代数微积分中英文名词对照.xlsx

英文中文 set builder notation集合符号 interval notation间隔符号 function函数 function notation方程符号 independent variable自变量 dependent variable因变量 implied domain隐含域 piecewise defined function 分段定义函数 relevant domain相关域 zeros零 roots根 line symmetry线对称 point symmetry点对称 x interceptsx轴截距 y interceptsy轴截距 even function偶函数 odd function奇函数 domian 函数的 域 range 函数的 范围 continuity连续性 end behavior趋于正负无限的极限值 limit极限 theorem定理 intermediate value theorem 介值定理 中值定理 continuous function连续函数 limit极限 discontinuous function 不连续函数 infinite discontinuity 无限不连续 jump discontinuity跳跃不连续 removable discontinuity 可移除不连续 nonremovable不可移除 discontinuity不连续 corollary推论 the location principle 位置原理 conjecture推测 猜想 increasing增加 decreasing减少 constant常量 critical point临界点 extrema极值 maximum最大 minimum最小 point of inflection拐点 average rate of change 平均变化率 secant line切割线 tangent line正切线 切线 parent function父函数 constant function常数函数 zero function零函数 identity function恒等函数 quadratic function二次函数 cubic function三次函数 square root function平方根函数 reciprocal function倒数函数 absolute value function 绝对值函数 step function阶梯函数 greatest integer function 最大整数函数 transformation变换 translation平移 reflection映像 dilation膨胀 polynomial多项式 rigid transformation平移变换 nonrigid transformation 非平移变换 composition复合 合成 sum和 product积 difference差 quotient商 denominator分母 numerator分子 inverse relation反比例关系 逆关系 inverse function反函数 one to one parametric equation参数方程 differential calculus 微分 power function幂函数 monomial function单项函数 radical function根函数 extraneous solution无效解 额外解 exponent指数 scatter plot散布图 散点分析 regression model回归模型 polynomial function多项式函数 polynomial function of degree n n阶多项式函数 leading coefficient首项系数 leading term test首项测试 quartic function四次函数 turning point转折点 remainder余数 factor theorem因子定理 因式定理 synthetic division综合除法 depressed polynomial降次多项式 synthetic substitution 综合替代 dividend被除数 divisor除数 perimeter周长 diameter直径 equilateral triangle等边三角形 rational zero theorem 有理数零值定理 lower bound下限 upper bound上限 Descartes Rule of Signs 笛卡尔符号规则 Fundamental Theorem of Algebra 代数学基本定理 Linear Factorization Theorem 线性因式分解定理 Conjugate Root Theorem 共轭根定理 complex conjugates复数共轭 irreducible over the reals 不能复归的实数 corollary推论 rational function有理函数 asymptote渐近线 vertical asymptote垂直渐近线 horizontal asymptote水平渐近线 oblique asymptote斜渐近线 holes洞 reciprocal倒数 hyperbola双曲线 polynomial inequality 多项式不等式 sign chart符号图 rational inequality有理数不等式 algebraic function代数函数 transcendental function 超越函数 exponential function指数函数 natural base自然底 continuous compound连续复合 interest利息 logarithmic function with base b 底为b的对数函数 logarithm对数 common logrithm常用对数 natural logarithm自然对数 logistic growth function linearize 逻辑斯蒂增长函数线性化 trigonometric ratios三角比 trigonometric functions 三角函数 sine正弦 cosine余弦 tangent正切 cosecant余割 secant正割 割线 cotangent余切 reciprocal function倒数函数 inverse trigonometric function 反三角函数 inverse sine反正弦 inverse cosine反余弦 inverse tangent反正切 angle of elevation仰角 angle of depression俯角 solve a right triangle 解直角三角形 Pythagorean Theorem勾股定理 毕氏定理 vertex顶点 initial side初始边 开始边 terminal side结束边 standard position标准位置 radian弧度 coterminal angles共边角 linear speed线速率 angular speed角速率 sector扇区 circumference周长 quadrantal angle象限角 reference angle基准角 unit circle单位园 circular function园函数 三角函数 periodic function周期函数 period周期 sinuosid正弦曲线 amplitude幅度 frequency频率 phase shift相位平移 vertical shift垂直平移 midline中线 damped trigonometric function 阻尼三角函数 damping factor阻尼因子 damped oscillation阻尼振荡 damped wave阻尼波 damped harmonic motion 阻尼谐运动 arcsine function反正弦函数 arccosine function反余弦函数 arctangent function反正切函数 oblique triangles斜三角形 law of sines正弦定理 ambiguous case模糊情况 law of cosine余弦定理 Heron s Formula海伦公式 obtuse钝角 acute锐角 right直角 identity恒等式 trigonometric identity 三角恒等式 cofunction余函数 complementary angle余角 conjugate共轭 multivariable linear system 多变量线性系统 row echelon form阶梯形矩阵 Gaussian elimination高斯消元法 augmented matrix增广矩阵 coefficient matrix系数矩阵 reduced row echelon form 行简化阶梯形矩阵 Gauss Jordan elimination 高斯 约当消去法 identity matrix单位矩阵 inverse matrix逆矩阵 inverse求逆 invertible可逆的 singular matrix奇异矩阵 determinant行列式 square system平方系统 Ctramer s Rule partial fraction部分分式 partial fraction decomposition 部分分式分解 optimization最优化 