) ……155 12.2 可分离变量的微分方程(Separable Differential Equation) ………156 12.3 齐次方程(Homogeneous Equation) ………………………………156 12.4 一次线性微分方程(Linear Differential Equation of theFirst Order) (157)12.5 全微分方程(Total Differential Equation) …………………………158 12.6 可降阶的高阶微分方程(Higher-order DifferentialEquation Turned to Lower-order DifferentialEquation) (159)12.7 高阶线性微分方程(Linear Differential Equation of Higher Order) …159 12.8 常系数齐次线性微分方程(Homogeneous LinearDifferential Equation with Constant Coefficient) (163)12.9 常系数非齐次线性微分方程(Non HomogeneousDifferential Equation with Constant Coefficient) (164)12.10 欧拉方程(Euler Equation) …………………………………………164 12.11 微分方程的幂级数解法(Power Series Solutionto Differential Equation) (164)第三部分常用数学符号的英文表达Part 3 English Expression of the Mathematical Symbol in Common Use第一部分英汉微积分词汇Part1 English-Chinese Calculus Vocabulary映射 mappingX到Y的映射 mapping of X ontoY 满射 surjection 单射 injection一一映射 one-to-one mapping 双射 bijection 算子 operator变化 transformation 函数 function逆映射 inverse mapping复合映射 composite mapping 自变量 independent variable 因变量 dependent variable 定义域 domain函数值 value of function 函数关系 function relation 值域 range自然定义域 natural domain 单值函数 single valued function 多值函数 multiple valued function 单值分支 one-valued branch 函数图形 graph of a function 绝对值函数 absolute value 符号函数 sigh function 整数部分 integral part 阶梯曲线 step curve 第一章函数与极限Chapter1 Function and Limit 集合 set元素 element 子集 subset 空集 empty set 并集 union交集 intersection 差集 difference of set 基本集 basic set补集 complement set 直积 direct product笛卡儿积 Cartesian product 开区间 open interval 闭区间 closed interval 半开区间half open interval 有限区间 finite interval区间的长度 length of an interval 无限区间 infinite interval 领域 neighborhood领域的中心 centre of a neighborhood 领域的半径 radius of a neighborhood 左领域left neighborhood 右领域 right neighborhood当且仅当 if and only if(iff) 分段函数 piecewise function 上界 upper bound 下界lower bound 有界 boundedness 无界 unbounded函数的单调性 monotonicity of a function 单调增加的 increasing 单调减少的decreasing单调函数 monotone function函数的奇偶性 parity(odevity) of a function对称 symmetry 偶函数 even function 奇函数 odd function函数的周期性 periodicity of a function 周期 period反函数 inverse function 直接函数 direct function 复合函数 composite function 中间变量 intermediate variable 函数的运算 operation of function基本初等函数 basic elementary function 初等函数 elementary function 幂函数 power function指数函数 exponential function 对数函数 logarithmic function 三角函数 trigonometric function反三角函数 inverse trigonometric function 常数函数 constant function 双曲函数hyperbolic function 双曲正弦 hyperbolic sine 双曲余弦 hyperbolic cosine 双曲正切hyperbolic tangent反双曲正弦 inverse hyperbolic sine 反双曲余弦 inverse hyperbolic cosine 反双曲正切 inverse hyperbolic tangent 极限 limit数列 sequence of number 收敛 convergence 收敛于 a converge to a 发散 divergent极限的唯一性 uniqueness of limits收敛数列的有界性 boundedness of aconvergent sequence子列 subsequence函数的极限 limits of functions函数f(x)当x趋于x0时的极限 limit of functions f(x) as x approaches x0 左极限 left limit 右极限 right limit单侧极限 one-sided limits水平渐近线 horizontal asymptote 无穷小 infinitesimal 无穷大 infinity铅直渐近线 vertical asymptote 夹逼准则 squeeze rule单调数列 monotonic sequence高阶无穷小 infinitesimal of higher order 低阶无穷小 infinitesimal of lower order 同阶无穷小 infinitesimal of the same order 等阶无穷小 equivalent infinitesimal 函数的连续性 continuity of a function 增量 increment函数f(x)在x0连续 the function f(x) is continuous at x0左连续 left continuous 右连续 right continuous区间上的连续函数 continuous function 函数f(x)在该区间上连续 function f(x) is continuous on an interval 不连续点 discontinuity point第一类间断点 discontinuity point of the first kind第二类间断点 discontinuity point of the second kind初等函数的连续性 continuity of the elementary functions定义区间 defined interval最大值 global maximum value (absolute maximum)最小值 global minimum value (absolute minimum)零点定理 the zero point theorem介值定理 intermediate value theorem 第二章导数与微分Chapter2 Derivative and Differential 速度 velocity匀速运动 uniform motion 平均速度 average velocity瞬时速度 instantaneous velocity 圆的切线 tangent line of a circle 切线 tangent line切线的斜率 slope of the tangent line 位置函数 position function 导数 derivative 可导derivable函数的变化率问题 problem of the change rate of a function导函数 derived function 左导数 left-hand derivative 右导数 right-hand derivative 单侧导数 one-sided derivativesf(x)在闭区间【a,b】上可导 f(x)isderivable on the closed interval [a,b] 切线方程 tangent equation 角速度 angular velocity 成本函数 cost function 边际成本 marginal cost 链式法则 chain rule隐函数 implicit function 显函数 explicit function 二阶函数 second derivative 三阶导数 third derivative 高阶导数 nth derivative莱布尼茨公式 Leibniz formula 对数求导法 log- derivative 参数方程 parametric equation 相关变化率 correlative change rata 微分 differential 可微的 differentiable 函数的微分 differential of function自变量的微分 differential of independent variable微商 differential quotient间接测量误差 indirect measurement error 绝对误差 absolute error相对误差 relative error第三章微分中值定理与导数的应用Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives 罗马定理Rolle’s theorem 费马引理Fermat’s lemma拉格朗日中值定理Lagrange’s mean value theorem驻点 stationary point 稳定点 stable point 临界点 critical point辅助函数 auxiliary function拉格朗日中值公式Lagrange’s mean value formula柯西中值定理Cauchy’s mean value theorem洛必达法则L’Hospital’s Rule0/0型不定式 indeterminate form of type 0/0不定式 indeterminate form泰勒中值定理Taylor’s mean value theorem泰勒公式 Taylor formula 余项 remainder term拉格朗日余项 Lagrange remainder term 麦克劳林公式Maclaurin’s formula 佩亚诺公式 Peano remainder term 凹凸性 concavity凹向上的 concave upward, cancave up 凹向下的，向上凸的concave downward’ concave down拐点 inflection point函数的极值 extremum of function 极大值 local(relative) maximum 最大值global(absolute) mximum 极小值 local(relative) minimum 最小值 global(absolute) minimum 目标函数 objective function 曲率 curvature弧微分 arc differential平均曲率 average curvature 曲率园 circle of curvature 曲率中心 center of curvature 曲率半径 radius of curvature渐屈线 evolute 渐伸线 involute根的隔离 isolation of root 隔离区间 isolation interval 切线法 tangent line method第四章不定积分Chapter4 Indefinite Integrals原函数 primitive function(antiderivative) 积分号 sign of integration 被积函数integrand积分变量 integral variable 积分曲线 integral curve 积分表 table of integrals换元积分法 integration by substitution 分部积分法 integration by parts分部积分公式 formula of integration by