11Homogeneous Linear System

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Linear Algebra (chapter1)02

§1.4 The Matrix Equation Ax=b
1. Definition 2. Existence of Solutions 3. Computation of Ax 4. Properties of the Matrix-Vector Product Ax
§1.4 The Matrix Equation Ax=b
§1.4 The Matrix Equation Ax=b
2. Existence of Solutions
If the equation Ax=b is consistent, b must satisfy:
This is the equation of a plane through the origin in R3:
§1.4 The Matrix Equation Ax=b
2. Existence of Solutions
Sol. Row reduce the augmented matrix for Ax=b:
∵ ∴
=
≠ 0 (for some choices of b)
ห้องสมุดไป่ตู้
The equation Ax=b is not consistent for every b.
§1.5 Solution Set of Linear Systems
Use vector notation to describe solutions sets of linear system 1. Homogeneous Linear Systems （齐次线性方程组） 2. Parametric Vector Form 3. Solutions of Nonhomogeneous Systems

n元非齐次线性方程组

n元非齐次线性方程组
元非齐次线性方程组（Unhomogeneous Linear Equation System）绝对是数学家在解线性方程组的过程中的重要的可行性前言，它可以解决多种复杂的线性方程组试题，发挥助推作用。

元非齐次线性方程组是根据线性空间给定方程与空间中各独立向量的关系，以求得空间中独立向量不同取法调节方程组的系数关系来解决线性方程组。

它利用了线性空间提供的有效信息，能够解决复杂问题，极大地提高了数学求解能力。

有效运用元非齐次线性方程组，可以极大地降低数学模型的求解难度，的确是数学家的不可或缺的工具。

因为它具有建模灵活性、调整灵活性强、定量描述可能性大等优点，在模型建立、参数设定、数据处理和结果验证方面能发挥重要作用。

例如，在机械设计、微机控制、科学计算、运筹学解决多类别线性方程组试题时，运用元非齐次线性方程组一定程度上能够减轻任务量，缩短解题时间，这给数学家带来了极大的便利。

综上所述，元非齐次线性方程组的运用为解决线性方程组提供了可能性，它的建模灵活性、调整灵活性强、定量描述可能性大等许多优势，让数学家在解决多类线性方程组试题时有效地减轻了任务量，缩短解题时间，绝对是数学家不可或缺的工具，值得大家推荐。

放射物理单词

the fluorescent yield：产生的荧光
vacancy：空的
favored：可能是拼错了
Auger：同锇歇电子
Fraction：部分
Isomer：同质异能素（质子数和中子数都同，核能态不同）
Enunciate：清晰讲述/解释等
Penetrate：穿过
Instructive：指导的
nitrogen 氮
Chapter 4 (2)
1. dosimetry 放射剂量学
2. tissue-air 组织
3. backscatter逆散射
4. depict 描述描写
5. irradiate 辐射照射
6. calibration 教标
7. dosimeter 放射剂量计
perturb 扰动摄动
homogeneous 同类的, 相似的
photon 光子
negligible 可忽略的
perturbation 扰动摄动
finite 有限的
geometry 几何
composite 组成
equivalent 等效
affix 词缀使附于
bracket 括号
Cumulate：应该是 accumulate 积累
Hypothetical：假设
Exponentially：指数地
rectangle ：长方形
dosage：剂量值
proportional：正比的
vertical：垂直的
horizontal：水平的
intersection：交叉的
collision 碰撞
bremsstrahlung 轫致（辐射）

数学专业英语词汇（N）

数学专业英语词汇(N)n ary relation n元关系n ball n维球n cell n维胞腔n chromatic graph n色图n coboundary n上边缘n cocycle n上循环n connected space n连通空间n dimensional column vector n维列向量n dimensional euclidean space n维欧几里得空间n dimensional rectangular parallelepiped n维长方体n dimensional row vector n维行向量n dimensional simplex n单形n dimensional skeleton n维骨架n disk n维圆盘n element set n元集n fold extension n重扩张n gon n角n graph n图n homogeneous variety n齐次簇n person game n人对策n simplex n单形n sphere bundle n球丛n th member 第n项n th partial quotient 第n偏商n th power operation n次幂运算n th root n次根n th term 第n项n times continuously differentiable n次连续可微的n times continuously differentiable function n次连续可微函数n tuple n组n tuply connected domain n重连通域n universal bundle n通用丛nabla 倒三角算子nabla calculation 倒三角算子计算nabla operator 倒三角算子napier's logarithm 讷代对数natural boundary 自然边界natural boundary condition 自然边界条件natural coordinates 自然坐标natural equation 自然方程natural equivalence 自然等价natural exponential function 自然指数函数natural frequency 固有频率natural geometry 自然几何natural injection 自然单射natural isomorphism 自然等价natural language 自然语言natural logarithm 自然对数natural mapping 自然映射natural number 自然数natural oscillation 固有振荡natural sine 正弦真数natural transformation 自然变换naught 零necessary and sufficient conditions 必要充分的条件necessary and sufficient statistic 必要充分统计量necessary condition 必要条件necessity 必然性negation 否定negation sign 否定符号negation symbol 否定符号negative 负数negative angle 负角negative binomial distribution 负二项分布negative complex 负复形negative correlation 负相关negative definite form 负定型negative definite hermitian form 负定埃尔米特形式negative definite quadratic form 负定二次形式negative function 负函数negative number 负数negative operator 负算子negative parity 负电阻negative part 负部分negative particular proposition 否定特称命题negative proposition 否定命题negative rotation 反时针方向旋转negative semidefinite 半负定的negative semidefinite eigenvalue problem 半负定特盏问题negative semidefinite form 半负定型negative semidefinite quadratic form 半负定二次形式negative sign 负号negative skewness 负偏斜性negative variation 负变差negligible quantity 可除量neighborhood 邻域neighborhood base 邻域基neighborhood basis 邻域基neighborhood filter 邻域滤子neighborhood retract 邻域收缩核neighborhood space 邻域空间neighborhood system 邻域系neighborhood topology 邻域拓扑neighboring vertex 邻近项点nephroid 肾脏线nerve 神经nested intervals 区间套net 网net function 网格函数net of curves 曲线网net of lines 直线网network 网络network analysis 网络分析network flow problem 网络潦题network matrix 网络矩阵neumann boundary condition 诺伊曼边界条件neumann function 诺伊曼函数neumann problem 诺伊曼问题neumann series 诺伊曼级数neutral element 零元素neutral line 中线neutral plane 中性平面neutral point 中性点newton diagram 牛顿多边形newton formula 牛顿公式newton identities 牛顿恒等式newton interpolation polynomial 牛顿插值多项式newton method 牛顿法newton potential 牛顿位势newtonian mechanics 牛顿力学nice function 佳函数nil ideal 零理想nil radical 幂零根基nilalgebra 幂零代数nilpotency 幂零nilpotent 幂零nilpotent algebra 幂零代数nilpotent element 幂零元素nilpotent group 幂零群nilpotent ideal 幂零理想nilpotent matrix 幂零矩阵nilpotent radical 幂零根基nine point circle 九点圆nine point finite difference scheme 九点有限差分格式niveau line 等位线niveau surface 等位面nodal curve 结点曲线nodal line 交点线nodal point 节点node 节点node locus 结点轨迹node of a curve 曲线的结点noetherian category 诺特范畴noetherian object 诺特对象nomogram 算图nomographic 列线图的nomographic chart 算图nomography 图算法non additivity 非加性non archimedean geometry 非阿基米德几何non archimedean valuation 非阿基米德赋值non countable set 不可数集non critical point 非奇点non denumerable 不可数的non denumerable set 不可数集non developable ruled surface 非可展直纹曲面non enumerable set 不可数集non euclidean geometry 非欧几里得几何学non euclidean motion 非欧几里得运动non euclidean space 非欧几里得空间non euclidean translation 非欧几里得平移non euclidean trigonometry 非欧几里得三角学non homogeneity 非齐non homogeneous chain 非齐次马尔可夫链non homogeneous markov chain 非齐次马尔可夫链non isotropic plane 非迷向平面non linear 非线性的non negative semidefinite matrix 非负半正定阵non oriented graph 无向图non parametric test 无分布检验non pascalian geometry 非拍斯卡几何non ramified extension 非分歧扩张non rational function 无理分数non relativistic approximation 非相对性近似non reversibility 不可逆性non singular 非奇的non stationary random process 不平稳随机过程non steady state 不稳定状态non symmetric 非对称的non symmetry 非对称non zero sum game 非零和对策nonabsolutely convergent series 非绝对收敛级数nonagon 九边形nonassociate 非结合的nonassociative ring 非结合环nonbasic variable 非基本变量noncentral chi squre distribution 非中心分布noncentral f distribution 非中心f分布noncentral t distribution 非中心t分布noncentrality parameter 非中心参数nonclosed group 非闭群noncommutative group 非交换群noncommutative ring 非交换环noncommutative valuation 非交换赋值noncommuting operators 非交换算子noncomparable elements 非可比元素nondegeneracy 非退化nondegenerate collineation 非退化直射变换nondegenerate conic 非退化二次曲线nondegenerate critical point 非退化临界点nondegenerate distribution 非退化分布nondegenerate set 非退化集nondense set 疏集nondenumerability 不可数性nondeterministic automaton 不确定性自动机nondiagonal element 非对角元nondiscrete space 非离散空间nonexistence 不存在性nonfinite set 非有限集nonholonomic constraint 不完全约束nonhomogeneity 非齐性nonhomogeneous 非齐次的nonhomogeneous linear boundary value problem 非齐次线性边值问题nonhomogeneous linear differential equation 非齐次线性微分方程nonhomogeneous linear system of differential equations 非齐次线性微分方程组nonisotropic line 非迷向线nonlimiting ordinal 非极限序数nonlinear equation 非线性方程nonlinear functional analysis 非线性泛函分析nonlinear lattice dynamics 非线性点阵力学nonlinear operator 非线性算子nonlinear optimization 非线性最优化nonlinear oscillations 非线性振动nonlinear problem 非线性问题nonlinear programming 非线性最优化nonlinear restriction 非线性限制nonlinear system 非线性系统nonlinear trend 非线性瞧nonlinear vibration 非线性振动nonlinearity 非线性nonlogical axiom 非逻辑公理nonlogical constant 非逻辑常数nonmeager set 非贫集nonmeasurable set 不可测集nonnegative divisor 非负除数nonnegative number 非负数nonnumeric algorithm 非数值的算法nonorientable contour 不可定向周线nonorientable surface 不可定向的曲面nonorthogonal factor 非正交因子nonparametric confidence region 非参数置信区域nonparametric estimation 非参数估计nonparametric method 非参数法nonparametric test 非参数检定nonperfect set 非完备集nonperiodic 非周期的nonperiodical function 非周期函数nonplanar graph 非平面图形nonprincipal character 非重贞nonrandom sample 非随机样本nonrandomized test 非随机化检验nonrational function 非有理函数nonremovable discontinuity 非可去不连续点nonrepresentative sampling 非代表抽样nonresidue 非剩余nonsense correlation 产生错觉相关nonsingular bilinear form 非奇双线性型nonsingular curve 非奇曲线nonsingular linear transformation 非退化线性变换nonsingular matrix 非退化阵nonspecial group 非特殊群nonstable 不稳定的nonstable homotopy group 非稳定的同伦群nonstandard analysis 非标准分析nonstandard model 非标准模型nonstandard numbers 非标准数nonsymmetric relation 非对称关系nonsymmetry 非对称nontangential 不相切的nontrivial element 非平凡元素nontrivial solution 非平凡解nonuniform convergence 非一致收敛nonvoid proper subset 非空真子集nonvoid set 非空集nonzero vector 非零向量norm 范数norm axioms 范数公理norm form 范形式norm of a matrix 阵的范数norm of vector 向量的模norm preserving mapping 保范映射norm residue 范数剩余norm residue symbol 范数剩余符号norm topology 范拓朴normability 可模性normal 法线normal algorithm 正规算法normal basis theorem 正规基定理normal bundle 法丛normal chain 正规链normal cone 法锥面normal congruence 法汇normal coordinates 正规坐标normal correlation 正态相关normal curvature 法曲率normal curvature vector 法曲率向量normal curve 正规曲线normal density 正规密度normal derivative 法向导数normal dispersion 正常色散normal distribution 正态分布normal distribution function 正态分布函数normal equations 正规方程normal error model 正规误差模型normal extension 正规开拓normal family 正规族normal force 法向力normal form 标准型normal form problem 标准形问题normal form theorem 正规形式定理normal function 正规函数normal homomorphism 正规同态normal integral 正规积分normal linear operator 正规线性算子normal mapping 正规映射normal matrix 正规矩阵normal number 正规数normal operator 正规算子normal order 良序normal plane 法面normal polygon 正规多角形normal polynomial 正规多项式normal population 正态总体normal probability paper 正态概率纸normal process 高斯过程normal sequence 正规序列normal series 正规列normal set 良序集normal simplicial mapping 正规单形映射normal solvable operator 正规可解算子normal space 正规空间normal surface 法曲面normal tensor 正规张量normal to the surface 曲面的法线normal valuation 正规赋值normal variate 正常变量normal variety 正规簇normal vector 法向量normality 正规性normalization 标准化normalization theorem 正规化定理normalize 正规化normalized basis 正规化基normalized function 规范化函数normalized variate 正规化变量normalized vector 正规化向量normalizer 正规化子normalizing factor 正则化因数normed algebra 赋范代数normed linear space 赋范线性空间normed space 赋范线性空间northwest corner rule 北午角规则notation 记法notation free from bracket 无括号记号notation of backus 巴科斯记号notion 概念nought 零nowhere convergent sequence 无处收敛序列nowhere convergent series 无处收敛级数nowhere dense 无处稠密的nowhere dense set 无处稠密点集nowhere dense subset 无处稠密子集nuclear operator 核算子nuclear space 核空间nucleus of an integral equation 积分方程的核null 零null class 零类null divisor 零因子null ellipse 零椭圆null function 零函数null hypothesis 虚假设null line 零线null matrix 零矩阵null method 衡消法null plane 零面null point 零点null ray 零射线null relation 零关系null representation 零表示null sequence 零序列null set 空集null solution 零解null system 零系null transformation 零变换null vector 零向量nullity 退化阶数nullring 零环nullspace 零空间number 数number defined by cut 切断数number defined by the dedekind cut 切断数number field 数域number interval 数区间number line 数值轴number notation 数记法number of partitions 划分数number of repetitions 重复数number of replications 重复数number of sheets 叶数number sequence 数列number set 数集number system 数系number theory 数论number variable 数变量numeration 计算numerator 分子numeric representation of information 信息的数值表示numerical 数值的numerical algorithm 数值算法numerical axis 数值轴numerical calculation 数值计算numerical coding 数值编码numerical coefficient 数字系数numerical computation 数值计算numerical constant 数值常数numerical data 数值数据numerical determinant 数字行列式numerical differentiation 数值微分numerical equality 数值等式numerical equation 数字方程numerical error 数值误差numerical example 数值例numerical function 数值函数numerical inequality 数值不等式numerical integration 数值积分法numerical invariant 不变数numerical mathematics 数值数学numerical method 数值法numerical model 数值模型numerical operator 数字算子numerical quadrature 数值积分法numerical series 数值级数numerical solution 数值解numerical solution of linear equations 线性方程组的数值解法numerical stability 数值稳定性numerical table 数表numerical value 数值numerical value equation 数值方程nutation 章动。