linear programming线性规划 objective function目标函数 constraints约束条件 限制 feasible solutions可行解 multiple optimal solutions 多个最优解 unbounded无边界 无限制 conic section二次曲线 圆锥曲线 degenerate conic退化圆锥曲线 locus轨迹 parabola抛物线 focus焦点 directrix准线 axis of symmetry对称轴 vertex顶点 latus rectum正焦弦 ellipse椭圆 isosceles triangle等腰三角形 focifocus的复数 焦点 major axis长轴 主轴 center中心 minor axis短轴 vertices长轴顶点 co vertices短轴顶点 eccentricity离心率 偏心率 congruent全等的 一致的 transverse axis横截轴 水平轴 conjugate axis共轭轴 parameter参数 orientation方向 parametic curve参数曲线 rectangular form直角坐标形式 projectile motion抛物线运动 抛物体运动 scalar标量 vector矢量 向量 initial point初始点 terminal point终点 direction方向 magnitude大小 量级 quadrant bearing象限角 true bearing真实角 parallel vectors平行矢量 equivalent vectors等效矢量 resultant合成 矢量的和 triangle method三角形法 parallelogram method平行四边形法 zero vector零矢量 components分量 rectangular components 正交分量 protractor分度器 component form分量形式 unit vector单位矢量 linear combination线性组合 dot product两个矢量的点积 orthogonal正交 vector projection矢量投影 three dimensional coordinate system 三维坐标系 z axisz轴 octant卦限 三维坐标系的象限 orderd triple有序三元组 cross product叉积 外积 向量积 torque扭矩 parallelepiped平行六面体 triple scalar product 三重标积 polar coordinate system 极坐标系 pole极点 极坐标的原点 polar axis极轴 polar coordinates极坐标 polar equation极坐标方程 polar graph极图 limacon蜗牛线 cardioid心形线 rose玫瑰形线 lemniscate双纽线 spiral of Archimedes阿基米德螺旋线 complex plane复平面 real axis实轴 imaginary axis虚轴 Argand plane阿尔冈平面 absolute value of a complex number 复数的绝对值 polar form极坐标形式 trigonometric form三角函数形式 modulus模数 模 argument幅角 p th roots of unityp次单位根 directed distance有向距离 directed angle有向角度 binomial二项式 sequence序列 term项 finite sequence有限序列 infinite sequence无限序列 recursive sequence递归序列 explicit sequence显示序列 Fibonacci sequence斐波纳契数列 converge收敛 diverge发散 series级数 finite series有限级数 n th partial sumn项部分和 infinite series无限级数 sigma notation西格马记号 arithmetic sequence等差数列 common difference公差 arithmetic means等差中项 first difference一次差 second difference二次差 arithmetic series等差级数 geometric sequence等比数列 等比序列 common ratio公比 geometric means等比中项 geometric series principle of mathematical induction 数学归纳法 anchor step启始步骤 第一步 inductive hypothesis归纳假设 inductive step归纳步骤 extended principle of mathematical induction 扩展数学归纳法 binomial coefficients 二项式系数 Pascal s triangle帕斯卡三角形 杨辉三角形 Binomial Theorem二项式定理 power series幂级数 exponential series指数级数 Euler s Formula欧拉公式 transcendental function 超越函数 Descriptive Statistics 描述统计学 univariate单变量的 negatively skewed distribution 负偏态分布 symmetrical distribution 对称分布 positively skewed distribution 正偏态分布 resistant statistic抗性统计量 cluster族 子组 bimodal distribution双峰分布 percentiles百分位数值 百分位点 percentile graph outlier异常值 uniform distribution均匀分布 box and whisker plot盒须图 箱线图 quartile四分位数 四分点 fractile分位数 分位点 decile十分位数 random variable随机变量 discrete random variable 离散随机变量 contiinuous random variable 连续随机变量 probability distribution 概率分布 expected vaule期望值 binomial experiment二项实验 binomial distribution 二项分布 binomial probability distribution function 二元概率分布函数 frequency distrubution 频数分布 normal distribution正态分布 empirical rule经验公式 z valuez值 standard normal distribution 标准正态分布 sampling distribution 抽样分布 standard error of the mean 平均标准差 sampling error抽样误差 continuity correction factor 连续性校正因子 备注 When you are given a function with an unspecified domain the implied domain is the set of all real numbers for which the expression used to define the function is real A function that is defined using two or more equations for different intervals of the domain is called a piecewise defined function The x intercepts of the graph of a function are also called the zeros of a function The solutions of the corresponding equation are called the roots Graphs with line symmetry can be folded along a line so that two halves match exactly Graphs that have point symmetry can be rotated 180 with respect to a point and appear unchanged f x f x f x f x 介值定理 是闭区间上连续函数的性质之一 The graph of a continuous function has no breaks holes or gaps You can trace the graph of a continuous function without lifting your pencil The concept of approaching a value without necessarily ever reaching it is called a limit Critical points of a function are those points at which a