parts有理函数 rational function 真分式 proper fraction 假分式 improper fraction第五章定积分Chapter5 Definite Integrals 曲边梯形 trapezoid with 曲边 curve edge窄矩形 narrow rectangle曲边梯形的面积 area of trapezoid with curved edge积分下限 lower limit of integral 积分上限 upper limit of integral 积分区间 integral interval 分割 partition积分和 integral sum 可积 integrable矩形法 rectangle method积分中值定理 mean value theorem of integrals函数在区间上的平均值 average value of a function on an integvals牛顿－莱布尼茨公式 Newton-Leibniz formula微积分基本公式 fundamental formula of calculus换元公式 formula for integration by substitution递推公式 recurrence formula 反常积分 improper integral反常积分发散 the improper integral is divergent反常积分收敛 the improper integral is convergent无穷限的反常积分 improper integral on an infinite interval无界函数的反常积分 improper integral of unbounded functions绝对收敛 absolutely convergent第六章定积分的应用Chapter6 Applications of the Definite Integrals元素法 the element method 面积元素 element of area平面图形的面积 area of a luane figure 直角坐标又称“笛卡儿坐标 (Cartesian coordinates)”极坐标 polar coordinates 抛物线 parabola 椭圆 ellipse旋转体的面积 volume of a solid of rotation旋转椭球体 ellipsoid of revolution, ellipsoid of rotation曲线的弧长 arc length of acurve 可求长的 rectifiable 光滑 smooth 功 work水压力 water pressure 引力 gravitation 变力 variable force第七章空间解析几何与向量代数Chapter7 Space Analytic Geometry and Vector Algebra向量 vector自由向量 free vector 单位向量 unit vector 零向量 zero vector 相等 equal 平行parallel向量的线性运算 linear poeration of vector 三角法则 triangle rule平行四边形法则 parallelogram rule 交换律 commutative law 结合律 associative law 负向量 negative vector 差 difference分配律 distributive law空间直角坐标系 space rectangular coordinates坐标面 coordinate plane 卦限 octant向量的模 modulus of vector向量a与b的夹角 angle between vector a and b方向余弦 direction cosine 方向角 direction angle向量在轴上的投影 projection of a vector onto an axis数量积，外积，叉积 scalar product,dot product,inner product曲面方程 equation for a surface 球面 sphere旋转曲面 surface of revolution 母线 generating line 轴 axis圆锥面 cone 顶点 vertex旋转单叶双曲面 revolution hyperboloids of one sheet旋转双叶双曲面 revolution hyperboloids of two sheets柱面 cylindrical surface ,cylinder 圆柱面 cylindrical surface 准线 directrix抛物柱面 parabolic cylinder 二次曲面 quadric surface 椭圆锥面 dlliptic cone 椭球面ellipsoid单叶双曲面 hyperboloid of one sheet 双叶双曲面 hyperboloid of two sheets 旋转椭球面 ellipsoid of revolution 椭圆抛物面 elliptic paraboloid旋转抛物面 paraboloid of revolution 双曲抛物面 hyperbolic paraboloid 马鞍面 saddle surface椭圆柱面 elliptic cylinder 双曲柱面 hyperbolic cylinder 抛物柱面 parabolic cylinder 空间曲线 space curve空间曲线的一般方程 general form equations of a space curve空间曲线的参数方程 parametric equations of a space curve 螺转线 spiral 螺矩 pitch 投影柱面 projecting cylinder 投影 projection平面的点法式方程 pointnorm form eqyation of a plane法向量 normal vector平面的一般方程 general form equation of a plane两平面的夹角 angle between two planes 点到平面的距离 distance from a point to a plane空间直线的一般方程 general equation of a line in space方向向量 direction vector直线的点向式方程 pointdirection form equations of a line方向数 direction number直线的参数方程 parametric equations of a line两直线的夹角 angle between two lines 垂直 perpendicular直线与平面的夹角 angle between a line and a planes平面束 pencil of planes平面束的方程 equation of a pencil of planes行列式 determinant系数行列式 coefficient determinant第八章多元函数微分法及其应用Chapter8 Differentiation of Functions of Several Variables and Its Application 一元函数 function of one variable 多元函数 function of several variables 内点 interior point 外点 exterior point 边界点 frontier point,boundary point 聚点 point of accumulation 开集 openset 闭集 closed set 连通集 connected set 开区域 open region 闭区域 closed region有界集 bounded set 无界集 unbounded setn维空间 n-dimentional space 二重极限 double limit 多元函数的连续性 continuity of function of seveal 连续函数 continuous function 不连续点 discontinuity point 一致连续 uniformly continuous 偏导数 partial derivative 对自变量x的偏导数 partial derivative with respect to independent variable x 高阶偏导数 partial derivative of higher order 二阶偏导数 second order partial derivative 混合偏导数 hybrid partial derivative 全微分 total differential 偏增量 oartial increment 偏微分 partial differential 全增量 total increment 可微分 differentiable 必要条件 necessary condition充分条件 sufficient condition 叠加原理 superpostition principle 全导数 total derivative中间变量 intermediate variable 隐函数存在定理 theorem of the existence of implicit function 曲线的切向量 tangent vector of a curve 法平面 normal plane 向量方程vector equation 向量值函数 vector-valued function 切平面 tangent plane 法线 normal line 方向导数 directional derivative梯度 gradient数量场 scalar field 梯度场 gradient field 向量场 vector field 势场 potential field 引力场 gravitational field 引力势 gravitational potential 曲面在一点的切平面 tangent plane to asurface at a point 曲线在一点的法线 normal line to asurface at a point 无条件极值 unconditional extreme values 条件极值 conditional extreme values 拉格朗日乘数法 Lagrange multiplier method 拉格朗日乘子 Lagrange multiplier 经验公式 empirical formula 最小二乘法 method of least squares 均方误差mean square error 第九章重积分 Chapter9 Multiple Integrals 二重积分 double integral 可加性 additivity累次积分 iterated integral 体积元素 volume element 三重积分 triple integral 直角坐标系中的体积元素 volumeelement in rectangular coordinate system 柱面坐标 cylindrical coordinates 柱面坐标系中的体积元素 volumeelement in cylindrical coordinate system 球面坐标 spherical coordinates 球面坐标系中的体积元素 volumeelement in spherical coordinate system 反常二重积分 improper double integral 曲面的面积 area of a surface 质心 centre of mass 静矩 static moment 密度 density 形心centroid 转动惯量 moment of inertia 参变量 parametric variable 第十章曲线积分与曲面积分Chapter10 Line(Curve)Integrals and Surface Integrals对弧长的曲线积分 line integrals with respect to arc hength第一类曲线积分 line integrals of the first type对坐标的曲线积分 line integrals with respect to x,y,and z第二类曲线积分 line integrals of the second type有向曲线弧 directed arc单连通区域 simple connected region 复连通区域 complex connected region 格林公式Green formula第一类曲面积分 surface integrals of the first type对面的曲面积分 surface integrals with respect to area有向曲面 directed surface对坐标的曲面积分 surface integrals with respect to coordinate elements第二类曲面积分 surface integrals of the second type有向曲面元 element of directed surface 高斯公式 gauss formula拉普拉斯算子 Laplace operator 格林第一公式Green’s first formula 通量 flux散度 divergence斯托克斯公式 Stokes formula 环流量 circulation 旋度 