数学英文词汇大全

1、微积分第一章函数与极限Chapterl Function and Limit 集合set元素 element 子集 subset 空集 empty set 并集 union 交集 intersection 差集 differenee of set 根本集 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 ope n in terval 有限区间 finite in terval 区间的长度len gth of a

2、n in terval无限区间 infinite in terval 领域 neighborhood 领域的中心 centre of a n eighborhood 领域的半径 radius of a n eighborhood 左领域 left neighborhood 右领域 right neighborhood 映射 mappingX 至i Y 的映射 mapping of X ontoY 满射 surjection 单射 injection一一映射 on e-to-one mapp ing 双射 bijection算子 operator 变化 transformation 函数 fun

3、ction 逆映射 in verse mapp ing 复合映射 composite mapp ing 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 relati on 值域 range 自然定义域n atural domai n单值函数 sin gle valued function 多值函数 multiple valued fun ctio n 单值分支 on e-valued branch 函数图形 graph of a fun cti on 绝

4、对值函数 absolute value 符号函数 sigh fun ctio n 整数局部 in tegral part 阶梯曲线 step curve 当且仅当 if and only if(iff) 分段函数 piecewise fun cti on 上界 upper bound 下界 lower bound 有界 boundedness 无界 unbounded 函数的单调性monotoni city of a function单调增加的in creasi ng 单调减少的 decreas ing 单调函数 monotone function 函数的奇偶性parity(odevity)

5、of a fun ction对称 symmetry 偶函数 even function 奇函数 odd function 函数的周期性 periodicity of a fun ctio n 周期 period 反函数 in verse fun ctio n 直接函数 direct fun ctio n 复合函数 composite function 中间变量 in termediate variable 函数的运算 operatio n of function 根本初等函数basic eleme ntary fun ctio n初等函数 eleme ntary function 幕函数 po

6、wer function 指数函数 exp onen tial function 对数函数 logarithmic fun ction 三角函数 trig ono metric function 反三角函数 in verse trigo no metric fun ctio n 常数函数 con sta nt function 双曲函数 hyperbolic fun ctio n 双曲正弦 hyperbolic sine 双曲余弦 hyperbolic cos ine 双曲正切 hyperbolic tangent 反双曲正弦 in verse hyperbolic sine 反双曲余弦 in

7、 verse hyperbolic cos ine 反双曲正切 in verse hyperbolic tangent极限limit数列 sequenee of number收敛 eon verge nee收敛于 a con verge to a发散 diverge nt极限的唯一性uniquen ess of limits收敛数列的有界性boun ded ness of a con verge nt seque nee子列 subsequenee函数的极限 limits of fun etio ns函数 当 x 趋于 x0 时的极限 limit of functions as x appro

8、aehes x0 左极限left limit 右极限 right limit单侧极限 on e-sided limits水平渐近线 horiz on tal asymptote无穷小 infinitesimal无穷大 infinity铅直渐近线 vertical asymptote夹逼准贝U squeeze rule单调数歹 U monotonic seque nee高阶无穷小 infin itesimal of higher order 低阶无穷小 infinitesimal of lower order 同阶无穷小 infin itesimal of the same order2高等数学

9、-翻译等阶无穷小equivale nt infin itesimal函数的连续性 con ti nuity of a fun etion增量 in creme nt函数 在 x0 连续 the funetion is continuous at x0左连续 left continuous右连续 right continuous区间上的连续函数contin uous fun etio n函数 在该区间上连续function is continuous on an interval不连续点 disc on ti nuity point第一类间断点disc ontinuity point of th

10、e first kind第二类间断点disc on ti nuity point of the sec ond kind初等函数的连续性con ti nu ity of the eleme ntary fun eti ons定义区间 defi ned in terval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 in termediate value theorem第二章导数与微分Chapter2 Der

11、ivative and Differen tial 速度 velocity 匀速运动 uniform moti on 平均速度 average velocity 瞬时速度 in sta ntan eous velocity 圆的切线 tangent line of a circle 切线 tangent line 切线的斜率slope of the tan ge nt line位置函数 positi on fun cti on 导数 derivative 可导 derivable 函数的变化率问题problem of the cha nge rate of a function导函数 deri