HomogeneousSystems：齐次系统

Homogeneous SystemsAny system of linear equations can be written in matrix form AX=B.The system is called homogeneous,if the constant matrix B=0.X=0is a solution for this system. Any solution which is not equal to zero,is called a non-trivial solution.Example13.The following system is a homogeneous system.x1−2x2+x3+x4=0−x1+2x2+x4=02x1−4x2+x3=0Obviously,x1=0,x2=0,x3=0,x4=0is a solution for this system.We can check that x1=2,x2=1,x3=0,x4=0is also a solution for this system.This solution is a non-trivial solution.Example14.Solve the following homogeneous system.2x+4y+6z=04x+5y+6z=03x+y−2z=0.Solution.The augmented matrix isAG=2460456031−20.By applying elementary operations,we have toﬁnd its reduced row-echelon form.2460456031−2012R1−→12394562431−20R2−4R1,R3−3R1−→12300−3−600−5−110−1 3R2−→123001200−5−110R3+5R2−→1230012000−10−R3−→123001200010.The corresponding system of equation is:x+2y+3z=0y+2z=0z=0.Therefore,the only solution for this system is X=xyz=0.Remark6.There are two possibilities for the set of solutions for a homogeneous system.1.Unique solution X=02.Inﬁnitely many solutionsBasic SolutionsConsider the homogeneous system AX=0.If this system has a nontrivial solutions, then by Gaussian elimination we canﬁnd non-trivial solutions X1,···,X k such that any other solution of the system is in the formt1X1+t2X2+···+t k X k,where t1,···,t k are numbers.X1,···,X k are called basic solutions for the system and a solution of the form t1X1+t2X2+···+t k X k is called a linear combination of X1,···,X k. Example15.Solve the following homogeneous system of linear equations.x+2y+−z=03x+−3y+2z=0−x+−11y+6z=0.Solution.The augmented matrix isAG=12−103−320−1−1160.By applying elementary operations,we have toﬁnd its reduced row-echelon form.12−103−320−1−1160R2−3R1,R3+R1−→12−100−9500−950R3+R2,−19R2−→12−1001−590000R1−2R2−→101901−590000.The corresponding system of equation is:x++19z=0y+−59z=0.Take z=t.Therefore,the solutions are in the formX=xyz=−19t59tt=t−19591.Here,X1=−19591is the basic solution.Example16.Find the basic solutions for the following homogeneous system.x1−2x2+4x3−x4+5x6=0−2x1+4x2−7x3+x4+2x5−8x6=03x1−6x2+12x3−3x4+x5+15x6=02x1−4x2+9x3−3x4+3x5+12x6=0 Solutions:1−24−1050−24−712−803−612−311502−49−33120R2+2R1,R3−3R1,R3−2R1−→1−24−1050001−12200000100001−1320R4−2R2−→1−24−1050001−122000001000000020R4−2R3,R1−4R2−→1−203−8−30001−122000001000000000R1+8R3,R2−2R3−→1−2030−30001−102000001000000000Assign non-leading variables as parameters.Then,x2=t,x4=s,x6=u,x5=0,x3= t−2u,x1=2t−3s+3u.The solutions are:X=x1x2x3x4x5x6=2t−3s+3uts−2usu=2tt+−3sss+3u−2uu=t21+s−311+u3−21.Therefore,the basic solutions are X1=21,X2=−311,X2=3−21.Remark7.Consider a homogeneous system of linear equation with n variables.If the augmented matrix of the system has rank r,then solutions consist of n−r parameters. Thus,we can express any solution as a linear combination of n−r basic solutions.Consider the linear system AX=B.The linear system AX=0is called the associated homogeneous system for the system AX=B.Let Y be a solution for the homogeneous system and X0be a particular solution for the system AX=B.Then,sinceA(X0+Y)=AX0+AY=B+0=B(X0+Y)also is a solution for the system.Conversely,if Z be a solution for the system thenA(Z−X0)=B−B=0.Thus,Y=Z−X0is a solution for the associated system.This shows any solution is in the form X0+Y.Example17.Example18.Solve the following system of equations.x−y−z=22x−y−3z=6x−2z=4.Solution.The augmented matrix isAG=1−1−122−1−3610−24.By applying elementary operations,we have toﬁnd its reduced row-echelon form.1−1−122−1−3610−24R2−2R1,R3−R1−→1−1−1201−1201−12R3−R2−→1−1−1201−120000R2+R1−→10−2401−120000.The corresponding system of equation is:x−2z=4y−z=20=0.z is non-leading variable.Therefore,we assign it as a parameter.If z=t,then the solution has the parametric formx=2t+4y=t+2z=t. In this example the particular solution is X=42and the general solution for theassociated homogeneous system is Y=t211.Example19.Express the solutions of the following system as the sum of particular solution and general solution of the associated homogeneous system.x1−2x2−x3+3x4=12x1−4x2+x3=5x1−2x2+2x3−3x4=4The augmented matrix is:AG=1−2−1312−41051−22−35.Apply elementary operations to get the row-echelon form.1−2−1312−41051−22−35R2−2R1,R3−R1−→1−2−131003−63003−63R3−R2,13R2−→1−2−131001−2100000R1+R2−→1−2012001−2100000.The corresponding system of equations is:x1−2x2+x4=2x3−2x4=10=0 Let x2=t,x4=s.Then,the set of solutions are:X=x1x2x3x4=2+2t−st1+2ss=21+t21+s−121.In this example the particular solution is:21The general solutions for the associated homogeneous system is:t21+s−121.Matrix InversesLet A be a square matrix of size n.A matrix B is called inverse of A ifAB=BA=I.If A has an inverse,then we say that A is invertible.The inverse of A is unique and wedenote it by A−1. Example20.Let A=1101.Then A−1=1−101.Example21.If A=a bc dand ad−bc=0then A−1=1ad−bcd−b−c a.Example22.A=14−1271130.Then,A−1=12−3−31111−3−11−1.Theorem6.If a square matrix A,has a zero row(zero column),then A is not invertible. Proof.Suppose that the i-th row of A is zero.For any square matrix C,the(i,i)-entry of AC is equal to dot product of the i-th row of A with i-th column of C.Therefore,(i,i)-entry of AC is0.But,the(i,i)-entry of identity matrix is equal to1.Thus,AC=I for any C.Therefore,A is notinvertible.Example23.A=112133000099110932and B=10591120951108214021140677are not invertible.Theorem7.If A and B are square matrices,then•If A is invertible,then A−1is invertible,and(A−1)−1=A.•If A and B are invertible,then AB is invertible,and(AB)−1=B−1A−1.•If A is invertible,then A T is invertible,and(A T)−1=(A−1)T.•If A is invertible,then1c A is invertible for a number c=0,and(cA)−1=1cA−1.Example24.A,B,and C are invertible matrices.SimplifyC T B(AB)−1[C−1A T]T.Solution:C T B(AB)−1[C−1A T]T=C T B(B−1A−1)[(A T)T(C−1)T]=C T IA−1[A(C−1)T]=C T I(C−1)T=I.Example25.Find the matrix A.211−23−5A−1T=(−14A T)−1.Solution:211−23T−5(A T)−1=−4(A T)−1Thus,211−23T=(A−1)T.Then,A=1103−121.。

2. Linear Systems of Equations and Gaussian Elimination

(2.2)
amn
The steps of Gaussian elimination are carried out by elementary row operations applied to the augmented matrix. These are:
3
(1) Any row of the matrix may be multiplied throughout by any nonzero number. (2) Any two rows of the matrix may be interchanged. (3) Any multiple of one row may be added to another row.
Linear Algebra and Matrix Theory
Chapter 1 - Linear Systems, Matrices and Determinants
This is a very brief outline of some basic deﬁnitions and theorems of linear algebra. We will assume that you know elementary facts such as how to add two matrices, how to multiply a matrix by a number, how to multiply two matrices, what an identity matrix is, and what a solution of a linear system of equations is. Hardly any of the theorems will be proved. More complete treatments may be found in the following references.

数学专业英语词汇(部分)