rotation,curl第十一章无穷级数Chapter11 Infinite Series 一般项 general term 部分和 partial sum 余项 remainder term 等比级数 geometric series 几何级数 geometric series 公比 common ratio调和级数 harmonic series柯西收敛准则 Cauchy convergence criteria, Cauchy criteria for convergence 正项级数series of positive terms 达朗贝尔判别法D’Alembert test 柯西判别法 Cauchy test交错级数 alternating series 绝对收敛 absolutely convergent 条件收敛 conditionally convergent 柯西乘积 Cauchy product 函数项级数 series of functions 发散点 point of divergence 收敛点 point of convergence 收敛域 convergence domain 和函数 sum function 幂级数 power series幂级数的系数 coeffcients of power series 阿贝尔定理 Abel Theorem收敛半径 radius of convergence 收敛区间 interval of convergence 泰勒级数 Taylor series麦克劳林级数 Maclaurin series 二项展开式 binomial expansion 近似计算approximate calculation舍入误差 round-off error,rounding error 欧拉公式Euler’s formula魏尔斯特拉丝判别法 Weierstrass test 三角级数 trigonometric series 振幅 amplitude 角频率 angular frequency 初相 initial phase 矩形波 square wave谐波分析 harmonic analysis 直流分量 direct component 基波 fundamental wave 二次谐波 second harmonic三角函数系 trigonometric function system 傅立叶系数 Fourier coefficient 傅立叶级数 Forrier series 周期延拓 periodic prolongation 正弦级数 sine series 余弦级数cosine series 奇延拓 odd prolongation 偶延拓 even prolongation傅立叶级数的复数形式 complex form of Fourier series第十二章微分方程Chapter12 Differential Equation解微分方程 solve a dirrerential equation 常微分方程 ordinary differential equation偏微分方程 partial differential equation,PDE微分方程的阶 order of a differential equation微分方程的解 solution of a differential equation微分方程的通解 general solution of a differential equation初始条件 initial condition微分方程的特解 particular solution of a differential equation初值问题 initial value problem微分方程的积分曲线 integral curve of a differential equation可分离变量的微分方程 variable separable differential equation隐式解 implicit solution隐式通解 inplicit general solution 衰变系数 decay coefficient 衰变 decay齐次方程 homogeneous equation一阶线性方程 linear differential equation of first order非齐次 non-homogeneous齐次线性方程 homogeneous linear equation非齐次线性方程 non-homogeneous linear equation常数变易法 method of variation of constant暂态电流 transient stata current 稳态电流 steady state current 伯努利方程 Bernoulli equation全微分方程 total differential equation 积分因子 integrating factor高阶微分方程 differential equation of higher order悬链线 catenary高阶线性微分方程 linera differentialequation of higher order自由振动的微分方程 differential equation of free vibration强迫振动的微分方程 differential equation of forced oscillation串联电路的振荡方程 oscillation equation of series circuit二阶线性微分方程 second order linera differential equation线性相关 linearly dependence 线性无关 linearly independce二阶常系数齐次线性微分方程 second order homogeneour linear differential equation with constant coefficient二阶变系数齐次线性微分方程 second order homogeneous linear differential equation with variable coefficient 特征方程 characteristic equation无阻尼自由振动的微分方程 differential equation of free vibration with zero damping 固有频率 natural frequency简谐振动 simple harmonic oscillation,simple harmonic vibration微分算子 differential operator待定系数法 method of undetermined coefficient共振现象 resonance phenomenon 欧拉方程 Euler equation幂级数解法 power series solution 数值解法 numerial solution 勒让德方程 Legendre equation微分方程组 system of differential equations常系数线性微分方程组 system of linera differential equations with constant coefficient第二部分定理定义公式的英文表达Part2 English Expression for Theorem, Definition and Formula第一章函数与极限Chapter 1 Function and Limit1.1 映射与函数 (Mapping and Function)一、集合 (Set)二、映射 (Mapping)映射概念 (The Concept of Mapping) 设X, Y是两个非空集合 , 如果存在一个法则f，使得对X中每个元素x，按法则f，在Y中有唯一确定的元素y与之对应 ,则称f为从X到 Y的映射 , 记作f:X→Y。

数值分析中常用数学词汇英中文对照abbreviation 简写符号;简写absolute error 绝对误差absolute value 绝对值accelerate 加速accumulation 累积accuracy 准确度act on 施于action 作用; 作用力add 加addition 加法addition formula 加法公式addition law 加法定律additive property 可加性adjoint matrix 伴随矩阵algebra 代数algebraic 代数的algebraic equation 代数方程algebraic expression 代数式algebraic fraction 代数分式;代数分数式algebraic inequality 代数不等式algebraic number 代数数algebraic operation 代数运算algorithm 算法系统; 规则系统alternating series 交错级数alternative hypothesis 择一假设; 备择假设; 另一假设analysis 分析;解析angle 角anti-clockwise direction 逆时针方向;返时针方向anti-derivative 反导数; 反微商anti-logarithm 逆对数;反对数anti-symmetric 反对称approach 接近;趋近approximate value 近似值approximation 近似;略计;逼近Arabic system 阿刺伯数字系统arbitrary 任意arbitrary constant 任意常数arc 弧arc-cosine function 反余弦函数arc-sin function 反正弦函数arc-tangent function 反正切函数area 面积argument (1论证; (2辐角argument of a function 函数的自变量arithmetic 算术array 数组; 数组ascending order 递升序ascending powers of X X 的升幂assumption 假定;假设asymmetrical 非对称asymptote 渐近augmented matrix 增广矩阵average 平均;平均数;平均值axiom 公理back substitution 回代base (1底;(2基;基数basis 基belong to 属于bias 偏差;偏倚billion 十亿binary number 二进数binary operation 二元运算binary system 二进制binomial 二项式bisection method 分半法;分半方法boundary condition 边界条件boundary line 界(线;边界bounded 有界的bounded above 有上界的;上有界的bounded below 有下界的;下有界的bounded function 有界函数bounded sequence 有界序列brace 大括号bracket 括号breadth 阔度calculation 计算calculator 计算器;计算器calculus (1 微积分学; (2 演算cancel 消法;相消Cartesian coordinates 笛卡儿坐标category 类型;范畴centre 中心;心chain rule 链式法则chance 机会change of base 基的变换change of variable 换元;变量的换characteristic equation 特征(征方程characteristic function 特征(征函数characteristic root 特征(征根chart 图;图表check digit 检验数位checking 验算circle 圆classification 分类clockwise direction 顺时针方向clockwise moment 顺时针力矩closed convex region 闭凸区域closed interval 闭区间coefficient 系数cofactor 余因子; 余因式coincide 迭合;重合collection of terms 并项collinear 共线collinear planes 共线面column (1列;纵行;(2 柱column matrix 列矩阵column vector 列向量combination 组合common denominator 同分母;公分母common difference 公差common divisor 公约数;公约common factor 公因子;公因子common multiple 公位数;公倍comparable 可比较的complement 余;补余completing the square 配方complex number 复数complex number plane 复数平面complex root 复数根component 分量composite function 复合函数; 合成函数computation 计算computer 计算机;电子计算器concept 概念conclusion 结论condition 条件conditional 条件句;条件式conjugate 共轭constant 常数constant of integration 积分常数constraint 约束;约束条件continuity 连续性continuous function 连续函数contradiction 矛盾converge 收敛convergence 收敛性convergent 收敛的convergent iteration 收敛的迭代convergent sequence 收敛序列convergent series 收敛级数convex 凸convexity 凸性coordinate 坐标corollary 系定理; 系; 推论correspondence 对应counter clockwise direction 逆时针方向;返时针方向counter example 反例counting 数数;计数criterion 准则critical point 临界点critical region 临界域cirtical value 临界值cube 正方体;立方;立方体cubic 三次方;立方;三次(的 cubic equation 三次方程cubic roots of unity 单位的立方根cumulative 累积的curve 曲线decimal 小数decimal place 小数位decimal point 小数点decimal system 十进制definite integral 定积分definition 定义degree (1 度; (2 次degree of a polynomial 多项式的次数degree of accuracy 准确度degree of ODE 常微分方程次数delete 删除; 删去denary number 十进数denominator 分母dependence (1相关; (2应变derivable 可导derivative 导数determinant 行列式diagonal 对角线diagonal matrix 对角矩阵difference 差difference equation 差分方程differentiable 可微differential 微分differential coefficient 微商; 微分系数differential equation 微分方程differential mean value theorem 微分中值定理differentiate 求...