12、ved function 左导数 left-hand derivative 右导数 right-hand derivative 单侧导数 on e-sided derivatives 在闭区间【a,b】上可导 is derivable on the closed interval a,b 切线方程 tangent equati on 角速度 angular velocity 本钱函数 cost fun ctio n 边际本钱 marginal cost 链式法那么 chain rule 隐函数 implicit function 显函数 explicit function 二阶函数 sec o

13、nd derivative 三阶导数 third derivative 高阶导数 nth derivative 莱布尼茨公式Leib niz formula对数求导法 log- derivative 参数方程 parametric equati on 相关变化率 correlative cha nge rata 微分 differential 可微的 differentiable 函数的微分 differe ntial of fun ctio n自变量的微分differe ntial of in depe ndent variable微商 differential quotient间接测量误差

14、in direct measureme nt 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 Mean Value Theorem of Differen tials and the Applicati on of Derivatives 罗马定理 Rolle ' s theorem费马引理 Fermat' s lemma拉格朗日中值定理Lagra nge' s mean value theorem驻点 stationary point 稳定点 stable point 临界点 c

15、ritical point 辅助函数 auxiliary function拉格朗日中值公式Lagra nge' s mean value formula柯西中值定理Cauchy' s mean value theorem洛必达法那么L' Hospital ' s Rule0/0 型不定式 in determi nate form of type 0/0不定式 in determi nate 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 L

16、agra nge remain der term 麦克劳林公式Maclaurin ' s formula佩亚诺公式Pea no remain der term凹凸性 con cavity 凹向上的 con cave upward, can cave up 凹向下的，向上凸的con cave dow nward 'con cave dow n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

17、) minimum 最小值 global(absolute) minimum 目标函数 objective fun ctio n 曲率 curvature弧微分 arc differential平均曲率 average curvature 曲率园 circle of curvature 曲率中心 cen ter of curvature 曲率半径 radius of curvature 渐屈线evolute 渐伸线in volute 根的隔离 isolation of root 隔离区间 isolation in terval 切线法 tangent line method第四章不定积分Cha

18、pter4 In defi nite In tegrals 原函数 primitive function(antiderivative) 积分号 sign of integration 被积函数 in tegra nd积分变量 in tegral variable积分曲线 in tegral curve积分表 table of integrals换元积分法 in tegrati on by substituti on分部积分法 in tegrati on by parts分部积分公式 formula of in tegrati on by parts有理函数 rati onal functio

19、n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 in tegral积分上限 upper limit of in tegral积分区间 in tegral in terval分害9 partition积分禾口 integral sum可积 integrable矩形法 rect

20、angle method积分中值定理mea n value theorem of in tegrals函数在区间上的平均值average value of a function on an in tegvals牛顿莱布尼茨公式Newto n-Leib niz formula微积分根本公式fun dame ntal formula of calculus换元公式 formula for in tegrati on by substituti on递推公式 recurre nee formula反常积分 improper in tegral反常积分发散 the improper in tegral

21、 is diverge nt反常积分收敛 the improper in tegral is con verge nt无穷限的反常积分improper in tegral on an infin ite in terval无界函数的反常积分improper in tegral of unboun ded fun cti ons绝对收敛 absolutely con verge nt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 eleme nt of area平面图形的面积ar

22、ea of a luane figure直角坐标又称"笛卡儿坐标(Cartesian coordi nates)极坐标 polar coord in ates抛物线 parabola椭圆 ellipse旋转体的面积 volume of a solid of rotati on旋转椭球体 ellipsoid of revoluti on, ellipsoid of rotati on曲线的弧长 arc len gth of acurve可求长的 rectifiable光滑smooth功 work水压力 water pressure弓丨力 gravitation变力 variable f

23、orce第七章 空间解析几何与向量代数Chapter7 Space An alytic Geometry and Vector Algebra向量 vector自由向量 free vector单位向量 un it vector零向量 zero vector相等equal平行 parallel向量的线性运算lin ear poerati on of vector三角法贝U triangle rule平行四边形法那么parallelogram rule交换律 commutative law结合律 associative law负向量 negative vector差 differenee分配律 d