数学专业英语词汇（部分）n ary relation n元关系n ball n维球n cell n维胞腔n chromatic graph n色图n coboundary n上边缘n cocycle n上循环n connected space n连通空间n dimensional column vector n维列向量n dimensional euclidean space n维欧几里得空间n dimensional rectangular parallelepiped n维长方体n dimensional row vector n维行向量n dimensional simplex n单形n dimensional skeleton n维骨架n disk n维圆盘n element set n元集n fold extension n重扩张n gon n角n graph n图n homogeneous variety n齐次簇n person game n人对策n simplex n单形n sphere bundle n球丛n th member 第n项n th partial quotient 第n偏商n th power operation n次幂运算n th root n次根n th term 第n项n times continuously differentiable n次连续可微的n times continuously differentiable function n次连续可微函数n tuple n组n tuply connected domain n重连通域n universal bundle n通用丛nabla 倒三角算子nabla calculation 倒三角算子计算nabla operator 倒三角算子napier's logarithm 讷代对数natural boundary 自然边界natural boundary condition 自然边界条件natural coordinates 自然坐标natural equation 自然方程natural equivalence 自然等价natural exponential function 自然指数函数natural frequency 固有频率natural geometry 自然几何natural injection 自然单射natural isomorphism 自然等价natural language 自然语言natural logarithm 自然对数natural mapping 自然映射natural number 自然数natural oscillation 固有振荡natural sine 正弦真数natural transformation 自然变换naught 零necessary and sufficient conditions 必要充分的条件necessary and sufficient statistic 必要充分统计量necessary condition 必要条件necessity 必然性negation 否定negation sign 否定符号negation symbol 否定符号negative 负数negative angle 负角negative binomial distribution 负二项分布negative complex 负复形negative correlation 负相关negative definite form 负定型negative definite hermitian form 负定埃尔米特形式negative definite quadratic form 负定二次形式negative function 负函数negative number 负数negative operator 负算子negative parity 负电阻negative part 负部分negative particular proposition 否定特称命题negative proposition 否定命题negative rotation 反时针方向旋转negative semidefinite 半负定的negative semidefinite eigenvalue problem 半负定特盏问题negative semidefinite form 半负定型negative semidefinite quadratic form 半负定二次形式negative sign 负号negative skewness 负偏斜性negative variation 负变差negligible quantity 可除量neighborhood 邻域neighborhood base 邻域基neighborhood basis 邻域基neighborhood filter 邻域滤子neighborhood retract 邻域收缩核neighborhood space 邻域空间neighborhood system 邻域系neighborhood topology 邻域拓扑neighboring vertex 邻近项点nephroid 肾脏线nerve 神经nested intervals 区间套net 网net function 网格函数net of curves 曲线网net of lines 直线网network 网络network analysis 网络分析network flow problem 网络潦题network matrix 网络矩阵neumann boundary condition 诺伊曼边界条件neumann function 诺伊曼函数neumann problem 诺伊曼问题neumann series 诺伊曼级数neutral element 零元素neutral line 中线neutral plane 中性平面neutral point 中性点newton diagram 牛顿多边形newton formula 牛顿公式newton identities 牛顿恒等式newton interpolation polynomial 牛顿插值多项式newton method 牛顿法newton potential 牛顿位势newtonian mechanics 牛顿力学nice function 佳函数nil ideal 零理想nil radical 幂零根基nilalgebra 幂零代数nilpotency 幂零nilpotent 幂零nilpotent algebra 幂零代数nilpotent element 幂零元素nilpotent group 幂零群nilpotent ideal 幂零理想nilpotent matrix 幂零矩阵nilpotent radical 幂零根基nine point circle 九点圆nine point finite difference scheme 九点有限差分格式niveau line 等位线niveau surface 等位面nodal curve 结点曲线nodal line 交点线nodal point 节点node 节点node locus 结点轨迹node of a curve 曲线的结点noetherian category 诺特范畴noetherian object 诺特对象nomogram 算图nomographic 列线图的nomographic chart 算图nomography 图算法non additivity 非加性non archimedean geometry 非阿基米德几何non archimedean valuation 非阿基米德赋值non countable set 不可数集non critical point 非奇点non denumerable 不可数的non denumerable set 不可数集non developable ruled surface 非可展直纹曲面non enumerable set 不可数集non euclidean geometry 非欧几里得几何学non euclidean motion 非欧几里得运动non euclidean space 非欧几里得空间non euclidean translation 非欧几里得平移non euclidean trigonometry 非欧几里得三角学non homogeneity 非齐non homogeneous chain 非齐次马尔可夫链non homogeneous markov chain 非齐次马尔可夫链non isotropic plane 非迷向平面non linear 非线性的non negative semidefinite matrix 非负半正定阵non oriented graph 无向图non parametric test 无分布检验non pascalian geometry 非拍斯卡几何non ramified extension 非分歧扩张non rational function 无理分数non relativistic approximation 非相对性近似non reversibility 不可逆性non singular 非奇的non stationary random process 不平稳随机过程non steady state 不稳定状态non symmetric 非对称的non symmetry 非对称non zero sum game 非零和对策nonabsolutely convergent series 非绝对收敛级数nonagon 九边形nonassociate 非结合的nonassociative ring 非结合环nonbasic variable 非基本变量noncentral chi squre distribution 非中心分布noncentral f distribution 非中心f分布noncentral t distribution 非中心t分布noncentrality parameter 非中心参数nonclosed group 非闭群noncommutative group 非交换群noncommutative ring 非交换环noncommutative valuation 非交换赋值noncommuting operators 非交换算子noncomparable elements 非可比元素nondegeneracy 非退化nondegenerate collineation 非退化直射变换nondegenerate conic 非退化二次曲线nondegenerate critical point 非退化临界点nondegenerate distribution 非退化分布nondegenerate set 非退化集nondense set 疏集nondenumerability 不可数性nondeterministic automaton 不确定性自动机nondiagonal element 非对角元nondiscrete space 非离散空间nonexistence 不存在性nonfinite set 非有限集nonholonomic constraint 不完全约束nonhomogeneity 非齐性nonhomogeneous 非齐次的nonhomogeneous linear boundary value problem 非齐次线性边值问题nonhomogeneous linear differential equation 非齐次线性微分方程nonhomogeneous linear system of differential equations 非齐次线性微分方程组nonisotropic line 非迷向线nonlimiting ordinal 非极限序数nonlinear equation 非线性方程nonlinear functional analysis 非线性泛函分析nonlinear lattice dynamics 非线性点阵力学nonlinear operator 非线性算子nonlinear optimization 非线性最优化nonlinear oscillations 非线性振动nonlinear problem 非线性问题nonlinear programming 非线性最优化nonlinear restriction 非线性限制nonlinear system 非线性系统nonlinear trend 非线性瞧nonlinear vibration 非线性振动nonlinearity 非线性nonlogical axiom 非逻辑公理nonlogical constant 非逻辑常数nonmeager set 非贫集nonmeasurable set 不可测集nonnegative divisor 非负除数nonnegative number 非负数nonnumeric algorithm 非数值的算法nonorientable contour 不可定向周线nonorientable surface 不可定向的曲面nonorthogonal factor 非正交因子nonparametric confidence region 非参数置信区域nonparametric estimation 非参数估计nonparametric method 非参数法nonparametric test 非参数检定nonperfect set 非完备集nonperiodic 非周期的nonperiodical function 非周期函数nonplanar graph 非平面图形nonprincipal character 非重贞nonrandom sample 非随机样本nonrandomized test 非随机化检验nonrational function 非有理函数nonremovable discontinuity 非可去不连续点nonrepresentative sampling 非代表抽样nonresidue 非剩余nonsense correlation 产生错觉相关nonsingular bilinear form 非奇双线性型nonsingular curve 非奇曲线nonsingular linear transformation 非退化线性变换nonsingular matrix 非退化阵nonspecial group 非特殊群nonstable 不稳定的nonstable homotopy group 非稳定的同伦群nonstandard analysis 非标准分析nonstandard model 非标准模型nonstandard numbers 非标准数nonsymmetric relation 非对称关系nonsymmetry 非对称nontangential 不相切的nontrivial element 非平凡元素nontrivial solution 非平凡解nonuniform convergence 非一致收敛nonvoid proper subset 非空真子集nonvoid set 非空集nonzero vector 非零向量norm 范数norm axioms 范数公理norm form 范形式norm of a matrix 阵的范数norm of vector 向量的模norm preserving mapping 保范映射norm residue 范数剩余norm residue symbol 范数剩余符号norm topology 范拓朴normability 可模性normal 法线normal algorithm 正规算法normal basis theorem 正规基定理normal bundle 法丛normal chain 正规链normal cone 法锥面normal congruence 法汇normal coordinates 正规坐标normal correlation 正态相关normal curvature 法曲率normal curvature vector 法曲率向量normal curve 正规曲线normal density 正规密度normal derivative 法向导数normal dispersion 正常色散normal distribution 正态分布normal distribution function 正态分布函数normal equations 正规方程normal error model 正规误差模型normal extension 正规开拓normal family 正规族normal force 法向力normal form 标准型normal form problem 标准形问题normal form theorem 正规形式定理normal function 正规函数normal homomorphism 正规同态normal integral 正规积分normal linear operator 正规线性算子normal mapping 正规映射normal matrix 正规矩阵normal number 正规数normal operator 正规算子normal order 良序normal plane 法面normal polygon 正规多角形normal polynomial 正规多项式normal population 正态总体normal probability paper 正态概率纸normal process 高斯过程normal sequence 正规序列normal series 正规列normal set 良序集normal simplicial mapping 正规单形映射normal solvable operator 正规可解算子normal space 正规空间normal surface 法曲面normal tensor 正规张量normal to the surface 曲面的法线normal valuation 正规赋值normal variate 正常变量normal variety 正规簇normal vector 法向量normality 正规性normalization 标准化normalization theorem 正规化定理normalize 正规化normalized basis 正规化基normalized function 规范化函数normalized variate 正规化变量normalized vector 正规化向量normalizer 正规化子normalizing factor 正则化因数normed algebra 赋范代数normed linear space 赋范线性空间normed space 赋范线性空间northwest corner rule 北午角规则notation 记法notation free from bracket 无括号记号notation of backus 巴科斯记号notion 概念nought 零nowhere convergent sequence 无处收敛序列nowhere convergent series 无处收敛级数nowhere dense 无处稠密的nowhere dense set 无处稠密点集nowhere dense subset 无处稠密子集nuclear operator 核算子nuclear space 核空间nucleus of an integral equation 积分方程的核null 零null class 零类null divisor 零因子null ellipse 零椭圆null function 零函数null hypothesis 虚假设null line 零线null matrix 零矩阵null method 衡消法null plane 零面null point 零点null ray 零射线null relation 零关系null representation 零表示null sequence 零序列null set 空集null solution 零解null system 零系null transformation 零变换null vector 零向量nullity 退化阶数nullring 零环nullspace 零空间number 数number defined by cut 切断数number defined by the dedekind cut 切断数number field 数域number interval 数区间number line 数值轴number notation 数记法number of partitions 划分数number of repetitions 重复数number of replications 重复数number of sheets 叶数number sequence 数列number set 数集number system 数系number theory 数论number variable 数变量numeration 计算numerator 分子numeric representation of information 信息的数值表示numerical 数值的numerical algorithm 数值算法numerical axis 数值轴numerical calculation 数值计算numerical coding 数值编码numerical coefficient 数字系数numerical computation 数值计算numerical constant 数值常数numerical data 数值数据numerical determinant 数字行列式numerical differentiation 数值微分numerical equality 数值等式numerical equation 数字方程numerical error 数值误差numerical example 数值例numerical function 数值函数numerical inequality 数值不等式numerical integration 数值积分法numerical invariant 不变数numerical mathematics 数值数学numerical method 数值法numerical model 数值模型numerical operator 数字算子numerical quadrature 数值积分法numerical series 数值级数numerical solution 数值解numerical solution of linear equations 线性方程组的数值解法numerical stability 数值稳定性numerical table 数表numerical value 数值numerical value equation 数值方程nutation 章动obelisk 方尖形object 对象object language 对象语言object variable 对象变数objective analysis 客观分析objective function 目标函数oblate ellipsoid 扁椭面oblate spheroid 扁椭面oblique angle 斜角oblique angled 斜角的oblique astroid 斜星形线oblique circular cone 斜圆锥oblique circular cylinder 斜圆柱oblique cone 斜圆锥oblique coordinate system 斜角坐标系oblique coordinates 斜角坐标oblique parallelepiped 斜六面体oblique prism 斜棱柱oblique pyramid 斜棱锥oblique strophoid 斜环诉oblique triangle 斜三角形observable 可观测的observable component 可观测分量observation 观测observation function 观测函数observational error 观测误差observer 观察器观测员obstruction 障碍obstruction cocycle 障碍闭上链obstruction theory 障碍理论obstruction to lifting f 提升的障碍obtuse 钝的obtuse angle 钝角obtuse triangle 钝角三角形octagon 八角形octahedral 八面体octahedral form 八面体形式octahedral group 八面体群octahedron 八面体octal digit 八进制数字octal notation 八进记数法octal system 八进制系octant 卦限octuple 八倍的odd 奇的odd dimensional space 奇维空间odd even check 奇偶校验odd function 奇函数odd number 奇数odd parity 负电阻odd permutation 奇置换oddness 奇数性omega consistent 相容性omega group 群one address 单地址one address instruction 单地址指令one digit 单位的one dimensional 一维的one dimensional boundary value problem 一维边值问题one dimensional differential equation 一维微分方程one dimensional integral 单积分one dimensional space 一维空间one figure 单位的one figure number 单位数one parameter 单参数的one parameter family of curves 曲线的单参数族one place number 单位数one place predicate calculus 一元谓词演算one point compactification 单点紧化one point set 退化集one point union 一点并one sample method 单样本法one sided 单侧的one sided continuity 单侧连续性one sided derivative 单边导数one sided differentiability 单侧可微性one sided limit 单侧极限one sided lower approximate limit 单侧下近似极限one sided surface 单侧曲面one sided test 单侧检验one sided upper approximate limit 单侧偏大近似极限one term 单项的one to many correspondence 一对多对应one to many mapping 一对多映射one to one 一对一的one to one correspondence 一一对应one to one mapping 一一映射one to one relation 一一关系one to one sequence 一一序列one valued 单值的one valued function 单值函数onevaluedness 单值性onto hpmpmprphism 满射同态onto mapping 满射open ball 开球open base 开底open cover 开覆盖open disk 开圆盘open interval 开区间open manifold 开廖open map 开映射open mapping theorem 开映射定理open neighborhood 开邻域open ordered set 开有序集open parallelepiped 开平行六面体open rectangular parallelepiped 开长方体open relation 开关系open segment 开线段open semicircle 开半圆open set 开集open sphere 开球open star 开星形open subprogram 开型子程序open subroutine 开型子程序open surface 开曲面operand 运算对象operating characteristic 运算特征operating system 控制系统operation 运算operation code 操纂operation of symmetric difference 对称差运算operational 运算的operational amplifler 运算放大器operational calculus 算子演算operational code 操纂operational research 运筹学operational unit 运算部件operations research 运筹学operator 算子operator algebra 算子代数operator automorphism 算子同构operator domain 算子域operator equation 算子方程operator function 算子函数operator homomorphism 算子同态operator isomorphism 算子同构operator method 符号法operator norm 算子范数operator of finite rank 有限秩算子operator set 算子域operator valued function 算子函数oppose 反对opposite 逆的opposite angles 对角opposite category 对偶范畴opposite sides 对边opposite sign 导号opposite vector 反向向量opposite vertex 对顶opposition 对立optimal 最佳的optimal control 最优控制optimal disjunctive normal form 最优析取范式optimal normal form 最优标准形optimal policy 最优策略optimal position 最优位置optimal process 最优过程optimal step size 最优步长optimal strategy 最优策略optimal trajectory 最优轨道optimal value function 最优值函数optimality 最优性optimality criterion 最优性判别optimality policy 最优策略optimality principle 最优性原理optimalization problem 最优化问题optimally useful direction 最优可用方向optimization 最优化optimization of scheduling 工序的最优化optimization problem 最优化问题optimum 最佳optimum conditions 最优条件optimum programming 最优规划optimum solution 最优解optimum strategy 最优策略optimum system 最佳系统optimum system control 最佳系统控制optimum value 最优值optional sampling 任意抽样optional selection 任意抽样orbit 轨道orbit curve 轨道曲线orbit determination 轨道计算orbit space 轨道空间orbital stability 轨道稳定性order 次数order bounded set 有序有界集order boundedness 有序有界性order code 指令码order complete set 有序完全集order continuous topology 有序连续的拓扑order convergence 有序收敛order function 序函数order homomorphic group 序同态群order homomorphic image 序同态象order homomorphism 序同态order homomorphism operator 序同态算子order interval 有序区间order isomorphic field 序同构域order isomorphic group 序同构群order of a differential equation 微分方程的阶order of a group 群的阶order of an infinitesimal 无穷小的阶order of approximation 逼近的阶order of branch point 支点的阶数order of contact 接触度order of convergence 收敛的阶order of infinities 无穷大的阶order of infinity 无穷大的阶order of magnitude 绝对值的阶order of polynomial 多项式的阶order of rational integral function 有理整函数的阶order of units 位数order of zero point 零点的阶order preserving correspondence 保序对应order preserving isomorphism 保序同构order register 指令寄存器order relation 序关系order simple group 序单群order statistic 顺序统计量order type 有序型ordered 有序的ordered chain complex 有序链复形ordered factor group 有序商群ordered field 有序域ordered group 有序群ordered linear space 有序线性空间ordered module 有序模ordered pair 序对ordered product 有序积ordered sample 有序样本ordered set 有序集ordered set bounded below 下有界有序集ordered simplex 有序单形ordered singular boundary 有序奇异边界ordered triplet 有序三个一组orderisomorphism 序同构orderpreserving relation 保序关系ordinal 序数ordinal number 序数ordinal number class 序数类ordinal number of the second class 第二类的序数ordinal product 序数积ordinal series 序数列ordinal type 有序型ordinary 导常的ordinary differential equation 常微分方程ordinary differential operator 常微分算子ordinary dirichlet series 狄利克雷级数ordinary integral element 寻常积分元素ordinary linear differential equation 线性常微分方程ordinary multiple point 寻常多重点ordinary point 单点ordinary singularity 寻常奇点ordinate 纵坐标ordinate axis 纵轴orient 定向orientability 可定向性orientable 可定向的orientable surface 可定向曲面orientation 定向orientation class 定向类orientation of surface 曲面的定向orientation of torsion 挠率的定向orientation preserving automorphism 保持定向自同构orientation preserving isomorphism 保持定向同构orientation preserving parameter transformation 保持定向参数变换orientation reversing 反转定向的oriented chain complex 有向链复形oriented circle 有向圆oriented contour 有向围道oriented element 有向元oriented homology group 有向同岛oriented intersection 有向交叉oriented line 有向直线oriented plane 有向平面oriented polygon 有向多角形oriented space 有向空间oriented sphere bundle 有向球丛oriented surface 有向曲面origin 坐标的原点origin of coordinates 坐标的原点original 初始的ortho pinacoid 正交平行双面orthocenter 垂心orthocentric 垂心的orthocentric quadrangle 垂心四边形orthocentric tetrahedron 垂心四面体orthocomplement 正交补orthogonal 直交的orthogonal axonometry 正轴测射影法orthogonal basis 正交基orthogonal circle 正交圆orthogonal complement 正交补orthogonal coordinate system 正交坐标系orthogonal coordinates 正交坐标orthogonal decomposition 正交分解orthogonal expansion 正交函数展开orthogonal functions 正交函数orthogonal groups 正交群orthogonal involution 正交对合orthogonal matrix 正交矩阵orthogonal polynomial expansion 正交多项式展开orthogonal polynomials 正交多项式orthogonal projection 正射影orthogonal projector 正交射影算子orthogonal sequence 正交序列orthogonal series 正交级数orthogonal space 正交空间orthogonal square 正交方格orthogonal stochastic process 正交随机过程orthogonal subspaces 正交子空间orthogonal substitution 正交代换orthogonal sum 正交和orthogonal system 正交系orthogonal tests 独立检验orthogonal trajectory 正交轨线orthogonal transformation 正交变换orthogonal vectors 正交向量orthogonality 正交性orthogonality of columns 列正交性orthogonality of lines 行正交性orthogonality relation 正交关系orthogonality rows 行正交性orthogonalization procedure 正交化过程orthogonalization process 正交化过程orthogonally irreducible representation 正交不可约表示orthography 正投影法orthoheliotropism 直向阳性orthohexagonal 正六方的orthomorphism 正交射orthonormal 规格化正交的orthonormal basis 标准正交基orthonormal sequence 标准正交序列orthonormality 标准正交性orthonormalization 标准正交化orthonormalization process 标准正交化过程orthonormalized basis 标准正交化基orthopole 正交极orthotomy 面正交性oscillate 振动oscillating divergent series 振动发散级数oscillating infinite determinant 振动无穷行列式oscillating series 振荡级数oscillation 振动oscillation equation 振动方程oscillation function 振动函数oscillation of a function 函数的振幅oscillation theorem 振动定理oscillatory 振动的osculating circle 密切圆osculating cone 密切锥面osculating conic 密切二次曲线osculating curve 密切曲线osculating figure 密切图形osculating helix 密切螺旋线osculating parabola 密切抛物线osculating plane 密切平面osculating quadric 密切二次曲面osculating sphere 密切球面osculation 密切osculatory 密切的outdegree 出度outer 外部的outer automorphism 外自同构outer boundary 外边界outer capacity 外容量outer diameter 外径outer direct product 外直积outer lebesgue measure 勒贝格外测度outer measure 外测度outer point 外点outer product 外积outer semidirect product 外半直积output 输出output alphabet 输出字母表output device 输出装置output function 输出函数output quantity 输出量output signal 输出信号output state 输出状态output unit 输出设备outside 外部outward normal 外法线oval 卵形线oval surface 卵形曲面overconvergence 过度收敛overcrossing point 上交叉点overdetermined problem 超定问题overdetermined system 超定组overdetermined system of partial differential equations 偏微分方程的超定组overfield 扩张域overflow 溢出overidentification 过分识别overlap 交叠overlapping domains 交叠域overrelaxation 超松弛p adic algebra p进代数p adic fraction p进分数p adic integer p进整数p adic number p进数p adic representation p进表示p adic system p进法p adic valuation p进赋值pack 束pair 对paired comparison 成对比较法paired samples 成双样本pairing 配对pairwise 两两的pairwise independent events 互相独立事件paleogeometry 古几何学pantograph 比例画器放大器parabola 抛物线parabola of order n n阶抛物线parabolic coordinates 抛物线坐标parabolic curve 抛物曲线parabolic cusp 抛物尖点parabolic cylinder 抛物柱面parabolic cylinder function 抛物柱面函数parabolic differential equation 抛物型微分方程parabolic folium 抛物叶形线parabolic orbit 抛物线轨道parabolic point 抛物点parabolic regression 抛物回归parabolic segment 抛物线段parabolic spiral 抛物螺线parabolic type 抛物型parabolograph 抛物图形paraboloid 抛物面paraboloid of revolution 回转抛物面paraboloidal coordinates 抛物面坐标paracompact space 仿紧空间paradox 悖论paradoxical 荒谬的paradoxical set 不合理集合parallactic displacement 视差位移parallel 平行线parallel algorithm 并联算法parallel angle 平行角parallel axiom 平行公理parallel body 平行体parallel circle 平行圆parallel coordinates 平行坐标parallel curve 平行曲线parallel displacement 平行位移parallel edge 平行棱parallel line 平行线parallel operation 并行运算parallel plane 平面平行的parallel projection 平行射影parallel rule 平行直尺parallel shift 并行进位parallel slit 平行缝隙parallel slit domain 平行裂纹域parallel strip 平行带parallel subspace 平行子空间parallel surface 平行曲面parallel translation 并行进位parallelepiped 平行六面体parallelepipedal neighborhood 平行六面体邻域parallelism 平行parallelizability 可平行性parallelizable 可平行的parallelizable manifold 可平行廖parallelizable variety 可平行廖parallelogram 平行四边形parallelogram axiom 平行四边形公理parallelogram identity 平行四边形恒等式parallelogram law 平行四边形定律parallelogram of forces 力的平行四边形parallelotope 超平行体parallels of latitude 纬度线parameter 参数parameter curve 参数曲线parameter group 参数群parameter integral 参数积分parameter representation 参数表示parameter space 参数空间parameter variety 参数簇parametric curvature 参数曲率parametric curve 参数曲线parametric equation 参数方程parametric estimation 参数估计parametric hypothesis 参数假设parametric optimal solution 参数最优解parametric optimization 参数最优化parametric programming 参数规划parametric representation 参数表示parametric surface 参数曲面parametric test 参数检验parametric variable 参变数parametrics 参数学parametrix 拟基本解parametrization 参数化法parametron 变参数元件parastatistics 仲统计法paraxial 旁轴的paraxial rays 旁轴光线parent population 母体parenthesis 圈括弧parenthesize 引入括弧内parity 奇偶性parity check 奇偶校验parity digit 奇偶校验位parseval equality 帕谢互尔等式parted hyperboloid 双叶双曲面partial 部分的partial carry 部分进位partial confounding 部分混区partial correlation 偏相关partial correlation coefficient 偏相关系数partial cross section 部分截面partial denominator 偏分母partial derivative 偏导数partial difference 偏差partial difference equation 偏差分方程partial difference quotient 偏差商partial differential 偏微分partial differential coefficient 偏导数partial differential equation 偏微分方程partial differential equation of elliptic type 椭圆型偏微分方程partial differential equation of first order 一阶偏微分方程partial differential equation of hyperbolic type 双曲型偏微分方程partial differential equation of mixed type 混合型偏微分方程partial differential equation of parabolic type 抛物型偏微分方程partial differential operator 偏微分算子partial differentiation 偏微分法partial fraction 部分分数partial fraction decomposition 部分分数展开partial fraction expansion 部分分数展开partial function 部分函数partial functor 部分函子partial graph 部分图partial linear differential equation 线性偏微分方程partial mapping 部分映射partial matrix 子阵partial numerator 偏分子partial ordering 偏序partial product 部分积partial rank correlation coefficient 偏等级相关系数partial recursive function 部分递归函数partial recursive scheme 部分递归格式partial regression 偏回归partial subgraph 部分子图partial sum 部分和partially adjoint operator 部分伴随算子partially computable function 部分可计算的函数partially differentiable function 可偏微函数partially isometric operator 部分等距算子partially ordered set 半序集partially ordered space 半序空间particular 特别的particular integral 特别积分particular solution 特解partition 分划partition function 分折函数partition of an integer 整数的分拆partition of unity 单位分解partition problem 划分问题partly well ordered set 半良序集pascal distribution 帕斯卡分布pascal hexagon 帕斯卡六边形pascal line 帕斯卡线pascal triangle 帕斯卡三角形passive 被动的path 道路path component 道路连通区path connected space 道路连通空间path matrix 道路矩阵path of a projectile 弹道path of integration 积分路线path space 道路空间pathological function 病态函数pattern 图形pauli matrices 泡利阵payoff 支付payoff function 支付函数payoff matrix 支付阵peak 峰pearson distribution 皮尔逊分布pedal 垂足线pedal circle 垂足圆pedal curve 垂足线pedal surface 垂足曲面pedal transformation 垂足变换pedal triangle 垂足三角形peirce decomposition 皮尔斯分解penalty function 罚函数penalty method 补偿法pencil 束pencil of circles 圆束pencil of conics 二次曲线束pencil of curves 曲线束pencil of lines 线束pencil of parallel lines 平行线束pencil of planes 面束pencil of spheres 球束pendulum 摆pentad 拼五小组pentadecagon 十五边形pentagon 五角形pentagonal number 五角数pentagonal pyramid 五角锥pentagram 五角星pentahedron 五面体pentaspherical coordinates 五球坐标percent 百分率percent error 百分误差percentage 百分率percentile 百分位数perfect cube 完全立方perfect field 完全域perfect form 完全型perfect group 完全群perfect information 完全信息perfect magic square 完全幻方perfect mapping 完全映射perfect matching 全匹配perfect number 完全数perfect number of the second kind 第二类完全数perfect set 完备集perfect space 完全空间perfect square 完全平方perfectly normal space 完全正规空间perigon 周角perimeter 周围period 周期period matrix 周期矩阵period of a function 函数的周期period of oscillation 振荡的周期period relations 周期关系式period strip 周期带periodic 周期的periodic distribution 周期广义函数periodic element 周期元素periodic error 周期误差periodic function 周期函数periodic group 周期群periodic law 周期律periodic motion 周期运动periodic orbit 周期轨道periodic solution 周期解periodic system 周期系periodical decimal fraction 循环十进小数periodicity 周期性periodicity interval 周期性区间periodicity of function 函数的周期性periodogram 周期图periodogram analysis 周期图分析periodograph 周期图periodparallelogram 周期平行四边形peripheral 周边的peripheral device 外围设备peripheral unit 外围设备periphery 周边permanently convergent series 永久收敛级数permissible error 容许误差permissible function 容许函数permissible value 容许值permutation 置换。