的导数differentiation 微分法digit 数字dimension 量; 量网; 维(数direction 方向; 方位discontinuity 不连续性discontinuous 间断(的;连续(的; 不连续(的discontinuous point 不连续点discrete 分立; 离散distance 距离diverge 发散divergence 发散(性divergent 发散的divergent iteration 发散性迭代divergent sequence 发散序列divide 除dividend (1被除数;divisible 可整除division 除法division algorithm 除法算式divisor 除数;除式;因子dot 点dot product 点积echelon form 梯阵式echelon matrix 梯矩阵eigenvalue 本征值eigenvector 本征向量element 元素elementary row operation 基本行运算elimination 消法elimination method 消去法;消元法empty set 空集equivalent 等价(的error 误差error estimate 误差估计error term 误差项estimate 估计;估计量evaluate 计值exact 真确exact solution 准确解;精确解;真确解exact value 法确解;精确解;真确解example 例expand 展开experiment 实验;试验experimental 试验的exponent 指数exponential function 指数函数express…in terms of… 以………表达extreme point 极值点extreme value 极值extremum 极值factor 因子;因式;商factor method 因式分解法factorial 阶乘factorization 因子分解;因式分解fallacy 谬误FALSE 假(的falsehood 假值finite 有限finite sequence 有限序列first derivative 一阶导数first order differential equation 一阶微分方程fixed point 不动点fixed point iteration method 不动点迭代法for all X 对所有X for each /every X 对每一Xform 形式;型format 格式;规格formula(formulae 公式fraction 分数;分式function 函数fundamental theorem of calculus 微积分基本定理Gaussian elimination 高斯消去法general form 一般式;通式general solution 通解;一般解general term 通项given 给定;已知global 全局; 整体global maximum 全局极大值; 整体极大值global minimum 全局极小值; 整体极小值gradient (1斜率;倾斜率;(2梯度graph 图像;图形;图表graphical method 图解法graphical representation 图示;以图样表达graphical solution 图解growth 增长higher order derivative 高阶导数horizontal 水平的;水平hypothesis 假设identity 等(式identity matrix 恒等矩阵if and only if/iff 当且仅当;若且仅若if…, then 若….则;如果…..则illustration 例证;说明image 像点;像imaginary number 虚数implicit function 隐函数imply 蕴涵;蕴含improper integral 广义积分; 非正常积分increase 递增;增加indefinite integral 不定积分independence 独立;自变inequality 不等式;不等inequality sign 不等号infinite 无限;无穷infinite sequence 无限序列;无穷序列infinite series 无限级数;无穷级数infinitesimal 无限小;无穷小infinity 无限(大;无穷(大initial approximation 初始近似值initial condition 原始条件;初值条件initial value 初值;始值initial-value problem 初值问题inner product 内积input 输入integer 整数integral 积分integrate 积;积分;......的积分integration 积分法integration by parts 分部积分法integration by substitution 代换积分法;换元积分法interchange 互换intermediate value theorem 介值定理interpolating polynomial 插值多项式interpolation 插值interval 区间intuition 直观invalid 失效;无效invariance 不变性invariant (1不变的;(2不变量;不变式inverse 反的;逆的inverse function 反函数;逆函数inverse matrix 逆矩阵inverse problem 逆算问题invertible 可逆的invertible matrix 可逆矩阵iterate (1迭代值; (2迭代iteration 迭代iterative method 迭代法known 己知Lagrange interpolating polynomial 拉格朗日插值多项代leading coefficient 首项系数leading diagonal 主对角线lemma 引理limit 极限limit of sequence 序列的极限line of best-fit 最佳拟合line segment 线段linear 线性;一次linear convergence 线性收敛性linear differeantial equation 线性微分方程linear equation 线性方程;一次方程linear equation in two unknowns 二元一次方程;二元线性方程linearly dependent 线性相关的linearly independent 线性无关的local maximum 局部极大(值local minimum 局部极小(值logic 逻辑long division method 长除法loop 回路lower bound 下界lower triangular matrix 下三角形矩阵Maclaurin expansion 麦克劳林展开式magnitude 量;数量;长度;大小mantissa 尾数matrix 阵; 矩阵matrix addition 矩阵加法matrix equation 矩阵方程matrix multiplication 矩阵乘法matrix operation 矩阵运算maximize 极大maximum absolute error 最大绝对误差mean value theorem 中值定理method of completing square 配方法method of interpolation 插值法; 内插法method of least squares 最小二乘法; 最小平方法method of substitution 代换法;换元法method of successive substitution 逐次代换法; 逐次调替法minimize 极小minus 减modulus of a complex number 复数的模monomial 单项式multiple 倍数multiple root 多重根multiplication 乘法multiplicity 重数multiplier 乘数;乘式multiply 乘mutually independent 独立; 互相独立mutually perpendicular lines 互相垂直n factorial n阶乘n th derivative n阶导数n th root n次根;n次方根n the root of unity 单位的n次根natural logarithm 自然对数necessary and sufficient condition 充要条件necessary condition 必要条件negative 负neighborhood 邻域Newton-Cote's rule 牛顿- 高斯法则Newton-Raphson's method 牛顿- 纳逊方法Newton's formula 牛顿公式Newton's method 牛顿方法non-linear 非线性non-linear equation 非线性方程non-negative 非负的non-singular (1满秩的; (2非奇异的non-singular matrix 满秩矩阵non-trivial 非平凡的non-zero 非零norm 模方; 范数normal (1垂直的;正交的;法线的(2正态的(3正常的;正规的normalize 正规化normalized form 标准型notation 记法;记号null 零; 空null set 空集null vector 零向量number 数numerator 分子numerical method 计算方法;数值法objective function 目标函数octant 卦限odd function 奇函数one-to-one 一个对一个one-one correspondence 一一对应operation 运算order of a matrix 矩阵的阶ordinary differential equation 常微分方程origin 原点orthogonal 正交orthogonality 正交性 outcome 结果 output 输出 parameter 参数；参变量parametric equation 参数方程 partition 分割; 划分 periodic function 周期函数permutation 排列 perpendicular 垂线；垂直(于 phase 相; 位相 pivot 支点 plot 绘图plus 加 point 点 polynomial 多项式 polynomial equation 多项式方程 positive 正 post-multiply 后乘; 自右乘 premultiply 前乘; 自左乘 prime 素 product 乘积；积 proper integral 正常积分 property 性质 quadratic convergence 二阶收敛性 quadratic formula 二次公式 quadratic function 二次函数 quadratic inequality 二次不等式 quadrature 求积法 quadrilateral 四边形 quotient 商；商式 quotient rule 商法则 R.H.S 右 rank 秩 rate of convergence 收敛率 ratio 比 ; 比率 rational function 有理函数 real number 实数 real part 实部 real root 实根 reciprocal 倒数 rectangle 长方形；矩形 recurrence formula 递推公式 recurrent 循环的 recurring decimal 循环小数 reduce 简化 region 区域 region of convergency 收敛区域 regular 正；规则 relative