24、istributive law空间直角坐标系 space rectan gular coord in ates坐标面 coord in ate pla ne圭卜限 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 direct ion cos ine方向角 direct ion an gle向量在轴上的投影project ion of a vector onto an axis数量积，外积，叉积scalar product,dot product,i nner product曲面方程 equati

25、 on for a surface球面 sphere旋转曲面 surface of revoluti on母线 generating line轴 axis圆锥面 cone顶点 vertex旋转单叶双曲面revolutio n hyperboloids of one sheet旋转双叶双曲面revolutio n hyperboloids of two sheets柱面 cylindrical surface ,cylinder 圆柱面 cylindrical surface 准线 directrix抛物柱面 parabolic cyli nder 二次曲面 quadric surface 椭圆

26、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 revoluti on 椭圆抛物面 elliptic paraboloid 旋转抛物面 paraboloid of revolutio n 双曲抛物面 hyperbolic paraboloid 马鞍面 saddle surface 椭圆柱面 elliptic cyli nder 双曲柱面 hyperbolic cyli nder 抛物柱面 parabolic cyli n

27、der 空间曲线 space curve 空间曲线的一般方程general form equati ons of a space curve空间曲线的参数方程parametric equati ons of a space curve螺转线spiral 螺矩pitch投影柱面 projecti ng cyli nder投影 projection平面的点法式方程pointnorm form eqyati on of a pla ne法向量 normal vector平面的一般方程gen eral form equatio n of a pla ne两平面的夹角 an gle betwee n t

28、wo pla nes 点至 U平面的距离dista nee from a point to a pla ne空间直线的一般方程general equatio n of a line in space方向向量 directi on vector直线的点向式方程poin tdirect ion form equatio ns of a line方向数 direct ion nu mber直线的参数方程parametric equati ons of a line两直线的夹角 an gle betwee n two lines 垂直 perpe ndicular直线与平面的夹角an gle betw

29、ee n a line and a pla nes平面束 pencil of planes 平面束的方程equatio n of a pen cil of pla nes行歹 U式 determ inant系数行列式 coefficie nt determ inant第八章多元函数微分法及其应用Chapter8 Differe ntiatio n of Functions of Several Variables and Its Applicati on 一元函数 function of one variable多元函数 function of several variables内点 inte

30、rior point夕卜点 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-dime nti onal space二重极限 double limit多元函数的连续性contin uity of fun ctio n of seveal连续函数 con ti nu ous funct

31、ion不连续点 disc on ti nuity point一致连续 uniformly con ti nu ous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 sec ond order partial derivative混合偏导数hybrid partial derivative全微分 total differential偏增量 oartial in creme

32、 nt偏微分 partial differential全增量 total in creme nt可微分 differentiable必要条件 n ecessary con diti on充分条件 sufficie nt con diti on叠加原理 superpostiti on prin ciple全导数 total derivative中间变量 in termediate variable隐函数存在定理theorem of the existe nee of implicit fun ctio n曲线的切向量 tangent vector of a curve法平面 normal pla

33、ne向量方程 vector equati on向量值函数 vector-valued fun ctio n切平面 tangent plane法线 normal line方向导数 direct ional 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 弓丨力势 gravitational potential 曲面在一点的切平面tangent pla ne to a surface at a point曲线在一

34、点的法线no rmal li ne to a surface at a point无条件极值 uncon diti onal extreme values 条件极值 con diti onal extreme values 拉格朗日乘数法Lagra nge multiplier method拉格朗日乘子 Lagra nge 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 in tegr

35、al可加性 additivity累次积分 iterated in tegral体积元素 volume eleme nt三重积分 triple in tegral直角坐标系中的体积元素volume eleme nt in rectan gular coord in ate system柱面坐标 cylindrical coord inates柱面坐标系中的体积元素volume eleme nt in cyli ndrical coord in ate system球面坐标 spherical coord in ates球面坐标系中的体积元素volume eleme nt in spherical

36、 coord in ate system反常二重积分improper double in tegral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 mome nt of in ertia参变量 parametric variable第十章曲线积分与曲面积分Chapter10 Li ne(Curve)l ntegrals and Surface In tegrals 对弧长的曲线积分li ne in tegrals with respect to arc hen gth第一类曲线