线代重点词汇

Chapter 1Equation 方程Coefficient matrix 系数矩阵Augmented matrix 增广矩阵Consistent inconsistent （不）相容（Reduced）echelon form （简化）阶梯型Equivalent 等价的Pivot 主元Basic （free）variable 基本（自由）变量General solution 通解If and only if 充分必要Parametric 参数Scalar multiple 数乘Geometric description 几何描述Linear combination 线性组合Weight 权值Subset 子集Span = generate 张成Corresponding 对应的Identity matrix 单位矩阵（non）homogeneous linear system （非）齐次线性方程组（non）Trivial solution （非）平凡解Parallel 平行Linear （in）dependent 线性（无）相关Linear transformation 线性变换Map 映射Domain 定义域Codomain 余定义域Image 像Range 值域Shear transformation 错切变换Stander matrix 标准矩阵Reflection through the x1-axis 沿着x1轴翻转Horizontal （vertical）contraction and expansion 水平（垂直）方向收缩和放大Horizontal （vertical）shear 水平（垂直）方向作错切变换Projection onto the x1-axis 投影在x1轴上Onto 满射（映上）One-to-one 单射Chapter 2Diagonal matrix 对角矩阵Square matrix 方阵Power 幂Transpose 转置Reverse order 反序Invertible matrix = nonsingular 可逆矩阵=非奇异矩阵Inverse 逆Singular matrix 奇异矩阵Determinant （det）行列式Elementary matrix 初等矩阵Partition （block）matrix 分块矩阵Conformable 一致的Outer product 外积Upper triangular matrix 上三角阵Factorization 分解Homogeneous coordinates 齐次坐标Composite transformation 组合变换Perspective projection 透视变换Subspace 子空间Property 特性Column space 列空间Null space 零空间Basis 基Isomorphism 同构Dimension 维Rank 秩Chapter 3Cofactor 余因子Cramer's rule 克拉默法则The Adjugate（classical adjiont）of A A的伴随矩阵Area 面积Volume 体积Parallelogram 平行四边形Parallelepiped 平行六面体Unit disk 单位圆Quadrant 象限Chapter 4Polynomial 多项式Isomorphism 同构（in）Finite-dimensional （无）有限维Chapter 5Eigenvalue 特征值Eigenvector 特征向量Eigenspace 特征空间Multiplicity （根的）重数Characteristic polynomial 特征多项式Similarity 相似性Diagonalization 对角化Distinct 不同的Complex 复数Chapter 6Orthogonality 正交性Inner （dot）product 内积，点乘Length 长度（模）= norm 范数Normalizing 单位化Orthogonal complement 正交补Orthogonal set （basis）正交集（基）Orthonormal set（bases）单位（标准）正交集Orthogonal matrix 正交矩阵Best approximation 最佳逼近Least-squares 最小二乘The normal equation 法方程Least-squares error 最小二乘误差Chapter 7Symmetric matrix 对称矩阵Arbitrary 随机的Orthogonally diagonalizable 正交对角化The spectral theorem 谱定理Spectral decomposition 谱分解Quadratic form 二次型Cross-product 交叉型Principal axes 主轴Positive definite 正定的Negative definite 负定的Indefinite 不定的。

中山大学~线性代数期末总复习

Step3 Use row replacement operations to create zeros in all
positions below the pivot. Step4 Apply steps 1-3 to the submatrix that remains. Repeat the
process until there are no more nonzero rows to modify.
inconsistent
consistent
｝ 3. Infinitely many solutions.
§1.1 Systems of Linear Equations

Solving a Linear System

Elementary Row Operations 1. (Replacement) Replace one row by the sum of itself and a
1. Is the system consistent; that is, does at least one solution exist?
2. If a solution exists, is it the only one; that is, is the solution unique?
§1.2 Row Reduction and Echelon Forms
Each matrix is row equivalent to one and only one reduced echelon matrix.
§1.2 Row Reduction and Echelon Forms