error 相对误差 remainder term 余项root 根 rotation 旋转 rounded number 舍数 rounding(off 舍入；四舍五入 row 行；棋行 row vector 行向量; 行矢量 rule 规则；法(则 satisfy 满足；适合 scalar 纯量; 无向量, 标量 scalar matrix 纯量矩阵 scale 比例尺；标度；图尺 scientific notation 科学记数法 secant (1正割; (2割线 secant method 正割法 second derivative 二阶导数 second order ordinary differential equation 二阶常微分方程 sentence 句；语句 sequence 序列series 级数 set 集 shaded portion 有阴影部分 shape 形状 shear 位移 side 边；侧 sign 符号；记号 signed number 有符号数 significant figure 有效数字 signum 正负号函数similar 相似 simplify 简化 Simpson's integral 森逊积分 Simpson's rule 森逊法则singular 奇的 singular matrix 奇异矩阵; 不可逆矩阵 span 生成 square (1平方；(2正方形 square bracket 方括号square matrix 方(矩阵 stability 稳度 stationary 平稳 stationary point 平稳点; 逗留点; 驻点 straight line 直线 subset 子集 substitute 代入 substitution 代入; 代入法subtract 减 subtraction 减法 successive approximation 逐次逼近法 successive derivative 逐次导数 successive differentiation 逐次微分法 sufficiency 充份性 sufficient and necessary condition 充要条件 sufficient condition 充份条件 sufficiently close 充份接近suffix 下标 sum 和 summation 求和法; 总和 symbol 符号; 记号 symmetry 对称; 对称性Taylor’s expansion 泰勒展开式 term 项 transpose 移项；转置 transpose of matrix 倒置矩阵；转置矩阵 trapezium 梯形 trapezoidal integral 梯形积分 trapezoidal rule 梯形法则 trial 试；试验 triangle 三角形 triangular matrix 三角矩阵 trigonometric equation 三角方程 trigonometric function 三角函数 triple 三倍 trivial solution 平凡解truncation error 截断误差 undefined 未下定义(的 undetermined coefficient 待定系数unequal 不等 unique solution 唯一解 uniqueness 唯一性 unit 单位 unit area 单位面积unit circle 单位圆 unknown 未知数；未知量 upper bound 上界 upper limit 上限 upper triangular matrix 上三角形矩阵 validity 真确性; 有效性 variable 变项；变量；元；变元；变数 vector 向量; 矢量 vector function 向量函数; 矢量函数 vector product 矢量积; 矢量积 vector space 向量空间 verify 证明；验证 weight (1重量；(2权 weighted average, weighted mean 加权平均数 without loss of generality 不失一般性 x-axis x 轴x-coordinate x 坐标 x-intercept x 轴截距 y-axis y 轴 y-coordinate y 坐标 y-intercept y轴截距 zero 零 zero factor 零因子 zero matrix 零矩阵 zero vector 零向量 zeros of a function 函数零值。

数学专业英语词汇摘要数学是一门广泛的学科，涉及到各种概念、理论和方法。

为了有效地学习和交流数学，我们需要掌握一些基本的数学专业英语词汇。

本文根据不同的数学分支，列出了一些常见的数学术语及其中英文对照，包括算术、代数、几何、三角学、微积分、概率论和统计学等。

本文旨在帮助数学专业的考研复试者和其他对数学感兴趣的人士提高英语水平，增强数学素养。

算术（Arithmetic）算术是数学的基础，主要研究数字和基本运算。

以下是一些常用的算术术语及其中英文对照：中文英文数字number整数integer自然数natural number偶数even number奇数odd number质数prime number合数composite number分数fraction小数decimal有理数rational number无理数irrational number实数real number复数complex number运算operation加法addition减法subtraction乘法multiplication除法division指数exponentiation对数logarithm四则运算arithmetic operations平方根square root立方根cube root四次根fourth rootn次根nth root代数（Algebra）代数是研究符号和规则的一门数学分支，主要用于解决方程和不等式。

以下是一些常用的代数术语及其中英文对照：中文英文符号symbol变量variable常量constant系数coefficient项term表达式expression方程equation不等式inequality解solution根root一元方程equation in one variable二元方程equation in two variables多元方程equation in more than two variables一次方程linear equation二次方程quadratic equation高次方程higher degree equation方程组system of equations代数式algebraic expression多项式polynomial单项式monomial二项式binomial几何（Geometry）几何是研究形状、大小和位置的一门数学分支，主要用于描述空间中的对象。

目录第一部分英汉微积分词汇Part 1 English-Chinese Calculus Vocabulary第一章函数与极限Chapter 1 function and Limit (1)第二章导数与微分Chapter 2 Derivative and Differential (2)第三章微分中值定理Chapter 3 Mean Value theorem of differentials and theApplicati on of Derivatives (3)第四章不定积分Chapter 4 Indefinite Intergrals (3)第五章定积分Chapter 5 Definite Integral (3)第六章定积分的应用Chapter 6 Application of the Definite Integrals (4)第七章空间解析几何与向量代数Chapter 7 Space Ana lytic Geomertry and Vector Algebra (4)第八章多元函数微分法及其应用Chapter 8 Differentiation of functions Several variablesand Its Application (5)第九章重积分Multiple Integrals (6)第十章曲线积分与曲面积分Chapter 10 Line(Curve ) Integrals and Sur face Integrals……………………6 第十一章无穷级数Chapter 11 Infinite Series……………………………………………………6 第十二章微分方程Chapter 12 Differential Equation (7)第二部分定理定义公式的英文表达 Part 2 English Expression for Theorem, Definition and Formula第一章函数与极限Chapter 1 Function and L imit (19)1.1 映射与函数(Mapping and Function ) (19)1.2 数列的极限(Limit of the Sequence of Number) (20)1.3 函数的极限(Limit of Function) (21)1.4 无穷小与无穷大(Infinitesimal and Inifinity) (23)1.5 极限运算法则(Operation Rule of L imit) (24)1.6 极限存在准则两个重要的极限(Rule for theExistence of Limits Two Important Limits) (25)1.7 无穷小的比较(The Comparison of infinitesimal) (26)1.8 函数的连续性与间断点(Continuity of FunctionAnd Discontinuity Points) (28)1.9 连续函数的运酸与初等函数的连续性(OperationOf Continuous Functions and Continuity ofElementary Functions) (28)1.10 闭区间上联系汗水的性质(Properties ofContinuous Functions on a Closed Interval) (30)第二章导数与数分Chapter2 Derivative and Differential (31)2.1 导数的概念(The Concept of Derivative) (31)2.2 函数的求导法则(Rules for Finding Derivatives) (33)2.3 高阶导数(Higher-order Derivatives) (34)2.4 隐函数及由参数方程所确定的函数的导数相关变化率(Derivatives of Implicit Functions and Functions Determined by Parametric Equation and Correlative Change Rate) (34)2.5 函数的微分(Differential of a Function) (35)第三章微分中值定理与导数的应用Chapter 3 Mean Value Theorem of Differentials and theApplication of Derivatives (36)3.1 微分中值定理(The Mean Value Theorem) (36)3.2 洛必达法则(L’Hopital’s Rule) (38)3.3 泰勒公式(Taylor’s Formula) (41)3.4 函数的单调性和曲线的凹凸性(Monotonicityof Functions and Concavity of Curves) (43)3.5 函数的极值与最大最小值(Extrema, Maximaand Minima of Functions) (46)3.6 函数图形的描绘(Graphing Functions) (49)3.7 曲率(Curvature) (50)3.8 方程的近似解(Solving Equation Numerically) (53)第四章不定积分Chapter 4 Indefinite Integrals (54)4.1 不定积分的概念与性质(The Concept andProperties of Indefinite Integrals) (54)4.2 换元积分法(Substitution Rule for Indefinite Integrals) (56)4.3 分部积分法(Integration by Parts) (57)4.4 有理函数的积分(Integration of Rational Functions) (58)第五章定积分Chapter 5 Definite Integrals (61)5.1 定积分的概念和性质(Concept of Definite Integraland its Properties) (61)5.2 微积分基本定理(Fundamental Theorem of Calculus) (67)5.3 定积分的换元法和分部积分法(Integration by Substitution andDefinite Integrals by Parts) (69)5.4 反常积分(Improper Integrals) (70)第六章定积分的应用Chapter 6 Applications of the Definite Integrals (75)6.1 定积分的元素法(The Element Method of Definite Integra (75)6.2 定积分在几何学上的应用(Applications of the DefiniteIntegrals to Geometry) (76)6.3 定积分在物理学上的应用(Applications