從知乎上面的答案OCR出來的，可以使用網(wǎng)頁搜索鲁捏。經(jīng)過了Word的簡單校對一汽。如果仍有錯誤可在評論區(qū)留言亚兄。我會修正。

第一章 函數(shù)與極限 Chaptcr1 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
補集 complement set
直積 direct product
笛卡兒積 Cartesian product
開區(qū)間 open interval
閉區(qū)間 closed interval
半開區(qū)間 half open interval
有限區(qū)間 finite interval
區(qū)間的長度 length of an interval
無限區(qū)問 infinite interval
領域 neighborhood
領域的中心 center of a neighborhood
領域的半徑 radius of a neighborhood
左領域 left neighborhood
右領域 right neighborhood
映射 mapping
X到Y的映射 mapping of X onto Y
滿射 surjection
單射 injection
映射 one-to-one mapping
雙射 bijection
算子 operator
變化 transformation
函數(shù) function
逆映射 inverse mapping
復合映射 composite mapping
白變量 independent variable
因變量 dependent variable
定義域 domain
函數(shù)值 value of function
函數(shù)關系 function relation
值域 range
自然定義域 natural domain
單值函數(shù) single valued function
多值函數(shù) multiple valued function
單值分支 one-valued branch
函數(shù)圖形 graph of a function
絕對值函數(shù) absolute value
符號函數(shù) sigh function
整數(shù)部分 integral part
階梯曲線 step curve
當且僅當 if and only if (iff)
分段函數(shù) piecewise function
上界 upper bound
下界 lower bound
有界 boundedness
無界 unbounded
函數(shù)的單調(diào)性 monotonicity of a function
單調(diào)增加的 increasing
單調(diào)減少的 decreasing
單調(diào)函數(shù) monotone function
函數(shù)的奇偶性 parity(odevity) of a function
對稱 symmetry
偶函數(shù) even function
奇函數(shù) odd function
函數(shù)的周期性 periodicity of a function
周期 period
反函數(shù) inverse function
直接函數(shù) direct function
復合函數(shù) composite function
中間變量 intermediate variable
函數(shù)的運算 operation of function
基本初等函數(shù) basic elementary function
初等函數(shù) elementary function
冪函數(shù) power function
指數(shù)函數(shù) exponential function
對數(shù)函數(shù) logarithmic function
三角函數(shù) trigonometric function
反三角函數(shù) inverse trigonometric function
常數(shù)函數(shù) constant function
雙曲函數(shù) hyperbolic function
雙曲正弦hyperbolic sine
雙曲余弦 hyperbolic cosine
雙曲正切 hyperbolic tangent
反雙曲正弦 inverse hyperbolic sine
反雙曲余弦 inverse hyperbolic cosine
反雙曲正切 inverse hyperbolic tangent
極限 limit
數(shù)列 sequence of number
收斂 convergence
收斂于 a converge to a
發(fā)散 divergent
極限的唯一性 uniqueness of limits
收斂數(shù)列的有界性 boundedness of a convergent sequence
子列 subsequence
函數(shù)的極限 limits of functions
函數(shù)當x趨于x0時的極限 limit of functions as x approaches x0
左極限 left limit
右極限 right limit
單側(cè)極限 one-sided limits
水平漸近線 horizontal asymptote
無窮小 infinitesimal
無窮大 infinity
鉛直漸近線 vertical asymptote
夾逼準則 squeeze rule
單調(diào)數(shù)列 monotonic sequence
高階無窮小 infinitesimal of higher order
低階無窮小 infinitesimal of lower order
同階無窮小 infinitesimal of the same order
等價無窮小 equivalent infinitesimal
函數(shù)的連續(xù)性 continuity of a function
增量 increment
函數(shù)在連續(xù) the function is continuous at
左連續(xù) left continuous
右連續(xù) right continuous
區(qū)問上的連續(xù)函數(shù) continuous function
函數(shù) 在該區(qū)間上連續(xù) function is continuous on an interval
不連續(xù)點 discontinuity point
第一類間斷點 discontinuity point of the first kind
第二類間斷點 discontinuity point of the second kind
初等函數(shù)的連續(xù)性 continuity of the elementary functions
定義區(qū)問 defined interval
最大值 global maximum value (absolute maximum)
最小值 global minimum value (absolute minimum)
零點定理 the zero point theorem
介值定理 intermediate value theorem

第二章 導數(shù)與微分 Chapter2 Derivative and Differential

速度 velocity
勻速運動 uniform motion
平均速度 average velocity
瞬時速度 instantaneous velocity
圓的切線 tangent line of a circle
切線 tangent line
切線的斜率 slope of the tangent line
位置函數(shù) position function
導數(shù) derivative
可導 derivable
函數(shù)的變化率問題 problem of the change rate of a function
導函數(shù) derived function
左導數(shù) left-hand derivative
右導數(shù) right-hand derivative
單側(cè)導數(shù) one-sided derivatives
在閉區(qū)間[a, b] 上可導 is derivable on the closed interval [a, b]
切線方程 tangent equation
角速度 angular velocity
成本函數(shù) cost function
邊際成本 marginal cost
鏈式法則 chain rule
隱函數(shù) implicit function
顯函數(shù) explicit function
二階導數(shù) second derivative
三階導數(shù) third derivative
高階導數(shù) nth derivative
萊布尼茨公式 Leibniz formula
對數(shù)求導法 log-derivative
參數(shù)方程 parametric equation
相關變化率 correlative change rate
微分 differential
可微的 differentiable
函數(shù)的微分 differential of function
自變量的微分 differential of independent variable
微商 differential quotient
間接測量誤差 indirect measurement error
絕對誤差 absolute error
相對誤差 relative error