The Row Reduction Algorithm

材料力学总结

材料力学总结材料力学名词解释及填空名词解释1、Stress(应力)the force per unit area , or intensity of the force distributed over a given section, is called stress. σ=F/A2、normal stress(正应力)The internal force is therefore normal to the plane of the section and the corresponding stress is described as the normal stress.3、Shearing stress(剪应力)The internal force is the shear on the plane of the section and the corresponding stress is described as the shearing stress.4、Linear Strain(应变)The normal strainεin a member can be defined as the deformation of the meter of the per unit length.5、The main objective of the study the mechanics of materials（材料力学的任务）is to provide the future engineer with the means of analyzing and designing various machines and loading-bearing structures.6、Saint-venant’s principle（圣维南原理）For two sets of statically equivalent forces, except in the immediate vicinity of the points of application of the loads, the stress distribution may be assumed independent of the actual mode of application of the loads (this statement is not only to axial load, but to practically any type of load)7、Work-energy principle(功能原理)The Work-energy Principle: In the process of the deformation of a elastomer, the strain energy which is stored in elastomer is equal to the work of the external force in number. This is the Work-energy Principle and it can be represented as Vε=W.8、effective length （有效长度）is defined as real length multiplied by factor of length9、principle plane(主平面)is the plane in which the shearing stress equals zero, and normal stresses achieve maximum or minimum.Principle stress(主应力)The normal stress which is exerted on the principle plane is called the principle stress.10、Radius of radius of gyration【revolution】（惯性半径）of an area can be calculated by the following formula i=I/AWhere i =the moment of inertia of an areaA=the area of an cross section11、isotropic materials （各向同性材料）are the materials whose elastic constants are independent of direction.12、homogeneous materials （均匀性材料）are the materials whose elastic properties are the same everywhere.13、The strain energy density(应变能密度)The strain energy in the unit volume can be defined as the strain energy density.14、Hooke’s law （胡克定律）may be expressed more fully by saying that1】when the stress increases,the measured strain increases in the same ratio2】when the stress diminishes, the measured strain diminishes in the same ratio3】when the stress is removed, no strain can be measuredFor a small deformation,the stress is directly proportional to the strain.15、Hooke’s law for shearing stress(剪切胡克定律)The relation τ=Gγis known as Hooke’s law for shearing stress. Strain and constant Gis called the modulus of rigidity or shear modulus of material.16、Generalized Hooke’s law（广义胡可定律）17、Poisson ratio (泊松比)is defined as the ratio of lateral contraction (strain) to longitudinal extension (strain) of a bar under terminal tension.18、factor of safety （安全因数）ultimate load over allowable load19、stress-concentration factor k（应力集中因数K）=maximum stress over average stress20、statically indeterminate problem（静不定问题）is the problem in which the reactions and internal forces can not be determined by staticonly , analysis of deformation is needed.21、neutral surface（中性层）is defined as the surface between the top and bottom of a beam in which longitudinal line do not change.22、Neutral axis （中性轴）①The neutral surface intersects a transverse section along a straight line called the neutral axis of the section.②The intersection of the neutral surface with a transverse section is called the neutral axis of the section.23、principle of superposition（叠加原理）for all linear systems (a beam can be modeled as a linear system ),24、the quantity the term λ=μl /i (柔度) is known as the slenderness ratio of the column. Where μl= effective lengthi= the radius of gyration25、The theory of strength(强度理论)The assumption concerning the damage or the losing effect of the material is called the theory of strength.26、buckling (失稳)A stage when the column suddenly becomes sharply curved instead of remaining straight as the load is applied is called buckling.27、The critical force (临界压力)The value of the compressive force which is right on the boundary between the stable balance and the unstable balance is called the critical force.28、The critical stress (临界应力)The corresponding stress of the critical force is described as the critical force.29、Euler’s Formula (欧拉公式)Euler’s Formula can be expressed asFcr=π²EI／le²in which: Fcr denotes the critical loadE denotes the modulusI denotes the minimum moment of inertia of areale denotes the equivalent length30、Assumption for a bar (拉压的平面假设) The hypothesis assumes that the section keeps being a plane after deformation.31、Assumption for torsion (扭转平面假设) When a circular shaft is subjected to a torsion, every cross section remains plane and undamaged.32、Assumption for bending (弯曲平面假设) Under bending, the cross section of the beam remains plane and has a constant curvature. And the new cross section still perpendicular to axis.32、极惯性矩The polar moment of inertia of an area is defined as the polar moment of inertia of an area with respect to a point as the integral Ip=∫ρ²dA33、惯性矩The moment of inertia of an area is defined as the second moment of the area with respect to an axis as the integral I=∫y²dA.34、静矩The static moment of an area is defined as the first moment of an area with respect to an axis as the integral Sz=∫ydA.填空题1 三个材料假设Homogeneousity assumption 、Continuity assumption 、Isotropy assumption2 三个关系Geometric relation 、Physical relation、Equilibrium relation3 限制梁挠度的三个条件Boundary condition 、Constraint condition、Continuity condition4 三种约束方式1）固定端fixed end2）固定铰支座fixed support of pin joint3）可动铰支座roller support of pin joint5 三种梁1）简支梁simply supported beam2）外伸梁overhang beam3）悬臂梁cantilever beam6 For perfect column, the factor of length for conditions both pinned; both fixed; one fixed the other free; one fixed the other pinned are 1、0.5、2、0.7 respectively.7 The four classic strength theories include maximum tensile stress theory、maximum elongated normal strain theory、maximum shearing stress theory and maximum distortional strain energy theory.8 The tensile diagram of low carbon steel consist of four stages: elastic stage 、yielding stage、hardening stage and necking stage.。

完整word版线性代数课程专业词汇表

线性代数课程专业词汇表英文单词或词组中文翻译书中出现页码Linear equation 线性方程 1Linear system(s) 线性方程组 1Consistent 有解 2Inconsistent 无解 2Solution set of linear system 线性方程组的解集合 2Equivalent systems 等价的线性方程组 3Row operations 行变换 5Strict triangular form 严格三角形式 5Back substitution 回代法 6Equivalent systems 等价的线性方程组 6Coefficient matrix 系数矩阵 7Coefficient matrix 系数矩阵 7Augmented matrix 增广矩阵 8Pivot 主元 8Free variables 自由未知量 14Lead variables 前变量 14Gaussian elimination 高斯消元法 15Overdetermined linear system 方程个数超过未知数个数的方程组 15 Row echelon form 行阶梯形 15Underdetermined linear system 方程个数低于未知数个数的方程组 17 Gauss-Jordan reduction 高斯-若当归纳法 18Reduced row echelon form 减少的行阶梯形 18Homogeneous linear system 齐次线性方程组 22Homogeneous system 齐次线性方程组 22nontrivial solution 非零解 22Trivial solution 平凡解，全零解 22Matrix algebra 矩阵代数 30Scalars 常数 30Column vector(s) 列向量 31Euclidean n-space 欧几里得空间 31Row vector(s) 行向量 31Vector(s）向量 31Addition of matrices 矩阵加法 32Addition of matrices 矩阵加法 32Equality of matrices 矩阵相等 32Scalar multiplication for matrices 矩阵的数乘 32Scalar multiplication of matrices 矩阵的数乘 32Zero matrix 零矩阵 33Scalar product 内积 34Linear combination 线性组合 36Consistency Theorem 解的存在性定理 3738矩阵乘法Multiplication of matrices Identity matrix 单位矩阵 47Inverse matrix 逆矩阵 48Invertible matrix 可逆矩阵 48 Nonsingular matrix 非奇异矩阵 48 Singular matrix 奇异矩阵 49 Transpose of a matrix 矩阵的转置 49 Transpose of matrix 矩阵的转置 49 Symmetric matrix 对称矩阵 51 Symmetric matrix 对称矩阵 51 Adjacency matrix 邻接矩阵 52Graph(s) 图 52Angle between vectors 向量的夹角 56 Markov chain(s） Markov链 57 Elementary matrix 初等矩阵 62Row equivalent 行等价 64Row equivalent matrices 行等价矩阵 64 Diagonal matrix 对角矩阵 67Lower triangular 下三角 67Triangular factorization 三角分解 67 Triangular matrix 三角形矩阵 67 Triangular matrix 三角形矩阵 67 Upper triangular 上三角 67Upper triangular matrix 上三角矩阵 67 LU factorization LU分解 68Matrix factorizations 矩阵分解 68 Partitioned matrices 分块矩阵 72 Vandermonde matrix 范德蒙矩阵 72 Block multiplication 分块乘法 74 Inner product 内积 78Determinant(s) 行列式 90Cofactor 代数余子式 93Minor 余子式 93Cofactor expansion 代数余子式展开 94 Determinant of matrix 矩阵的行列式 95 Skew symmetric 反对称 105Adjoint of a matrix 伴随矩阵 106 Cramer's rule 克莱姆法则 107 Cryptography 密码学 108Addition of vectors 向量的加法 119 Closure properties 封闭性 119Vector space 向量空间 119Zero vector 零向量 119C[a,b] 区间[a,b]上的连续函数 120123向量空间的同构Isomorphism between vector spaces Subspace(s) 子空间 123Zero subsapce 零空间 125Nullspace 零化空间 127Nullspace of matrix 矩阵的零化空间 127Span 张成 128Spanning set 生成集 129Linearly dependent 线性相关 136Linearly independent 线性无关 136Basis 基 145Dimension 维数 147Finite dimensional 有限维 147Infinite dimensional 无限维 147Standard basis 标准基 150change of basis 基的变换 151Coordinate vector 坐标向量 152Transition matrix 过渡矩阵 155Coordinates 坐标 157Column space 列空间 162Column space of matrix 矩阵的列空间 162Rank of a matrix 矩阵的秩 162Rank of matrix 矩阵的秩 162Row space 行空间 162Row space of matrix 矩阵的行空间 162Nullity 零化度 164Rank-Nullity Theorem Rank-Nullity定理 164Left inverse 左可逆 170Right inverse 右逆 170Full rank 满秩 171Linear transformation(s) 线性变换 175Linear operator 线性算子 176Image 象 181Kernel 核 181Contraction 收缩 192Dilation 扩张 192Similarity 相似性 199Similar matrices 相似矩阵 202Trace 迹 206Angle between vectors 向量的夹角 211Euclidean length 欧几里得长度 211Distance in 2-space 2维空间的距离 212Cauchy-Schwarz inequality 柯西-施瓦兹不等式 213Orthogonality 正交性 213Scalar projection 数量投影 214215平面方程equation of planeNonmal vector 正规向量 215Angle between vectors 向量的夹角 216Pythagorean Law Pythagorean 定理 216Correlations 相关 219Correlation matrix 相关矩阵 221Covariance 协方差 222Covariance matrix 协方差矩阵 222Factor analysis 因子分析 222Fundamental subspaces 基本子空间 227Range of a matrix 矩阵的值域 227Direct sum 直和 229Least squares problem(s) 最小二乘法问题 234Projection onto column space 列空间上的投射 236 Normal equations 正规方程 237Inner product space 内积空间 245Length in inner product spaces 内积空间中的长度 246 Orthogonal set(s) 正交集合 255Orthonormal set(s) 标准正交集 255orthonormal basis 标准正交基 256Orthonormal basis 标准正交基 256Orthogonal matrices 正交矩阵 258Orthogonal matrix 正交矩阵 258Approximation of functions 函数的逼近 264Fourier coefficients 傅里叶系数 266Fourier matrix 傅里叶矩阵 269Gram-Schmidt process Gram-Schmidt过程 274Dimension Theorem 维数定理 283Orthogonal polynomials 正交多项式 283Hermite polynomials Hermite 多项式 287Jacobi polynomials Jacobi多项式 287Lagrange's interpolating formula Lagrange 插值公式 288 Gaussian quadrature 高斯求积 289Characteristic value(s) 特征值 301Characteristic vector 特征向量 301Eigenvalue 特征值 301Eigenvector 特征向量 301Characteristic equation 特征方程 302Characteristic polynomial 特征多项式 302Eigenspace 特征空间 302Nilpotent 幂零的 311Companion matrix 友矩阵 313Linear differential equations 线性微分方程 313Initial value problems 初值问题 314326可对角化的矩阵Diagonalizable matrixDistance in n-space n维空间的距离 332Complex matrix 复矩阵 346Hermite matrix Hermite 矩阵 346Unitary matrix 酉矩阵 347Unitary matrix 酉矩阵 347Normal matrices 正规矩阵 351Singular values 奇异值 356Conic sections 二次曲线部分 371Quadratic equation in n variables n个变量的二次方程 376 Quadratic form in n variables n个变量的二次型 376 Definite quadratic form 定二次型 378Indefinite quadratic form 不定二次型 378Negative definite matrix 负定矩阵 378Negative definite quadratic form 负定二次型 378 Negative semidefinite matrix 半负定矩阵 378Negative semidefinite quadratic form 半负定二次型 378 Positive definite matrix 正定矩阵 378Positive definite quadratic form 正定二次型 378Positive semidefinite matrix 半正定矩阵 378Positive semidefinite quadratic form 半正定二次型 378 Local maximum 极大值 382Local minimum 极小值 382Positive definite matrix 正定矩阵 384Leading principal submatrix 顺序主子矩阵 385 Nonnegative matrix 非负矩阵 392Nonnegative vector 非负向量 392Positive matrix 正矩阵 392Positive matrix 正矩阵 392Reducible matrix 可约矩阵 394Frobenius theorem Frobenius 定理 395Absolute error 绝对误差 411Relative error 相对误差 411Back substitution 回代法 419QR factorization QR分解 448。

linear transform

• Let v = (s, t) Then
and so
3. LINEAR TRANSFORMATIONS AND MATRICES
2
T
= (s, t) = (t, s, 1 + t + s) = (rs, rt) = (rt, rs, 1 + rs + rt) = r (t, s, 1 + t + s) = r ( ) does not preserve scalar multiplication: hence it is not a linear transformation.
T (r1 v1 + r2 v2 + · · · + rk vk ) = r1 T (v1 ) + r2 T (v2 ) + · · · + rk T (vk )
transformation.
Example 11.2. Show that the transformation T :
R2
1
→ R3 : (s, t) → (t, s, 1 + t + s) is not a linear
1 1 1
A = [T (e1 ) , T (e2 )] = Ax =
1 1
−1
1 0

We conﬁrm
−1
1 0
x1
x2
x1 − x2 = x1 + x2 = Tx
x1
3. LINEAR TRANSFORMATIONS AND MATRICES
3 n x∈R n x∈R
= {y ∈ Rm | y = T (x) , for some x ∈Rn } = {y ∈ Rm | y = Ax , for some x ∈Rn } = column space of A Note also that the dimension n of the domain Rn of T is same as the number of column in the corresponding matrix A. Now from Theorem 10.6 of Lecture 10 we know (number of columns of A) = (dimension of null space of A) + (dimension of column space of A) In terms of notions of linear transformations this translates to (dimension of domain of T) = (dimension of kernel of T) + (dimension of range of T)