of the DefiniteIntegrals to Physics) (79)第七章空间解析几何与向量代数Chapter 7 Space Analytic Geometry and Vector Algebar (80)7.1 向量及其线性运算(Vector and Its Linear Operation) (80)7.2 数量积向量积(Dot Produc t and Cross Product) (86)7.3 曲面及其方程(Surface and Its Equation) (89)7.4 空间曲线及其方程(The Curve in Three-space and Its Equation (91)7.5 平面及其方程（Plane in Space and Its Equation) (93)7.6 空间直线及其方程（Lines in and Their Equations) (95)第八章多元函数微分法及其应用Chapter 8 Differentiation of Functions of SeveralVariables and Its Application (99)8.1 多元函数的基本概念（The Basic Concepts of Functionsof Several Variables) (99)8.2 偏导数(Partial Derivative) (102)8.3 全微分(Total Differential) (103)8.4 链式法则（The Chain Rule) (104)8.5 隐函数的求导公式(Derivative Formula for Implicit Functions). (104)8.6 多元函数微分学的几何应用(Geometric Applications of Differentiationof Ffunctions of Severalvariables) (106)8.7方向导数与梯度(Directional Derivatives and Gradients) (107)8.8多元函数的极值(Extreme Value of Functions of Several Variables) (108)第九章重积分Chapter 9 Multiple Integrals (111)9.1二重积分的概念与性质(The Concept of Double Integralsand Its Properities) (111)9.2二重积分的计算法(Evaluation of double Integrals) (114)9.3三重积分(Triple Integrals) (115)9.4重积分的应用(Applications of Multiple Itegrals) (120)第十章曲线积分与曲面积分Chapte 10 Line Integrals and Surface Integrals………………………………121 10.1 对弧长的曲线积分(line Intergrals with Respect to Arc Length) ………121 10.2 对坐标的曲线积分(Line Integrals with respect toCoordinate Variables) ……………………………………………………123 10.3 格林公式及其应用(Green's Formula and Its Applications) ………………124 10.4 对面积的曲面积分(Surface Integrals with Respect to Aarea) ……………126 10.5 对坐标的曲面积分(Surface Integrals with Respect toCoordinate Variables) ………………………………………………………128 10.6 高斯公式通量与散度(Gauss's Formula Flux and Divirgence) …… 130 10.7 斯托克斯公式环流量与旋度(Stokes's Formula Circulationand Rotation) (131)第十一章无穷级数Chapter 11 Infinite Series (133)11.1 常数项级数的概念与性质(The concept and Properties ofThe Constant series) ………………………………………………………133 11.2 常数项级数的审敛法(Test for Convergence of the Constant Series) ……137 11.3 幂级数(powe r Series). ……………………………………………………143 11.4 函数展开成幂级数(Represent the Function as Power Series) ……………148 11.5 函数的幂级数展开式的应用(the Appliacation of the Power Seriesrepresentation of a Function) (148)11.6 函数项级数的一致收敛性及一致收敛级数的基本性质(The Unanimous Convergence of the Ser ies of Functions and Its properties) (149)11.7 傅立叶级数（Fourier Series）.............................................152 11.8 一般周期函数的傅立叶级数(Fourier Series of Periodic Functions) (153)第十二章微分方程Chapter 12 Differential Equation……………………………………………155 12.1 微分方程的基本概念（The Concept of DifferentialEqu ation) ……155 12.2 可分离变量的微分方程(Separable Differential Equation) ………156 12.3 齐次方程(Homogeneous Equation) ………………………………156 12.4 一次线性微分方程(Linear Differential Equation of theFirst Order) (157)12.5 全微分方程(Total Differential Equation) …………………………158 12.6 可降阶的高阶微分方程(Higher-order DifferentialEquation Turned to Lower-order DifferentialEquation) (159)12.7 高阶线性微分方程(Linear Differential Equation of Higher Order) …159 12.8 常系数齐次线性微分方程(Homogeneous LinearDifferential Equation with Constant Coefficient) (163)12.9 常系数非齐次线性微分方程(Non HomogeneousDifferential Equation with Constant Coefficient) (164)12.10 欧拉方程(Euler Equation) …………………………………………164 12.11 微分方程的幂级数解法(Power Series Solutionto Differential Equation) (164)第三部分常用数学符号的英文表达Part 3 English Expression of the Mathematical Symbol in Common Use第一部分英汉微积分词汇Part1 English-Chinese Calculus Vocabulary映射 mappingX到Y的映射 mapping of X ontoY 满射 surjection 单射 injection一一映射 one-to-one mapping 双射 bijection 算子 operator变化 transformation 函数 function逆映射 inverse mapping复合映射 composite mapping 自变量 independent variable 因变量 dependent variable 定义域 domain函数值 value of function 函数关系 function relation 值域 range自然定义域 natural domain 单值函数 single valued function 多值函数 multiple valued function 单值分支 one-valued branch 函数图形 graph of a function 绝对值函数 absolute value 符号函数 sigh function 整数部分 integral part 阶梯曲线 step curve 第一章函数与极限Chapter1 Function and Limit 集合 set元素 element 子集 subset 空集 empty set 并集 union交集 intersection 差集 difference of set 基本集 basic set补集 complement set 直积 direct product笛卡儿积 Cartesian product 开区间 open interval 闭区间 closed interval 半开区间half open interval 有限区间 finite interval区间的长度 length of an interval 无限区间 infinite interval 领域 neighborhood领域的中心 centre of a neighborhood 领域的半径 radius of a neighborhood 左领域left neighborhood 右领域 right neighborhood当且仅当 if and only if(iff) 分段函数 piecewise function 上界 upper bound 下界lower bound 有界 boundedness 无界 unbounded函数的单调性 monotonicity of a function 单调增加的 increasing 单调减少的decreasing单调函数 monotone function函数的奇偶性 parity(odevity) of a function对称 symmetry 偶函数 even function 奇函数 odd function函数的周期性 periodicity of a function 周期 period反函数 inverse function 直接函数 direct function 复合函数 composite function 中间变量 intermediate variable 函数的运算 operation of function基本初等函数 basic elementary function 初等函数 elementary function 幂函数 power function指数函数 exponential function 对数函数 logarithmic function 三角函数 trigonometric function反三角函数 inverse trigonometric function 常数函数 constant function 双曲函数hyperbolic function 双曲正弦 hyperbolic sine 双曲余弦 hyperbolic cosine 双曲正切hyperbolic tangent反双曲正弦 inverse hyperbolic sine 反双曲余弦 inverse hyperbolic cosine 反双曲正切 inverse hyperbolic tangent 极限 limit数列 sequence of number 收敛 convergence 收敛于 a converge to a 发散 divergent极限的唯一性 uniqueness of limits收敛数列的有界性 boundedness of aconvergent sequence子列 subsequence函数的极限 limits of functions函数f(x)当x趋于x0时的极限 limit of functions f(x) as x approaches x0 左极限 left limit 右极限 right limit单侧极限 one-sided limits水平渐近线 horizontal asymptote 无穷小 infinitesimal 无穷大 infinity铅直渐近线 vertical asymptote 夹逼准则 squeeze rule单调数列 monotonic sequence高阶无穷小 infinitesimal of higher order 低阶无穷小 infinitesimal of lower order 同阶无穷小 infinitesimal of the same order 等阶无穷小 equivalent infinitesimal 函数的连续性 continuity of a function 增量 increment函数f(x)在x0连续 the function f(x) is continuous at x0左连续 left continuous 右连续 right continuous区间上的连续函数 continuous function 函数f(x)在该区间上连续 function f(x) is continuous on an interval 不连续点 discontinuity point第一类间断点 discontinuity point of the first