微积分双语词汇

MATHEMATICAL TERMS (Part 1)

calculus 微积分definition 定义theorem 定理lemma 引理

corollary推论prove 证明proof 证明show 证明

solution 解formula 公式if and only if ( iff ) 当且仅当

x X for all x X x X there exists an x X

such that 使得given 已知set集合finite set有限集

infinite set 无限集interval区间open interval开区间closed interval 闭区间neighborhood 邻域number 数natural number 自然数integer 整数

odd number 奇数even number 偶数real number 实数rational number 有理数irrational number 无理数positive number 正数

negative number 负数

mapping 映射function 函数monotone function 单调函数

increasing function 增函数decreasing function 减函数

bounded function 有界函数odd function 奇函数

even function 偶函数periodic function 周期函数

composite function 复合函数inverse function 反函数

domain 定义域range 值域variable 变量independent variable自变量dependent variable因变量sequence 数列convergent sequence收敛数列divergent sequence 发散数列bounded sequence 有界数列

decreasing sequence 递减数列increasing sequence 递增数列

limit极限one-sided limit 单侧极限left-hand limit 左极限right-hand limit 右极限The Squeeze Theorem 夹逼定理infinity 无穷大infinitesimal 无穷小equivalent infinitesimal 等价无穷小infinitesimal of higher order 高阶无穷小

order of infinitesimal 无穷小的阶infinitesimals of the same order 同阶无穷小

increment 增量continuous function 连续函数continuity 连续性

f(x) is continuous at x 在x连续f(x) is discontinuous at x 在x间断discontinuity 间断点discontinuity of the first (second) kind 第一（二）类间断点removable discontinuity 可去间断点jump discontinuity 跳跃间断点

infinite discontinuity 无穷间断点

intermediate value 介值The Intermediate Value Theorem 介值定理

zero point 零点The Zero Point Theorem 零点定理root 根

equation 方程uniform continuity 一致连续

derivative 导数rate of change 变化率velocity 速度

instantaneous velocity 瞬时速度tangent (line) 切线normal (line) 法线

slope 斜率left-hand derivative 左导数right-hand derivative 右导数

f(x) is differentiable at x f(x) 在x处可导(可微) differentiation 求导

The Chain Rule 链式法则differentiation formulas 求导公式

implicit function 隐函数explicit function 显函数

implicit differentiation 隐函数求导logarithm 对数

Logarithmic differentiation 对数求导法parameter 参数

parametric equation 参数方程parametric curve 参数曲线

hyperbolic function 双曲函数hyperbolic sine 双曲正弦

hyperbolic cosine 双曲余弦hyperbolic tangent 双曲正切

hyperbolic cotangent 双曲余切

MATHEMATICAL TERMS (Part 2)

differential 微分differential quotient 微商approximate value 近似值error 误差

relative error 相对误差absolute error 绝对误差

invariance of differential form 微分形式不变性higher derivative 高阶导数

first derivative 一阶导数second derivative 二阶导数

third derivative 三阶导数nth derivative n阶导数

twice differentiable 二阶可导acceleration 加速度

mean value 中值The Mean Value Theorem 中值定理

Rolle’s Theorem 罗尔定理Lagrange’s Mean Value Theorem 拉格朗日中值定理Cauchy’s Mean Value Theorem 柯西中值定理equality 等式

inequality 不等式indeterminate form 不定型(未定式) indeterminate form of type ( ) ( )型未定式

L’Hospital’s Rule 洛必达法则Taylor’s formula 泰勒公式polynomial 多项式nth-degree polynomial n次多项式

remaind 余项Lagrange’s form of remainder 拉格朗日型余项Peano’s form of remainder 皮亚诺型余项

Maclaurin formula 麦克劳林公式Taylor polynomial 泰勒多项式Mauclaurin polynomial 麦克劳林多项式polynomial approximation 多项式逼近accuracy 精确度margin 边际

marginal cost 边际成本marginal revenue 边际收益

elasticity 弹性density 密度

mass 质量extreme value 极值

local maximum value 极大值local minimum value 极小值

(absolute) maximum 最大值(absolute) minimum 最小值

stationary point 驻点（稳定点）critical point 临界点

The First (Second) Derivative Test （极值的）一（二）阶判别法

convex 凸的convex curve 凸曲线

concave 凹的concave curve 凹曲线

convex function 凸函数point of inflection 拐点

asymptote 渐近线horizontal asymptote 水平渐近线

vertical asymptote 垂直渐近线slant asymptote 斜渐近线

curve sketching 作图sketch a curve 作图

curvature 曲率The bisection method 二分法

The secant method 弦位法Newton’s method 牛顿（切线）法

The tangent method 切线法