线性代数英文单词

线性代数英语词汇大集合========================================================================= Aadjont(adjugate) of matrix A A 的伴随矩阵augmented matrix A 的增广矩阵Bblock diagonal matrix 块对角矩阵block matrix 块矩阵basic solution set 基础解系CCauchy-Schwarz inequality 柯西- 许瓦兹不等式characteristic equation 特征方程characteristic polynomial 特征多项式coffcient matrix 系数矩阵cofactor 代数余子式cofactor expansion 代数余子式展开column vector 列向量commuting matrices 交换矩阵consistent linear system 相容线性方程组Cramer's rule 克莱姆法则Cross- product term 交叉项DDeterminant 行列式Diagonal entries 对角元素Diagonal matrix 对角矩阵Dimension of a vector space V 向量空间V 的维数Eechelon matrix 梯形矩阵eigenspace 特征空间eigenvalue 特征值eigenvector 特征向量eigenvector basis 特征向量的基elementary matrix 初等矩阵elementary row operations 行初等变换Ffull rank 满秩fundermental set of solution 基础解系Ggrneral solution 通解Gram-Schmidt process 施密特正交化过程Hhomogeneous linear equations 齐次线性方程组Iidentity matrix 单位矩阵inconsistent linear system 不相容线性方程组indefinite matrix 不定矩阵indefinit quatratic form 不定二次型infinite-dimensional space 无限维空间inner product 内积inverse of matrix A 逆矩阵JKLlinear combination 线性组合linearly dependent 线性相关linearly independent 线性无关linear transformation 线性变换lower triangular matrix 下三角形矩阵Mmain diagonal of matrix A 矩阵的主对角matrix 矩阵Nnegative definite quaratic form 负定二次型negative semidefinite quadratic form 半负定二次型nonhomogeneous equations 非齐次线性方程组nonsigular matrix 非奇异矩阵nontrivial solution 非平凡解norm of vector V 向量V 的范数normalizing vector V 规范化向量Oorthogonal basis 正交基orthogonal complemen t 正交补orthogonal decomposition 正交分解orthogonally diagonalizable matrix 矩阵的正交对角化orthogonal matrix 正交矩阵orthogonal set 正交向量组orthonormal basis 规范正交基orthonomal set 规范正交向量组Ppartitioned matrix 分块矩阵positive definite matrix 正定矩阵positive definite quatratic form 正定二次型positive semidefinite matrix 半正定矩阵positive semidefinite quadratic form 半正定二次型Qquatratic form 二次型Rrank of matrix A 矩阵A 的秩r(A )reduced echelon matrix 最简梯形阵row vector 行向量Sset spanned by { } 由向量{ } 所生成similar matrices 相似矩阵similarity transformation 相似变换singular matrix 奇异矩阵solution set 解集合standard basis 标准基standard matrix 标准矩阵Isubmatrix 子矩阵subspace 子空间symmetric matrix 对称矩阵Ttrace of matrix A 矩阵A 的迹tr ( A )transpose of A 矩阵A 的转秩triangle inequlity 三角不等式trivial solution 平凡解Uunit vector 单位向量upper triangular matrix 上三角形矩阵Vvandermonde matrix 范得蒙矩阵vector 向量vector space 向量空间WZzero subspace 零子空间zero vector 零空间==============================================================================向量：vector 向量的长度（模）：零向量: zero vector负向量: 向量的加法：addition 三角形法则：平行四边形法则：多边形法则减法向量的标量乘积：scalar multiplication 向量的线性运算线性组合：linear combination 线性表示，线性相关（linearly dependent），线性无关（linearly independent），原点（origin）位置向量（position vector）线性流形（linear manifold）线性子空间（linear subspace）基（basis）仿射坐标（affine coordinates），仿射标架（affine frame），仿射坐标系（affine coordinate system）坐标轴（coordinate axis）坐标平面卦限（octant）右手系左手系定比分点线性方程组（system of linear equations齐次线性方程组（system of homogeneous linear equations）行列式（determinant）维向量向量的分量（component）向量的相等和向量零向量负向量标量乘积维向量空间（vector space）自然基行向量（row vector）列向量（column vector）单位向量（unit vector）直角坐标系（rectangular coordinate system），直角坐标（rectangular coordinates），射影（projection）向量在某方向上的分量，正交分解，向量的夹角，内积（inner product）标量积（scalar product），数量积，方向的方向角，方向的方向余弦；二重外积外积（exterior product），向量积（cross product），混合积（mixed product，scalar triple product）==================================================================================（映射（mapping）），（象（image）），（一个原象（preimage）），（定义域（domain）），（值域（range）），（变换（transformation）），（单射（injection）），（象集），（满射（surjection）），（一一映射，双射（bijection）），（原象），（映射的复合，映射的乘积），（恒同映射，恒同变换（identity mapping）），（逆映射（inverse mapping））；（置换（permutation）），（阶对称群（symmetric group）），（对换（transposition）），（逆序对），（逆序数），（置换的符号（sign）），（偶置换（even permutation）），（奇置换（odd permutation））；行列式（determinant），矩阵（matrix），矩阵的元（entry），（方阵（square matrix）），（零矩阵（zero matrix）），（对角元），（上三角形矩阵（upper triangular matrix）），（下三角形矩阵（lower triangular matrix）），（对角矩阵（diagonal matrix）），（单位矩阵（identity matrix）），转置矩阵（transpose matrix），初等行变换（elementary row transformation），初等列变换（elementary column transformation）；（反称矩阵（skew-symmetric matrix））；子矩阵（submatrix），子式（minor），余子式（cofactor），代数余子式（algebraic cofactor），（范德蒙德行列式（Vandermonde determinant））；（未知量），（系数矩阵），（方程的系数（coefficient）），（常数项（constant）），（线性方程组的解（solution）），（增广矩阵（augmented matrix）），（零解）；子式的余子式，子式的代数余子式===================================================================================线性方程组与线性子空间（阶梯形方程组），（方程组的初等变换），行阶梯矩阵（row echelon matrix），主元，简化行阶梯矩阵（reduced row echelon matrix），（高斯消元法（Gauss elimination）），（解向量），（同解），（自反性（reflexivity）），（对称性（symmetry）），（传递性（transitivity）），（等价关系（equivalence））；（齐次线性方程组的秩（rank））；（主变量），（自由位置量），（一般解），向量组线性相关，向量组线性无关，线性组合，线性表示，线性组合的系数，（向量组的延伸组）；线性子空间，由向量组张成的线性子空间；基，坐标，（自然基），向量组的秩；（解空间），线性子空间的维数（dimension），齐次线性方程组的基础解系（fundamental system of solutions）；（平面束（pencil of planes））（导出组），线性流形，（方向子空间），（线性流形的维数），（方程组的特解）；（方程组的零点），（方程组的图象），（平面的一般方程），（平面的三点式方程），（平面的截距式方程），（平面的参数方程），（参数），（方向向量）；（直线的方向向量），（直线的参数方程），（直线的标准方程），（直线的方向系数），（直线的两点式方程），（直线的一般方程）；=====================================================================================矩阵的秩与矩阵的运算线性表示，线性等价，极大线性无关组；（行空间，列空间），行秩（row rank），列秩（column rank），秩，满秩矩阵，行满秩矩阵，列满秩矩阵；线性映射（linear mapping），线性变换（linear transformation），线性函数（linear function）；（零映射），（负映射），（矩阵的和），（负矩阵），（线性映射的标量乘积），（矩阵的标量乘积），（矩阵的乘积），（零因子），（标量矩阵（scalar matrix）），（矩阵的多项式）；（退化的（degenerate）方阵），（非退化的（non-degenerate）方阵），（退化的线性变换），（非退化的线性变换），（逆矩阵（inverse matrix）），(可逆的（invertible），（伴随矩阵（adjoint matrix））；（分块矩阵（block matrix）），（分块对角矩阵（block diagonal matrix））；初等矩阵（elementary matrix），等价（equivalent）；（象空间），（核空间（kernel）），（线性映射的秩），（零化度（nullity））==================================================================================== transpose of matrix 倒置矩阵; 转置矩阵【数学词汇】transposed matrix 转置矩阵【机械专业词汇】matrix transpose 矩阵转置【主科技词汇】transposed inverse matrix 转置逆矩阵【数学词汇】transpose of a matrix 矩阵的转置【主科技词汇】permutation matrix 置换矩阵; 排列矩阵【主科技词汇】singular matrix 奇异矩阵; 退化矩阵; 降秩矩阵【主科技词汇】unitary matrix 单式矩阵; 酉矩阵; 幺正矩阵【主科技词汇】Hermitian matrix 厄密矩阵; 埃尔米特矩阵; 艾米矩阵【主科技词汇】inverse matrix 逆矩阵; 反矩阵; 反行列式; 矩阵反演; 矩阵求逆【主科技词汇】matrix notation 矩阵符号; 矩阵符号表示; 矩阵记号; 矩阵运算【主科技词汇】state transition matrix 状态转变矩阵; 状态转移矩阵【航海航天词汇】torque master 转矩传感器; 转矩检测装置【主科技词汇】spin matrix 自旋矩阵; 旋转矩阵【主科技词汇】moment matrix 动差矩阵; 矩量矩阵【航海航天词汇】Jacobian matrix 雅可比矩阵; 导数矩阵【主科技词汇】relay matrix 继电器矩阵; 插接矩阵【主科技词汇】matrix notation 矩阵表示法; 矩阵符号【航海航天词汇】permutation matrix 置换矩阵【航海航天词汇】transition matrix 转移矩阵【数学词汇】transition matrix 转移矩阵【机械专业词汇】transitionmatrix 转移矩阵【航海航天词汇】transition matrix 转移矩阵【计算机网络词汇】transfer matrix 转移矩阵【物理词汇】rotation matrix 旋转矩阵【石油词汇】transition matrix 转换矩阵【主科技词汇】circulant matrix 循环矩阵; 轮换矩阵【主科技词汇】payoff matrix 报偿矩阵; 支付矩阵【主科技词汇】switching matrix 开关矩阵; 切换矩阵【主科技词汇】method of transition matrices 转换矩阵法【航海航天词汇】stalling torque 堵转力矩, 颠覆力矩, 停转转矩, 逆转转矩【航海航天词汇】thin-film switching matrix 薄膜转换矩阵【航海航天词汇】rotated factor matrix 旋转因子矩阵【航海航天词汇】transfer function matrix 转移函数矩阵【航海航天词汇】transition probability matrix 转移概率矩阵【主科技词汇】energy transfer matrix 能量转移矩阵【主科技词汇】fuzzy transition matrix 模糊转移矩阵【主科技词汇】canonical transition matrix 规范转移矩阵【主科技词汇】matrix form 矩阵式; 矩阵组织【主科技词汇】stochastic state transition matrix 随机状态转移矩阵【主科技词汇】fuzzy state transition matrix 模糊状态转移矩阵【主科技词汇】matrix compiler 矩阵编码器; 矩阵编译程序【主科技词汇】test matrix 试验矩阵; 测试矩阵; 检验矩阵【主科技词汇】matrix circuit 矩阵变换电路; 矩阵线路【主科技词汇】reducible matrix 可简化的矩阵; 可约矩阵【主科技词汇】matrix norm 矩阵的模; 矩阵模; 矩阵模量【主科技词汇】rectangular matrix 矩形矩阵; 长方形矩阵【主科技词汇】running torque 额定转速时的转矩; 旋转力矩【航海航天词汇】transposed matrix 转置阵【数学词汇】covariance matrix 协变矩阵; 协方差矩阵【主科技词汇】unreduced matrix 未约矩阵; 不可约矩阵【主科技词汇】receiver matrix 接收机矩阵; 接收矩阵变换电路【主科技词汇】torque 传动转矩; 转矩; 阻力矩【航海航天词汇】pull-in torque 启动转矩; 输入转矩, 同步转矩, 整步转矩【航海航天词汇】parity matrix 奇偶校验矩阵; 一致校验矩阵【主科技词汇】bus admittance matrix 母线导纳矩阵; 节点导纳矩阵【主科技词汇】matrix printer 矩阵式打印机; 矩阵形印刷机; 点阵打印机【主科技词汇】dynamic matrix 动力矩阵; 动态矩阵【航海航天词汇】connection matrix 连接矩阵; 连通矩阵【主科技词汇】characteristic matrix 特征矩阵; 本征矩阵【主科技词汇】regular matrix 正则矩阵; 规则矩阵【主科技词汇】flexibility matrix 挠度矩阵; 柔度矩阵【主科技词汇】citation matrix 引文矩阵; 引用矩阵【主科技词汇】relational matrix 关系矩阵; 联系矩阵【主科技词汇】eigenmatrix 本征矩阵; 特征矩阵【主科技词汇】system matrix 系统矩阵; 体系矩阵【主科技词汇】system matrix 系数矩阵; 系统矩阵【航海航天词汇】recovery diode matrix 恢复二极管矩阵; 再生式二极管矩阵【主科技词汇】inverse of a square matrix 方阵的逆矩阵【主科技词汇】torquematic transmission 转矩传动装置【石油词汇】torque balancing device 转矩平衡装置【航海航天词汇】torque measuring device 转矩测量装置【主科技词汇】torque measuring apparatus 转矩测量装置【航海航天词汇】torque-tube type suspension 转矩管式悬置【主科技词汇】steering torque indicator 转向力矩测定仪; 转向转矩指示器【主科技词汇】magnetic dipole moment matrix 磁偶极矩矩阵【主科技词汇】matrix addressing 矩阵寻址; 矩阵寻址时频矩阵编址; 时频矩阵编址【航海航天词汇】stiffness matrix 劲度矩阵; 刚度矩阵; 劲度矩阵【航海航天词汇】first-moment matrix 一阶矩矩阵【主科技词汇】matrix circuit 矩阵变换电路; 矩阵电路【计算机网络词汇】reluctance torque 反应转矩; 磁阻转矩【主科技词汇】pull-in torque 启动转矩; 牵入转矩【主科技词汇】induction torque 感应转矩; 异步转矩【主科技词汇】nominal torque 额定转矩; 公称转矩【航海航天词汇】phototronics 矩阵光电电子学; 矩阵光电管【主科技词汇】column matrix 列矩阵; 直列矩阵【主科技词汇】inverse of a matrix 矩阵的逆; 逆矩阵【主科技词汇】lattice matrix 点阵矩阵【数学词汇】lattice matrix 点阵矩阵【物理词汇】canonical matrix 典型矩阵; 正则矩阵; 典型阵; 正则阵【航海航天词汇】moment matrix 矩量矩阵【主科技词汇】moment matrix 矩量矩阵【数学词汇】dynamic torque 动转矩; 加速转矩【主科技词汇】indecomposable matrix 不可分解矩阵; 不能分解矩阵【主科技词汇】printed matrix wiring 印刷矩阵布线; 印制矩阵布线【主科技词汇】decoder matrix circuit 解码矩阵电路; 译码矩阵电路【航海航天词汇】scalar matrix 标量矩阵; 标量阵; 纯量矩阵【主科技词汇】array 矩阵式组织; 数组; 阵列【计算机网络词汇】commutative matrix 可换矩阵; 可交换矩阵【主科技词汇】标准文档实用文案。