kind第二类间断点 discontinuity point of the second kind初等函数的连续性 continuity of the elementary functions定义区间 defined interval最大值 global maximum value (absolute maximum)最小值 global minimum value (absolute minimum)零点定理 the zero point theorem介值定理 intermediate value theorem 第二章导数与微分Chapter2 Derivative and Differential 速度 velocity匀速运动 uniform motion 平均速度 average velocity瞬时速度 instantaneous velocity 圆的切线 tangent line of a circle 切线 tangent line切线的斜率 slope of the tangent line 位置函数 position function 导数 derivative 可导derivable函数的变化率问题 problem of the change rate of a function导函数 derived function 左导数 left-hand derivative 右导数 right-hand derivative 单侧导数 one-sided derivativesf(x)在闭区间【a,b】上可导 f(x)isderivable on the closed interval [a,b] 切线方程 tangent equation 角速度 angular velocity 成本函数 cost function 边际成本 marginal cost 链式法则 chain rule隐函数 implicit function 显函数 explicit function 二阶函数 second derivative 三阶导数 third derivative 高阶导数 nth derivative莱布尼茨公式 Leibniz formula 对数求导法 log- derivative 参数方程 parametric equation 相关变化率 correlative change rata 微分 differential 可微的 differentiable 函数的微分 differential of function自变量的微分 differential of independent variable微商 differential quotient间接测量误差 indirect measurement error 绝对误差 absolute error相对误差 relative error第三章微分中值定理与导数的应用Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives 罗马定理Rolle’s theorem 费马引理Fermat’s lemma拉格朗日中值定理Lagrange’s mean value theorem驻点 stationary point 稳定点 stable point 临界点 critical point辅助函数 auxiliary function拉格朗日中值公式Lagrange’s mean value formula柯西中值定理Cauchy’s mean value theorem洛必达法则L’Hospital’s Rule0/0型不定式 indeterminate form of type 0/0不定式 indeterminate form泰勒中值定理Taylor’s mean value theorem泰勒公式 Taylor formula 余项 remainder term拉格朗日余项 Lagrange remainder term 麦克劳林公式Maclaurin’s formula 佩亚诺公式 Peano remainder term 凹凸性 concavity凹向上的 concave upward, cancave up 凹向下的，向上凸的concave downward’ concave down拐点 inflection point函数的极值 extremum of function 极大值 local(relative) maximum 最大值global(absolute) mximum 极小值 local(relative) minimum 最小值 global(absolute) minimum 目标函数 objective function 曲率 curvature弧微分 arc differential平均曲率 average curvature 曲率园 circle of curvature 曲率中心 center of curvature 曲率半径 radius of curvature渐屈线 evolute 渐伸线 involute根的隔离 isolation of root 隔离区间 isolation interval 切线法 tangent line method第四章不定积分Chapter4 Indefinite Integrals原函数 primitive function(antiderivative) 积分号 sign of integration 被积函数integrand积分变量 integral variable 积分曲线 integral curve 积分表 table of integrals换元积分法 integration by substitution 分部积分法 integration by parts分部积分公式 formula of integration by parts有理函数 rational function 真分式 proper fraction 假分式 improper fraction第五章定积分Chapter5 Definite Integrals 曲边梯形 trapezoid with 曲边 curve edge窄矩形 narrow rectangle曲边梯形的面积 area of trapezoid with curved edge积分下限 lower limit of integral 积分上限 upper limit of integral 积分区间 integral interval 分割 partition积分和 integral sum 可积 integrable矩形法 rectangle method积分中值定理 mean value theorem of integrals函数在区间上的平均值 average value of a function on an integvals牛顿－莱布尼茨公式 Newton-Leibniz formula微积分基本公式 fundamental formula of calculus换元公式 formula for integration by substitution递推公式 recurrence formula 反常积分 improper integral反常积分发散 the improper integral is divergent反常积分收敛 the improper integral is convergent无穷限的反常积分 improper integral on an infinite interval无界函数的反常积分 improper integral of unbounded functions绝对收敛 absolutely convergent第六章定积分的应用Chapter6 Applications of the Definite Integrals元素法 the element method 面积元素 element of area平面图形的面积 area of a luane figure 直角坐标又称“笛卡儿坐标 (Cartesian coordinates)”极坐标 polar coordinates 抛物线 parabola 椭圆 ellipse旋转体的面积 volume of a solid of rotation旋转椭球体 ellipsoid of revolution, ellipsoid of rotation曲线的弧长 arc length of acurve 可求长的 rectifiable 光滑 smooth 功 work水压力 water pressure 引力 gravitation 变力 variable force第七章空间解析几何与向量代数Chapter7 Space Analytic Geometry and Vector Algebra向量 vector自由向量 free vector 单位向量 unit vector 零向量 zero vector 相等 equal 平行parallel向量的线性运算 linear poeration of vector 三角法则 triangle rule平行四边形法则 parallelogram rule 交换律 commutative law 结合律 associative law 负向量 negative vector 差 difference分配律 distributive law空间直角坐标系 space rectangular coordinates坐标面 coordinate plane 卦限 octant向量的模 modulus of vector向量a与b的夹角 angle between vector a and b方向余弦 direction cosine 方向角 direction angle向量在轴上的投影 projection of a vector onto an axis数量积，外积，叉积 scalar product,dot product,inner product曲面方程 equation for a surface 球面 sphere旋转曲面 surface of revolution 母线 generating line 轴 axis圆锥面 cone 顶点 vertex旋转单叶双曲面 revolution hyperboloids of one sheet旋转双叶双曲面 revolution hyperboloids of two sheets柱面 cylindrical surface ,cylinder 圆柱面 cylindrical surface 准线 directrix抛物柱面 parabolic cylinder 二次曲面 quadric surface 椭圆锥面 dlliptic cone 椭球面ellipsoid单叶双曲面 hyperboloid of one sheet 双叶双曲面 hyperboloid of two sheets 旋转椭球面 ellipsoid of revolution 椭圆抛物面 elliptic paraboloid旋转抛物面 paraboloid of revolution 双曲抛物面 hyperbolic paraboloid 马鞍面 saddle surface椭圆柱面 elliptic cylinder 双曲柱面 hyperbolic cylinder 抛物柱面 parabolic cylinder 空间曲线 space curve空间曲线的一般方程 general form equations of a space curve空间曲线的参数方程 parametric equations of a space curve 螺转线 spiral 螺矩 pitch 投影柱面 projecting cylinder 投影 projection平面的点法式方程 pointnorm form eqyation of a plane法向量 normal vector平面的一般方程 general form equation of a plane两平面的夹角 angle between two planes 点到平面的距离 distance from a point to a plane空间直线的一般方程 general equation of a line in space方向向量 direction vector直线的点向式方程 pointdirection form equations of a line方向数 direction number直线的参数方程 parametric equations of a line两直线的夹角 angle between two lines 垂直 perpendicular直线与平面的夹角 angle between a line and a planes平面束 pencil of planes平面束的方程 equation of a pencil of planes行列式 determinant系数行列式 coefficient determinant第八章多元函数微分法及其应用Chapter8 Differentiation of Functions of Several Variables and Its Application 一元函数 function of one variable 多元函数 function of several variables 内点 interior point 外点 exterior point 边界点 frontier point,boundary point 聚点 point of accumulation 开集 openset 闭集 closed set 连通集 connected set 开区域 open region 闭区域 closed region有界集 