37、积分line in tegrals of the first type对坐标的曲线积分li ne in tegrals with respect to x,y,a nd z第二类曲线积分line in tegrals of the sec ond type有向曲线弧 directed arc单连通区域 simple conn ected region 复连通区域 complex conn ected region 格林公式Green formula 第一类曲面积分surface in tegrals of the first type对面的曲面积分surface in tegrals with

38、 respect to area有向曲面 directed surface对坐标的曲面积分surface in tegrals with respect to coord in ate eleme nts第二类曲面积分surface in tegrals of the sec ond type有向曲面元 eleme nt of directed surface高斯公式 gauss formula拉普拉斯算子Laplace operator格林第一公式Gree n' s first formula通量flux散度 diverge nee斯托克斯公式Stokes formula环流量 ci

39、rculation 旋度 rotation,curl第十一章无穷级数Chapter" Infinite Series 一般项 general term 局部和 partial sum 余项 remainder term 等比级数 geometric series 几何级数 geometric series 公比 com mon ratio 调和级数 harm onic series 柯西收敛准贝 UCauchy con verge nee criteria, Cauchy criteria for con verge nee正项级数 series of positive terms

40、达朗贝尔判别法D' Alembert test柯西判别法 Cauchy test 交错级数 alter nati ng series 绝对收敛 absolutely con verge nt 条件收敛 con diti on ally con verge nt 柯西乘积 Cauchy product 函数项级数 series of fun ctio ns 发散点 point of diverge nee 收敛点 point of con verge nee 收敛域 con verge nee doma in 禾口函数 sum function 幕级数 power series幕级数的系

41、数coeffcie nts of power series阿贝尔定理 Abel Theorem收敛半径 radius of con verge nee 收敛区间 in terval of con verge nee 泰勒级数Taylor series 麦克劳林级数Maclaurin series二项展开式 bino mial expa nsion 近似计算 approximate calculati on 舍入误差 roun d-off error,ro unding error 欧拉公式 Euler' s formula 魏尔斯特拉丝判别法Weierstrass test三角级数 t

42、rig ono metric series 振幅 amplitude 角频率 angular frequency 初相 initial phase 矩形波 square wave 谐波分析 harm onic an alysis 直流分量 direct comp onent 基波 fun dame ntal wave 二次谐波 sec ond harm onic 三角函数系 trig ono metric function system 傅立叶系数Fourier coefficie nt傅立叶级数 Forrier series 周期延拓 periodic proIon gati on 正弦级数

43、 si ne series 余弦级数 cos ine series 奇延拓 odd proIongation 偶延拓 even proIongation 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 dirrere ntial equati on 常微分方程 ordinary differe ntial equatio n 偏微分方程partial differe ntial equatio n,PDE微分方程的阶 order of a differe

44、ntial equati on 微分方程的解soluti on of a differe ntial equati on微分方程的通解gen eral solution of a differe ntial equati on初始条件 in itial co nditi on 微分方程的特解particular soluti on of a differe ntial equati on初值问题 in itial value problem 微分方程的积分曲线in tegral curve of a differe ntial equation可别离变量的微分方程variable separa

45、ble differe ntial equati on隐式解 implicit solution 隐式通解 in plicit gen eral soluti on 衰变系数 decay coefficie nt衰变decay齐次方程 homoge neous equati on一阶线性方程 lin ear differe ntial equati on of first order非齐次 non-homogeneous齐次线性方程 homoge neous lin ear equati on 非齐次线性方程non-homoge neous lin ear equati on常数变易法 met

46、hod of variati on of con sta nt暂态电流 tran sie nt stata curre nt稳态电流 steady state curre nt 伯努利方程 Bernoulli equati on 全微分方程 total differe ntial equatio n 积分因子 in tegrat ing factor 高阶微分方程differe ntial equati on of higher order悬链线 cate nary高阶线性微分方程linera differential equation of higher order自由振动的微分方程 强迫振

47、动的微分方程 串联电路的振荡方程二阶线性微分方程differe ntial equatio n of free vibrati on differential equation of forced oscillation oscillation equation of series circuitsec ond order linera differe ntial equati on线性相关 lin early depe ndence线性无关 lin early in depe ndce二阶常系数齐次线性微分方程second order homogeneour linear different