高等数学（微积分学）专业术语名词概念定理等英汉对照

高等数学（微积分学）专业术语名词概念定理等英汉对照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 Limi t (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 the Application 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 Analytic 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 variables and 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 Surface Integral s (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 Limi t (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 Limit) (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 ofImplicit Functions and Functions Determined by Parametric Equation andCorrelative 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 4Indefinite 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 Product 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(power 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 UnanimousConvergence of the Series 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 DifferentialEquation) (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 HigherOrder) (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 V ocabulary 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 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 a convergent 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 derivatives()f x在闭区间【a,b】上可导()f x is derivable 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 a surface at a point曲线在一点的法线normal line to a surface 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volume element in rectangular coordinate system柱面坐标cylindrical coordinates柱面坐标系中的体积元素volume element in cylindrical coordinate system球面坐标spherical coordinates球面坐标系中的体积元素volume element 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 differential equation 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 →。

增广矩阵为0求非齐次线性方程组

增广矩阵为0求非齐次线性方程组一、介绍非齐次线性方程组（Non-homogeneous Linear Equation System）是当等号右边有常数项时，系数矩阵A存在情况下，一组方程构成的线性方程组，其形式为：$$Ax=b$$子中A为系数矩阵，x为未知矩阵， b为增广矩阵为0时的常数矩阵，是此方程的解的属性。

二、解非齐次线性方程组的方法非齐次线性方程组可以由几种方法求解：（1）初等变换：即按照带入法的方法列出增广形式，然后使用下列方法解决：（2）高斯消元法：先将矩阵化为上三角矩阵，然后用反向序求解。

（3）高斯-约当法：先按照行对角线为主对角线将矩阵分解成上下两部分，然后求上三角矩阵，再求解。

（4）梯阵法：是基于高斯消元法的一种改进，把这一阶段的求解进行优化，从而提高效率。

三、增广矩阵为0求非齐次线性方程组当方程组的增广矩阵为0时，求非齐次线性方程组的方法如下：1. 先转化为增广矩阵的标准形式：令$b_i = 0$，将所有方程组转化成标准的增广形式，即$Ax = 0$，然后将其转化为一个线性方程组：$Ax = b$，其中$b_i = 0$，b为一个常数矩阵。

2. 通过线性变换消去系数矩阵A中的元素，将A转化为一个最简的上三角矩阵T，将b的值也做相应的变换，形成新的系数矩阵T，和新的右边常数矩阵$b'$，舍去$b'$中的0值，就成了一个最简的矩阵。

3. 由最简矩阵中求解$x_i$：最简矩阵求解时，由最右边开始，前置值即是右边值，然后不断反馈到前面，将每一步得到的结果带入到其前面系数中，从而可以求出$x_i$的值。

4. 将每一步求出的$x_i$值代入到初始方程组中，进行检验，若算得的结果与实际给出的解不同，则系数矩阵A中有多余的解，需要用可行解的标准型求解。

homogeneous system

homogeneous system
均相体系也称均相系统（英文名称Homogeneous system）是物理化学的一个基本概念。

“体系”又称为“系统”（英文名称system），是热力学中的一个概念，根据研究的需要，人为地把一部分物料从周围的物体中划分出来（可以是实际的，也可以是想像的）作为研究对象。

这一被划分出来的一部分物料成为体系或系统。

系统以外的那部分与系统有直接联系的物料统称为环境。

“相”（英文名称Phase）也是热力学的基本概念，是指系统内部物理和化学性能均匀，有明显的边界、用机械方法可以分离出来的部分称为“相”。

因此均相体系概念是指系统内只含一个相，即只含一个物质。

代数中的英语词汇

代数中的英语词汇（按拼音序）B半负定二次型(negative semidefinite quadraticform)半负定矩阵(negative semi&finite matrix)半正定二次型(positive semidefinite quadratic form)半正定矩阵(positive semidefinite matrix)伴随矩阵(adjoint matrix)标准单位向量(standard unit vector)标准形矩阵(normal form for a matrix)标准正交基(orthonormal basis)不定二次型(indefinite quadratic form)C初等矩阵(elementary matrix)代数余子式(algebraic cofactor)单位矩阵(identity matrix)单位向量(unit vector)等价的矩阵(equivalent matrices)D等价向量组(equivalent vector sets)对称变换(symmetric transformation)对称矩阵(symmetric matrix)对换(transposition)对合矩阵(involutory matrix)对角矩阵(diagonal matrix)对角行列式(diagonal determinant)En阶排列(permutation of order n)二次型(quadratic form)二次型的标准形(canonical form of a quadratic form)二次型的规范标准形(normal form of a quadratic form)二次型的矩阵(matrixofaquadraticform)二次型的秩(rankofaquadraticform)F方阵的行列式反对称矩阵(skew symmetric matrix)范德蒙行列式(Vandermonde determinant)方阵(squarematrix)方阵的幂(powers of a matrix)非齐次线性方程组(system of non-homogeneous linear equations)非奇异矩阵(nonsingular matrix)非退化的线性代换(non-degenerate linear substitution)分块初等矩阵(block elementary matrix)分块对角矩阵(block diagonal matrix)分块矩阵(block matrix或partitioned matrices)符号差(signature)负定二次型(negative definite quadratic form)负定矩阵(egative definite matrix)负惯性指数(negative index of inertia)复矩阵(complex matrix)G高斯消元法(Gauss elimination)格拉姆—施密特正交化方法(Gram—Schmidt orthogonalization process)共轭矩阵(conjugate matrix)惯性定理(law of inertia)规范的阶梯形矩阵(reduced row echelon form)过渡矩阵(transition matrix)H行向量(row vector)行标(row index)行矩阵(row matrix)行列式(determinant of order n)行列式乘积(multiplication of determinants)行列式展开式(determinantal expansion)行列式的主对角线(main diagonal of determinant)恒等变换(identity)化二次型为标准形正交代换法初等变换法矩阵J极大线性无关组(maximal linearly indepemdent systems)阶梯形矩阵(echelon matrix)基本向量(fundamental vector)基变换(change of bases)基础解系(system of fundamental solutions)矩阵(matrix)矩阵乘法(multiplication of matrices)矩阵的初等变换(elementary transformation of matrices)矩阵的行秩(row rank of matrix)矩阵的合同(congruence of matrices)矩阵的迹(trace of a matrix)矩阵的列秩(column rank of matrix)矩阵的数乘(scalar multiplication of matrix)矩阵的秩(rank of a matrix)矩阵的主对角线(maindiagonal of a squarematrix)矩阵加法(addition of matrices)矩阵相似于对角矩阵的条件矩阵的元素(entry of a matrix)KCauchy-Schwarz不等式(Cauchy-Schwarz inequality)可交换矩阵(commutable matrices)可逆矩阵(invertible matrix)克拉默法则(Cramers Rule)克罗内克符号函数(Kronecker sign function)L拉普拉斯展开式(Laplace expansion)X线性方程组的系数矩阵(coefficient matrix of simultaneous lineare quations)线性方程组的增广矩阵(augmented matrix of simultaneous linear equations)线性空间(linear space)线性空间的基(basis of linear space)线性空间的维数(dimension of linear space)线性无关(1inearly independent)线性相关(1inearly dependent)线性子空间(1inear subspace)相等的矩阵(equal matrices)相似矩阵(similar matrices)向量(vector)向量的夹角(angle between two vectors)向量的距离(distance between vectors)向量空间(vector space)向量的内积(inner product of vectors)向量的线性组linear combination of vectors)向量组的秩(rank of a vector set)旋转变换(rotated transformation)Y余子式(cofactor)Z正定二次型(positive definite quadratic form)。