line drawn tangent to the curve is horizontal or vertical Extrema are critical points at which a function changes its increasing or decreasing behavior At these points the function has a maximum or a minimum value either relative or absolute A point of inflection can also be a critical point At these points the graph changes its curve changes from being bent upward to being bent downward or vice versa A family of functions is a group of functions with graphs that display one or more similar characteristics A parent function is the simplest of the functions in a family This is the function that is transformed to create other members in a family of functions f x c f x 0 f x x f x 1 x The greatest integer function denoted f x x is defined as the greatest integer less than or equal to x the mirror image of the graph of a function with respect to a specific line a nonrigid transformation that has the effect of compressing shrinking or expanding enlarging the graph of a function vertically or horizontally Rigid transformations change only the position of the graph leaving the size and shape unchanged Nonrigid transformations distort the shape of the graph This combining of functions called composition is the result of one function being used to evaluate a second function f G x f g x f g x f x g x f g x f x g x f g x f x g x f g x f x g x g x 0 inverse relation is reflection of relation in the line y x interchangjing the independent and dependent variables horizontal line test the domain and range of f are equal to the range and domain of f 1 respectively If a function passes the horizontal line test then it is said to be one to one Parametric equations are equations that can express the position of an object as a function of time differential calculus is a branch of calculus that focuses on the rates of change of functions at individual points a solution thst does not satisfy the original equation The leading term test uses the power and coefficient of this term to determine polynomial end behavior Synthetic division is a shortcut for dividing a polynomial by a linear factor of the form x c The Remainder Theorem indicates that to evaluate a polynomial function f x for x c you can divide f x by x c using synthetic division The remainder will be f Using synthetic division to evaluate a function is called synthetic substitution 零值x p q x是常数项的因子 q是首项的因子 如果把一元实系数多项式按降幂方式排列 则多项式的正根的个 数要么等于相邻的非零系数的符号的变化次数 要么比它小一个 正偶数 而负根的个数则是把所有奇数次项的系数变号以后 所 得到的多项式的符号的变化次数 或者比它小一个正偶数 任何复系数一元n次多项式 方程在复数域上至少有一根 n 1 由此推出 n次复系数多项式方程在复数域内有且只有n个根 重根按重数计算 不可约的 不能削减的 不能复归的 slant asymptote When the numerator and denominator of a rational function have common factors the graph of the function has removable discontinuities called holes at the zeros of the common factors A hyperbola is the locus of all points in a plane such that the absolute value of the differences of the distances from two foci is constant The inverse of f x b x is called a logarithmic function with base b denoted logbx and read log base b of x 10为底的对数 e为底的对数 逻辑斯蒂增长函数线性化 Two noncolinear rays that share a common endpoint known as a vertex 一个角度开始旋转的边 旋转停止形成一个角度的边 In the coordinate plane an angle with its vertex at the origin and its initial side along the positive x axis is said to be in standard position two angles can have the same initial and terminal sides but fifferent measures Such angles are called coterminal angles When the terminal side of an angle that is in standard position lies on one of the coordinate axes the angle is called a quadrantal angle reference angle is the acute angle formed by the terminal side of and the x axis Unit circle is a circle of radius 1 centered at the origin The trigonometric functions are often called circular functions Functions with values that repeat at regular intervals are called periodic functions Any transformation of a sine function is called a sinusoid The parent functions y sin x and y cos x oscillate about the x axis After a vertical shift a new horizontal axis known as the midline becomes the reference line or equilibrium point about which the graph oscillates triangles that