bounded set 无界集 unbounded setn维空间 n-dimentional space 二重极限 double limit 多元函数的连续性 continuity of function of seveal 连续函数 continuous function 不连续点 discontinuity point 一致连续 uniformly continuous 偏导数 partial derivative 对自变量x的偏导数 partial derivative with respect to independent variable x 高阶偏导数 partial derivative of higher order 二阶偏导数 second order partial derivative 混合偏导数 hybrid partial derivative 全微分 total differential 偏增量 oartial increment 偏微分 partial differential 全增量 total increment 可微分 differentiable 必要条件 necessary condition充分条件 sufficient condition 叠加原理 superpostition principle 全导数 total derivative中间变量 intermediate variable 隐函数存在定理 theorem of the existence of implicit function 曲线的切向量 tangent vector of a curve 法平面 normal plane 向量方程vector equation 向量值函数 vector-valued function 切平面 tangent plane 法线 normal line 方向导数 directional derivative梯度 gradient数量场 scalar field 梯度场 gradient field 向量场 vector field 势场 potential field 引力场 gravitational field 引力势 gravitational potential 曲面在一点的切平面 tangent plane to asurface at a point 曲线在一点的法线 normal line to asurface at a point 无条件极值 unconditional extreme values 条件极值 conditional extreme values 拉格朗日乘数法 Lagrange multiplier method 拉格朗日乘子 Lagrange multiplier 经验公式 empirical formula 最小二乘法 method of least squares 均方误差mean square error 第九章重积分 Chapter9 Multiple Integrals 二重积分 double integral 可加性 additivity累次积分 iterated integral 体积元素 volume element 三重积分 triple integral 直角坐标系中的体积元素 volumeelement in rectangular coordinate system 柱面坐标 cylindrical coordinates 柱面坐标系中的体积元素 volumeelement in cylindrical coordinate system 球面坐标 spherical coordinates 球面坐标系中的体积元素 volumeelement in spherical coordinate system 反常二重积分 improper double integral 曲面的面积 area of a surface 质心 centre of mass 静矩 static moment 密度 density 形心centroid 转动惯量 moment of inertia 参变量 parametric variable 第十章曲线积分与曲面积分Chapter10 Line(Curve)Integrals and Surface Integrals对弧长的曲线积分 line integrals with respect to arc hength第一类曲线积分 line integrals of the first type对坐标的曲线积分 line integrals with respect to x,y,and z第二类曲线积分 line integrals of the second type有向曲线弧 directed arc单连通区域 simple connected region 复连通区域 complex connected region 格林公式Green formula第一类曲面积分 surface integrals of the first type对面的曲面积分 surface integrals with respect to area有向曲面 directed surface对坐标的曲面积分 surface integrals with respect to coordinate elements第二类曲面积分 surface integrals of the second type有向曲面元 element of directed surface 高斯公式 gauss formula拉普拉斯算子 Laplace operator 格林第一公式Green’s first formula 通量 flux散度 divergence斯托克斯公式 Stokes formula 环流量 circulation 旋度 rotation,curl第十一章无穷级数Chapter11 Infinite Series 一般项 general term 部分和 partial sum 余项 remainder term 等比级数 geometric series 几何级数 geometric series 公比 common ratio调和级数 harmonic series柯西收敛准则 Cauchy convergence criteria, Cauchy criteria for convergence 正项级数series of positive terms 达朗贝尔判别法D’Alembert test 柯西判别法 Cauchy test交错级数 alternating series 绝对收敛 absolutely convergent 条件收敛 conditionally convergent 柯西乘积 Cauchy product 函数项级数 series of functions 发散点 point of divergence 收敛点 point of convergence 收敛域 convergence domain 和函数 sum function 幂级数 power series幂级数的系数 coeffcients of power series 阿贝尔定理 Abel Theorem收敛半径 radius of convergence 收敛区间 interval of convergence 泰勒级数 Taylor series麦克劳林级数 Maclaurin series 二项展开式 binomial expansion 近似计算approximate calculation舍入误差 round-off error,rounding error 欧拉公式Euler’s formula魏尔斯特拉丝判别法 Weierstrass test 三角级数 trigonometric series 振幅 amplitude 角频率 angular frequency 初相 initial phase 矩形波 square wave谐波分析 harmonic analysis 直流分量 direct component 基波 fundamental wave 二次谐波 second harmonic三角函数系 trigonometric function system 傅立叶系数 Fourier coefficient 傅立叶级数 Forrier series 周期延拓 periodic prolongation 正弦级数 sine series 余弦级数cosine series 奇延拓 odd prolongation 偶延拓 even prolongation傅立叶级数的复数形式 complex form of Fourier series第十二章微分方程Chapter12 Differential Equation解微分方程 solve a dirrerential equation 常微分方程 ordinary differential equation偏微分方程 partial differential equation,PDE微分方程的阶 order of a differential equation微分方程的解 solution of a differential equation微分方程的通解 general solution of a differential equation初始条件 initial condition微分方程的特解 particular solution of a differential equation初值问题 initial value problem微分方程的积分曲线 integral curve of a differential equation可分离变量的微分方程 variable separable differential equation隐式解 implicit solution隐式通解 inplicit general solution 衰变系数 decay coefficient 衰变 decay齐次方程 homogeneous equation一阶线性方程 linear differential equation of first order非齐次 non-homogeneous齐次线性方程 homogeneous linear equation非齐次线性方程 non-homogeneous linear equation常数变易法 method of variation of constant暂态电流 transient stata current 稳态电流 steady state current 伯努利方程 Bernoulli equation全微分方程 total differential equation 积分因子 integrating factor高阶微分方程 differential equation of higher order悬链线 catenary高阶线性微分方程 linera differentialequation of higher order自由振动的微分方程 differential equation of free vibration强迫振动的微分方程 differential equation of forced oscillation串联电路的振荡方程 oscillation equation of series circuit二阶线性微分方程 second order linera differential equation线性相关 linearly dependence 线性无关 linearly independce二阶常系数齐次线性微分方程 second order homogeneour linear differential equation with constant coefficient二阶变系数齐次线性微分方程 second order homogeneous linear differential equation with variable coefficient 特征方程 characteristic equation无阻尼自由振动的微分方程 differential equation of free vibration with zero damping 固有频率 natural frequency简谐振动 simple harmonic oscillation,simple harmonic vibration微分算子 differential operator待定系数法 method of undetermined coefficient共振现象 resonance phenomenon 欧拉方程 Euler equation幂级数解法 power series solution 数值解法 numerial solution 勒让德方程 Legendre equation微分方程组 system of differential equations常系数线性微分方程组 system of linera differential equations with constant coefficient第二部分定理定义公式的英文表达Part2 English Expression for Theorem, Definition and Formula第一章函数与极限Chapter 1 Function and Limit1.1 映射与函数 (Mapping and Function)一、集合 (Set)二、映射 (Mapping)映射概念 (The Concept of Mapping) 设X, Y是两个非空集合 , 如果存在一个法则f，使得对X中每个元素x，按法则f，在Y中有唯一确定的元素y与之对应 ,则称f为从X到 Y的映射 , 记作f:X→Y。