英语数学名词大全

代数部分1.有关基本运算：add, plus加subtract减difference差multiply, times乘product积divide除divisible可被整除的divided evenly被整除dividend被除数divisor因子，除数quotient商remainder余数factorial阶乘power乘方radical sign, root sign根号round to四舍五入to the nearest四舍五入2.有关集合union并集proper subset真子集solution set解集3.有关代数式、方程和不等式algebraic term代数项like terms, similar terms同类项numerical coefficient数字系数literal coefficient字母系数inequality不等式triangle inequality三角不等式range值域original equation原方程equivalent equation同解方程等价方程linear equation线性方程(e.g.5 x +6=22) 4.有关分数和小数proper fraction真分数improper fraction假分数mixed number带分数vulgar fraction, common fraction普通分数simple fraction简分数complex fraction繁分数numerator分子denominator分母(least)common denominator(最小)公分母quarter四分之一decimal fraction纯小数infinite decimal无穷小数recurring decimal循环小数tenths unit十分位5.基本数学概念arithmetic mean算术平均值weighted average加权平均值geometric mean几何平均数exponent指数，幂base乘幂的底数,底边cube立方数，立方体square root平方根cube root立方根common logarithm常用对数digit数字constant常数variable变量inverse function反函数complementary function余函数linear一次的，线性的factorization因式分解absolute value绝对值，e.g.｜-32｜=32round off四舍五入6.有关数论natural number自然数positive number正数negative number负数odd integer, odd number奇数even integer, even number偶数integer, whole number整数positive whole number正整数negative whole number负整数consecutive number连续整数real number, rational number实数,有理数irrational(number)无理数composite number合数e.g.4,6,8,9,10,12,14,15……prime number质数e.g.2,3,5,7,11,13,15……reciprocal倒数common divisor公约数multiple倍数(least)common multiple(最小)公倍数(prime)factor(质)因子common factor公因子ordinary scale, decimal scale十进制nonnegative非负的tens十位units个位mode众数median中数common ratio公比7.数列arithmetic progression(sequence)等差数列geometric progression(sequence)等比数列8.其它approximate近似(anti)clockwise(逆)顺时针方向cardinal基数ordinal序数direct proportion正比distinct不同的estimation估计，近似parentheses括号proportion比例permutation排列combination组合table表格trigonometric function三角函数unit单位,位几何部分1.所有的角alternate angle内错角corresponding angle同位角vertical angle对顶角central angle圆心角interior angle内角exterior angle外角supplementary angles补角complementary angle余角adjacent angle邻角acute angle锐角obtuse angle钝角right angle直角round angle周角straight angle平角included angle夹角2.所有的三角形equilateral triangle等边三角形scalene triangle不等边三角形isosceles triangle等腰三角形right triangle直角三角形oblique斜三角形inscribed triangle内接三角形3.有关收敛的平面图形，除三角形外semicircle半圆concentric circles同心圆quadrilateral四边形pentagon五边形hexagon六边形heptagon七边形octagon八边形nonagon九边形decagon十边形polygon多边形parallelogram平行四边形equilateral等边形plane平面square正方形，平方rectangle长方形regular polygon正多边形rhombus菱形trapezoid梯形4.其它平面图形arc弧line, straight line直线line segment线段parallel lines平行线segment of a circle弧形5.有关立体图形cube立方体，立方数rectangular solid长方体regular solid/regular polyhedron正多面体circular cylinder圆柱体cone圆锥sphere球体solid立体的6.有关图形上的附属物altitude高depth深度side边长circumference, perimeter周长radian弧度surface area 表面积volume体积arm直角三角形的股cross section横截面center of a circle圆心chord弦radius半径angle bisector角平分线diagonal对角线diameter直径edge棱face of a solid立体的面hypotenuse斜边included side夹边leg三角形的直角边median of a triangle三角形的中线base底边，底数(e.g.2的5次方，2就是底数) opposite直角三角形中的对边midpoint中点endpoint端点vertex(复数形式vertices)顶点tangent切线的transversal截线intercept截距7.有关坐标coordinate system坐标系rectangular coordinate直角坐标系origin原点abscissa横坐标ordinate纵坐标number line数轴quadrant象限slope斜率complex plane复平面8. 其它plane geometry平面几何trigonometry三角学bisect平分circumscribe外切inscribe内切intersect相交perpendicular垂直Pythagorean theorem勾股定理congruent全等的multilateral多边的一般词汇数学 mathematics, maths(BrE), math(AmE)公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和sum减minus(prep.), subtract(v.), subtraction(n.)被减数 minuend减数 subtrahend差remainder乘times(prep.), multiply(v.), multiplication(n.) 被乘数 multiplicand,faciend乘数 multiplicator积product除divided by(prep.), divide(v.), division(n.)被除数 dividend除数 divisor商quotient等于 equals, is equalto, is equivalent to 大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator数字 digit数number自然数 naturalnumber整数 integer小数 decimal小数点 decimalpoint分数 fraction分子 numerator分母 denominator比ratio正positive负negative零null, zero, nought, nil十进制 decimalsystem二进制 binary system十六进制 hexadecimalsystem权weight, significance进位 carry截尾 truncation四舍五入 round下舍入 rounddown上舍入 roundup有效数字 significant digit无效数字 insignificantdigit代数 algebra公式 formula,formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown,x-factor, y-factor, z-factor 等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方 thepowerof four, thefourth powern 次方 thepowerof n, the nthpower开方evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth root n 次方根 theroot of n, the nth root集合 aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition值域 range常量 constant变量 variable单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.) 无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral有理数 rationalnumber无理数 irrationalnumber实数 realnumber虚数 imaginarynumber复数 complex number矩阵 matrix行列式 determinant几何 geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 rightangle钝角 obtuseangle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle 直角三角形 righttriangle 直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtusetriangle不等边三角形 scalenetriangle等腰三角形 isosceles triangle等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width菱形 rhomb, rhombus, rhombi(pl.), diamond 正方形 square梯形 trapezoid直角梯形 righttrapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon 圆 circle圆心 centre(BrE), center(AmE) 半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference周长 perimeter面积 area轨迹 locus, loca(pl.)相似 similar全等 congruent四面体 tetrahedron五面体 pentahedron六面体 hexahedron平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron 十二面体 dodecahedron 二十面体 icosahedron多面体 polyhedron棱锥 pyramid棱柱 prism棱台 frustum of a prism 旋转 rotation轴 axis圆锥 cone圆柱 cylinder圆台 frustum of a cone 球 sphere半球 hemisphere底面 undersurface表面积 surfacearea体积 volume空间 space坐标系 coordinates坐标轴 x-axis, y-axis, z-axis横坐标 x-coordinate纵坐标 y-coordinate原点 origin双曲线 hyperbola抛物线 parabola三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE),excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE), orthocenter(AmE)重心 barycentre(BrE), barycenter(AmE)内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation 比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormaldistribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken linegraph 曲线统计图 curve diagram扇形统计图 piediagram其他数学词汇：mathematics数学theorem定理calculation计算operation运算arithmetic算术，四则运算addition加法subtraction减法multiplication乘法division除法和remainder余product积quotient商2 plus 1 equals3二加一等于三4 minus2 equals 2四减二等于二4 multiplied by 5, 4 times5 四乘以五addend加数plus sign加号minussign减号multiplicand被乘数multiplierdivisor除数dividend被除数decimal point小数点noughtpoint four零点四fraction分数ratio比proportion比例numerator分子common denominator 公分母exponent指数differentialcalculus 微分学integral calculus积分slide rule计算尺function函数derivative导数power幂,乘方to raise to the power of five使乘五次方x squared某数的平方cube三次方threecubed三次方的to the fourth power,to the power of four 乘四次方square root平方根cube root立方根rule of three比例法logarithm对数logarithmtable对数表algebra代数equation等式，方程式unknown未知数simpleequation一次方程quadratic equation二次方程cubic equation三次方程微积分反函数: inverse 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: anti-trigonometric function.复合函数: compound function.初等函数: elementary function.双曲函数: hyperbolic function.反双曲函数: anti-hyperbolic function.无穷小:infinitesimal.无穷大:infinity.连续性:continuity.间断点:discontinuous point.介值定理:intermediate value theorem.导数:derivative. 微分:differential.函数的单调性:monotonicity of function.曲线:curve. 曲线的凹凸性:concavity of curve.曲线的拐点: keen point of curve.曲率:curvature.不定积分: indefinite integral(indeterminate integral). 定积分: definite integral.广义积分:improper integral.空间解析几何:space analytic geometry.向量代数:vector algebra.空间直角坐标系:space rectangular coordinate system. 数量积:scalar product.向量积:vector product.混合积:triple product.曲面:surface.二次曲面:second-degree surface.线性代数Aadjont(adjugate) of matrix A A 的伴随矩阵augmented matrix A 的增广矩阵Bblock diagonal matrix 块对角矩阵block matrix 块矩阵basic solution set 基础解系CCauchy-Schwarz inequality 柯西 - 许瓦兹不等式characteristic equation 特征方程characteristic polynomial 特征多项式coffcient matrix 系数矩阵cofactor 代数余子式cofactor expansion 代数余子式展开column vector 列向量commuting matrices 交换矩阵consistent linear system 相容线性方程组Cramer's rule 克莱姆法则Cross- product term 交叉项DDeterminant 行列式Diagonal entries 对角元素Diagonal matrix 对角矩阵Dimension of a vector space V 向量空间 V 的维数Eechelon matrix 梯形矩阵eigenspace 特征空间eigenvalue 特征值eigenvector 特征向量eigenvector basis 特征向量的基elementary matrix 初等矩阵elementary row operations 行初等变换Ffull rank 满秩fundermental set of solution 基础解系Ggrneral solution 通解Gram-Schmidt process 施密特正交化过程Hhomogeneous linear equations 齐次线性方程组Iidentity matrix 单位矩阵inconsistent linear system 不相容线性方程组indefinite matrix 不定矩阵indefinit quatratic form 不定二次型infinite-dimensional space 无限维空间inner product 内积inverse of matrix A 逆矩阵JKLlinear combination 线性组合linearly dependent 线性相关linearly independent 线性无关linear transformation 线性变换lower triangular matrix 下三角形矩阵Mmain diagonal of matrix A 矩阵的主对角matrix 矩阵Nnegative definite quaratic form 负定二次型negative semidefinite quadratic form 半负定二次型nonhomogeneous equations 非齐次线性方程组nonsigular matrix 非奇异矩阵nontrivial solution 非平凡解norm of vector V 向量 V 的范数normalizing vector V 规范化向量Oorthogonal basis 正交基orthogonal complemen t 正交补orthogonal decomposition 正交分解orthogonally diagonalizable matrix 矩阵的正交对角化orthogonal matrix 正交矩阵orthogonal set 正交向量组orthonormal basis 规范正交基orthonomal set 规范正交向量组Ppartitioned matrix 分块矩阵positive definite matrix 正定矩阵positive definite quatratic form 正定二次型positive semidefinite matrix 半正定矩阵positive semidefinite quadratic form 半正定二次型Qquatratic form 二次型rank of matrix A 矩阵 A 的秩 r(A )reduced echelon matrix 最简梯形阵row vector 行向量Sset spanned by { } 由向量 { } 所生成similar matrices 相似矩阵similarity transformation 相似变换singular matrix 奇异矩阵solution set 解集合standard basis 标准基standard matrix 标准矩阵 Isubmatrix 子矩阵subspace 子空间symmetric matrix 对称矩阵Ttrace of matrix A 矩阵 A 的迹 tr ( A )transpose of A 矩阵 A 的转秩triangle inequlity 三角不等式trivial solution 平凡解Uunit vector 单位向量upper triangular matrix 上三角形矩阵vandermonde matrix 范得蒙矩阵vector 向量vector space 向量空间WZzero subspace 零子空间zero vector 零空间概率与统计Probability theory 概率论mathematical statistics 数理统计deterministic phenomenon 确定性现象random phenomenon 随机现象sample space 样本空间random occurrence 随机事件fundamental event 基本事件certain event 必然事件impossible event 不可能事件random test 随机试验incompatible events 互不相容事件frequency 频率classical probabilistic model 古典概型geometric probability 几何概率conditional probability 条件概率multiplication theorem 乘法定理Bayes's formula 贝叶斯公式Prior probability 先验概率Posterior probability 后验概率Independent events 相互独立事件Bernoulli trials 贝努利试验random variable 随机变量probability distribution 概率分布distribution function 分布函数discrete random variable 离散随机变量distribution law 分布律hypergeometric distribution 超几何分布random sampling model 随机抽样模型binomial distribution 二项分布Poisson distribution 泊松分布geometric distribution 几何分布probability density 概率密度continuous random variable 连续随机变量uniformly distribution 均匀分布exponential distribution 指数分布numerical character 数字特征mathematical expectation 数学期望variance 方差moment 矩central moment 中心矩n-dimensional random variable n-维随机变量two-dimensional random variable 二维离散随机变量joint probability distribution 联合概率分布joint distribution law 联合分布律joint distribution function 联合分布函数boundary distribution law 边缘分布律boundary distribution function 边缘分布函数exponential distribution 二维指数分布continuous random variable 二维连续随机变量joint probability density 联合概率密度boundary probability density 边缘概率密度conditional distribution 条件分布conditional distribution law 条件分布律conditional probability density 条件概率密度covariance 协方差dependency coefficient 相关系数normal distribution 正态分布limit theorem 极限定理standard normal distribution 标准正态分布logarithmic normal distribution 对数正态分布covariance matrix 协方差矩阵central limit theorem 中心极限定理Chebyshev's inequality 切比雪夫不等式Bernoulli's law of large numbers 贝努利大数定律statistics 统计量simple random sample 简单随机样本sample distribution function 样本分布函数sample mean 样本均值sample variance 样本方差sample standard deviation 样本标准差sample covariance 样本协方差sample correlation coefficient 样本相关系数order statistics 顺序统计量sample median 样本中位数sample fractiles 样本极差sampling distribution 抽样分布parameter estimation 参数估计estimator 估计量estimate value 估计值unbiased estimator 无偏估计unbiassedness 无偏性biased error 偏差mean square error 均方误差relative efficient 相对有效性minimum variance 最小方差asymptotic unbiased estimator 渐近无偏估计量uniformly estimator 一致性估计量moment method of estimation 矩法估计maximum likelihood method of estimation 极大似然估计法likelihood function 似然函数maximum likelihood estimator 极大似然估计值interval estimation 区间估计hypothesis testing 假设检验statistical hypothesis 统计假设simple hypothesis 简单假设composite hypothesis 复合假设rejection region 拒绝域acceptance domain 接受域test statistics 检验统计量linear regression analysis 线性回归分析。

材料力学总结

材料力学总结材料力学名词解释及填空名词解释1、Stress(应力)the force per unit area , or intensity of the force distributed over a given section, is called stress.σ=F/A2、normal stress(正应力)The internal force is therefore normal to the plane of the section and the corresponding stress is described as the normal stress.3、Shearing stress(剪应力)The internal force is the shear on the plane of the section and the corresponding stress is described as the shearing stress.4、Linear Strain(应变)The normal strainεin a member can be defined as the deformation of the meter of the per unit length.5、The main objective of the study the mechanics of materials（材料力学的任务）is to provide the future engineer with the means of analyzing and designing various machines and loading-bearing structures.6、Saint-venant’s principle（圣维南原理）For two sets of statically equivalent forces,except in the immediate vicinity of the points of application of the loads, the stress distribution may be assumed independent of the actual mode of application of the loads (this statement is not only to axial load, but to practically any type of load)7、Work-energy principle(功能原理)The Work-energy Principle: In the process of the deformationof a elastomer, the strain energy which is stored in elastomer is equal to the work of the external force in number. This is the Work-energy Principle and it can be represented as Vε=W.8、effective length （有效长度）is defined as real length multiplied by factor of length9、principle plane(主平面)is the plane in which the shearing stress equals zero, and normal stresses achieve maximum or minimum.Principle stress(主应力)The normal stress which is exerted on the principle plane is called the principle stress.10、Radius of radius of gyration【revolution】（惯性半径）of an area can be calculated by thefollowing formula i=I/AWhere i =the moment of inertia of an areaA=the area of an cross section11、isotropic materials （各向同性材料）are the materials whose elastic constants are independent of direction.12、homogeneous materials（均匀性材料）are the materials whose elastic properties are the same everywhere.13、The strain energy density(应变能密度)The strain energy in the unit volume can be defined as the strain energy density.14、Hooke’s law （胡克定律）may be expressed more fully by saying that1】when the stress increases,the measured strain increases in the same ratio2】when the stress diminishes, the measured strain diminishes in the same ratio3】when the stress is removed, no strain can be measuredFor a small deformation,the stress is directly proportional to the strain.15、Hooke’s law for shearing stress(剪切胡克定律)The relation τ=Gγis known as Hooke’s law for shearing stress. Strain and constant Gis called the modulus of rigidity or shear modulus of material.16、Generalized Hooke’s law（广义胡可定律）17、Poisson ratio(泊松比)is defined as the ratio of lateral contraction (strain) to longitudinal extension (strain) of a bar under terminal tension.18、factor of safety （安全因数）ultimate load over allowable load19、stress-concentration factor k（应力集中因数K）=maximum stress over average stress20、statically indeterminate problem（静不定问题）is the problem in which the reactions and internal forces can not be determined by static only , analysis of deformation is needed.21、neutral surface（中性层）is defined as the surface between the top and bottom of a beam in which longitudinal line do not change.22、Neutral axis （中性轴）①The neutral surface intersects a transverse section along a straight line called the neutral axis of the section.②The intersection of the neutral surface with a transverse section is called the neutral axis of the section.23、principle of superposition（叠加原理）for all linear systems (a beam can be modeled as a linear system ),24、the quantity the term λ=μl /i (柔度) is known as the slenderness ratio of the column. Where μl= effective lengthi= the radius of gyration25、The theory of strength(强度理论)The assumption concerning the damage or the losing effect of the material is called the theory of strength.26、buckling (失稳)A stage when the column suddenly becomes sharply curved instead of remaining straight as the load is applied is called buckling.27、The critical force (临界压力)The value of the compressive force which is right on the boundary between the stable balance and the unstable balance is called the critical force.28、The critical stress (临界应力)The corresponding stress of the critical force is described as the critical force.29、Euler’s Formula (欧拉公式)Euler’s Formula can be expressed asFcr=π2EI／le2in which: Fcr denotes the critical loadE denotes the modulusI denotes the minimum moment of inertia of areale denotes the equivalent length30、Assumption for a bar (拉压的平面假设)The hypothesis assumes that the section keeps being a plane after deformation.31、Assumption for torsion (扭转平面假设)When a circular shaft is subjected to a torsion, every cross section remains plane and undamaged.32、Assumption for bending (弯曲平面假设)Under bending, the cross section of the beam remains planeand has a constant curvature. And the new cross section still perpendicular to axis.32、极惯性矩The polar moment of inertia of an area is defined as the polar moment of inertia of an area with respect to a point as the integral Ip=∫ρ2dA33、惯性矩The moment of inertia of an area is defined as the second moment of the area with respect to an axis as the integral I=∫y2dA.34、静矩The static moment of an area is defined as the first moment of an area with respect to an axis as the integral Sz=∫ydA.填空题1 三个材料假设Homogeneousity assumption 、Continuity assumption 、Isotropy assumption2 三个关系Geometric relation 、Physical relation、Equilibrium relation3 限制梁挠度的三个条件Boundary condition 、Constraint condition、Continuity condition4 三种约束方式1）固定端fixed end2）固定铰支座fixed support of pin joint3）可动铰支座roller support of pin joint5 三种梁1）简支梁simply supported beam2）外伸梁overhang beam3）悬臂梁cantilever beam6 For perfect column, the factor of length for conditions both pinned; both fixed; one fixed the other free; one fixed the other pinned are 1、0.5、2、0.7 respectively.7 The four classic strength theories include maximum tensile stress theory、maximum elongated normal strain theory、maximum shearing stress theory and maximum distortional strain energy theory.8 The tensile diagram of low carbon steel consist of four stages: elastic stage 、yielding stage、hardening stage and necking stage.。