48、ial equation with con sta nt coefficie nt二阶变系数齐次线性微分方程second order homogeneous linear differential equation withvariable coefficie nt特征方程 characteristic equati on无阻尼自由振动的微分方程differe ntial equati on of free vibrati on with zero damp ing固有频率 n atural freque ncy简谐振动 simple harm onic oscillati on, simpl

49、e harm onic vibratio n微分算子 differe ntial operator待定系数法 method of un determ ined coefficie nt共振现象 resonance phe nomenon欧拉方程 Euler equati on幕级数解法 power series soluti on数值解法 numerial solution勒让德方程 Lege ndre equati on微分方程组 system of differe ntial equati ons常系数线性微分方程组system of linera differe ntial equati

50、 ons with con sta nt coefficie nt线性代数adjon t(adjugate) of matrix A augme nted matrixBblock diagonal matrixblock matrixA的伴随矩阵A的增广矩阵块对角矩阵 块矩阵 根底解系basic soluti on setCCauchy-Schwarz in equality characteristic equatio n characteristic polyno mial coffcie nt matrix cofactor cofactor expa nsion colu mn ve

51、ctor commuti ng matrices con siste nt lin ear system Cramer' s rule Cross- product term柯西-许瓦兹不等式特征方程特征多项式系数矩阵代数余子式代数余子式展开列向量交换矩阵相容线性方程组克莱姆法那么交叉项行列式对角元素对角矩阵向量空间V的维数梯形矩阵 特征空间 特征值 特征向量 特征向量的基 初等矩阵 行初等变换DDeterm inantDiag onal en triesDiag onal matrixDime nsion of a vector space V echel on matrixeige

52、 nspaceeige nvalueeige nvectoreige nvector basiseleme ntary matrixeleme ntary row operatio nsfull rankfun derme ntal set of soluti onGcen tergrn eral soluti onGram-Schmidt processHhomoge neous lin ear equati onsIiden tity matrixincon siste nt li near systemindefinite matrixin defi nit quatratic form

53、infin ite-dime nsional spaceinner productin verse of matrix ALlin ear comb in ati onlin early depe ndentlin early in depe ndentlin ear tran sformatio nlower triangular matrixMmain diagonal of matrix Amatrix满秩根底解系通解施密特正交化过程齐次线性方程组单位矩阵不相容线性方程组 不定矩阵不定二次型无限维空间内积逆矩阵线性组合线性相关线性无关线性变换 下三角形矩阵矩阵的主对角矩阵cen tern

54、 egative defi nite quaratic formn egative semidefi nite quadratic formnon homoge neous equati onsnon sigular matrixnon trivial soluti onnorm of vector Vno rmaliz ing vector V负定二次型半负定二次型非齐次线性方程组非奇异矩阵非平凡解向量V的范数标准化向量orthogo nal basisorthogo nal compleme ntorthogo nal decompositi onorthogo nally diago n

55、alizable matrixorthogo nal matrixorthogo nal setortho no rmalbasisortho no mal set正交基正交补正交分解矩阵的正交对角化正交矩阵正交向量组标准正交基标准正交向量组bPpartitioned matrixpositive defi nite matrixpositive defi nite quatratic formpositive semidefinite matrixpositive semidefi nite quadratic form分块矩阵正定矩阵正定二次型半正定矩阵 半正定二次型Qquatratic

56、formcen terR/ce nterrank of matrix A reduced echel on matrix row vector二次型矩阵A的秩r(A)最简梯形阵行向量set spanned by similar matrices similarity tran sformatio n sin gular matrix soluti on set sta ndard basis sta ndard matrix submatrix subspace symmetric matrix由向量所生成相似矩阵相似变换奇异矩阵解集合标准基标准矩阵I子矩阵子空间对称矩阵矩阵A的迹tr(A)矩阵A的转秩三角不等式平凡解Ttrace of matrix A tran spose of A trian gle in equlity trivial soluti onUunit vectorupper tria ngular matrixVvan derm onde matrixvectorvector spaceZzero subspacezero vector单位向量上三角形矩阵