are not right triangles A trigonometric function f is a cofunction of another trigonometric function g if f a g b when a and b are complementary a binomial factor which when multipled by the original binomial factor has a product that is the difference of two squares A multivariable linear system or multivariate linear system is a system of linear equations in two or more variables 若矩阵A满足两条件 1 零行 元素全为0的行 在最下方 2 非零首元 即非零行的第一个不为零的元素 的列标号随 行标号的增加而严格递增 则称此矩阵A为阶梯形矩阵 若矩阵A满足两条件 1 它是阶梯形矩阵 2 非零首元所 在的列除了非零首元外 其余元素全为0 则称此矩阵A为行简化 阶梯形矩阵 If a system of linear equations has the same number of equations as variables then its coefficient matrix is square and the system is said to be a square system 用行列式解线性方程的方法 the process of finding a minimum value or a maximum value for a specific quantity when the quantity to be optimized is represented by a linear function this process is called linear programming a locus is a set of all points that fulfill a geometric property A parabola represents the locus of points in a plane that are equidistant from a fixed point called the focus and a specific line called the directrix A parabola is symmetric about the line perpendicular to the directrix through the focus called the axis of symmetry The latus rectum of a parabola is the line segment that passes through the focus is perpendicular to the axis of the parabola and has endpoints on the parabola The length of the latus rectum is 4p units where p is the distance from the vertex to the focus An ellipse is the locus of points in a plane such that the sum of the distances from two fixed points called foci is constant The segment that contains the foci of an ellipse and has endpoints on the ellipse is called the major axis and the midpoint of the major axis is the center The segment through the center with endpoints on the ellipse and perpendicular to the major axis is the minor axis The two endpoints of the major axis are the vertices and the endpoints of the minor axis are the co vertices The eccentricity of an ellipse is the ratio of c to a The value c represents the distance between one of the foci and the center of the ellipse The value a represents the distance between vertice and the center of the ellipse The transverse axis has a length of 2a units and connects the vertices The conjugate axis is perpendicular to the transverse passes through the center and has a length of 2b units If f and g are continuous functions of t on the interval l then the set of ordered pairs f t g t represent a parametric curve A vector is a quantity that has both magnitude and direction If a vector has its initial point at the origin it is in standard position The direction of a vector is the directed angle between the vector and the horizontal line that could be used to represent the positive x axis A quadrant bearing is a directional measurement between 0 and 90 east or west of the north south line A true bearing is a directional measurement where the angle is measured clockwise from north Parallel vectors have the same or opposite direction but not necessarily the same magnitude Equivalent vectors have the same magnitude and direction When two or more vectors are added their sum is a single vector called the resultant When you add two opposite vectors the resultant is the zero vector or null vector which has a magnitude of 0 and no specific direction Two or more vectors with a sum that is a vector r are called components The rectangular components of a vector are horizontal and vertical A vector that has a magnitude of 1 unit is called a unit vector 抛物线运动 抛物体运动 卦限 三维坐标系的象限 The complex plane may also be referred to as the Argand Plane ar GON The absolute value of a complex number is its distance from zero in the complex plane If a sequence has a limit such that the terms approach a unique number then it is said to converge If not the sequence is said to diverge A series is the indicated sum of all of the terms of a sequence A finite series is the indicated sum of all the terms of finite sequence The sum of the first n terms of a series is called the nth partial sum An infinite series is the indicated