第三章 微分中值定理與導數(shù)的應用 Chapter3 Mean Value Theorem of Differentials and the Application of Derivatives

羅馬定理 Rolle's theorem
費馬引理 Fermat's lemma
拉格朗日中值定理 Lagrange's mean value theorem
駐點 stationary point
穩(wěn)定點 stable point
臨界點 critical point
輔助函數(shù) 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
洛必達法則 L' Hospital's Rule
0/0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
余項 remainder term
拉格朗日余項 Lagrange remainder term
麥克勞林公式 Maclaurin's formula
佩亞諾公式 Peano remainder term
凹凸性 concavity
凹向上的 concave upward缤言，concave up
凹向下的宝当，向上凸的 concave downward , concave down
拐點 inflection point
函數(shù)的極值 extremum of function
極大值 local(relative)maximum
最大值 global(absolute)maximum
極小值 local(relative)minimum
最小值 global(absolute)minimum
目標函數(shù) objective function
曲率 curvature
弧微分 arc differential
平均曲率 average curvature
曲率圓 circle of curvature
曲率中心 center of curvature
曲率半徑 radius of curvature
漸屈線 evolute
漸伸線 involute
根的隔離 isolation of root
隔離區(qū)間 isolation interval
切線法 tangent line method

第四章 不定積分 Chapter4 Indefinite Integrals

原函數(shù) primitive function(antiderivative)
積分號 sign of integration
被積函數(shù) integrand
積分變量 integral variable
積分曲線 integral curve
積分表 table of integrals
換元積分法 integration by substitution
分部積分法 integration by parts
分部積分公式 formula of integration by parts
有理函數(shù) rational function
真分式 proper fraction
假分式 improper fraction

第五章 定積分 Chapter5 Definite Integrals

曲邊梯形 trapezoid with
曲邊 curve edge
窄矩形 narrow rectangle
曲邊梯形的面積 area of trapezoid with curved edge
積分下限 lower limit of integral
積分上限 upper limit of integral
積分區(qū)間 integral interval
分割 partition
積分和 integral sum
可積 integrable
矩形法 rectangle method
積分中值定理 mean value theorem of integrals
函數(shù)在區(qū)間上的平均值 average value of a function on an integrals
牛頓一菜布尼茨公式 Newton-Leibniz formula
微積分基本公式 fundamental formula of calculus
換元公式 formula for integration by substitution
遞推公式 recurrence formula
反常積分 improper integral
反常積分發(fā)散 the improper integral is divergent
反常積分收斂 the improper integral is convergent
無窮限的反常積分 improper integral on an infinite interval
無界函數(shù)的反常積分 improper integral of unbounded functions
絕對收斂 absolutely convergent

第六章 定積分的應用 Chapter6 Applications of the Definite Integrals

元素法 the element method
面積元素 clement of area
平面圖形的面積 area of a plane figure
直角坐標，又稱笛卡兒坐標 Cartesian coordinates
極坐標 polar coordinates
拋物線 parabola
橢圓 ellipse
旋轉(zhuǎn)體的面積 volume of a solid of rotation
旋轉(zhuǎn)橢球體 ellipsoid of revolution ellipsoid of rotation
曲線的弧長 arc length of a curve
可求長的 rectifiable
光滑 smooth
功 work
水壓力 water pressure
引力 gravitation
變力 variable force

第七章 空間解析幾何與向量代數(shù) Chapter7 Space Analytic Geometry and Vector Algebra

向量 vector
自由向量 free vector
單位向量 unit vector
零向量 zero vector
相等 equal
平行 parallel
向量的線性運算 linear operation of vector
三角法則 triangle rule
平行四邊形法則 parallelogram rule
交換律 commutative law
結合律 associative law
負向量 negative vector
差 difference
分配律 distributive law
空間直角坐標系 space rectangular coordinates
坐標面 coordinate plane
卦限 octant
向量的模 modulus of vector
向量a與b的夾角 angle between vector a and b
方向余弦 direction cosine
方向角 direction angle
向量在軸上的投影 projection of a vector onto an axis
數(shù)量積,外積,叉積 scalar product, dot product, inner product
曲面方程 equation for a surface
球面 sphere
旋轉(zhuǎn)曲面 surface of revolution
母線 generating line
軸 axis
圓錐面 cone
頂點 vertex
旋轉(zhuǎn)單葉雙曲面 revolution hyperboloids of one sheet
旋轉(zhuǎn)雙葉雙曲面 revolution hyperboloids of two sheet
柱面 cylindrical surface cylinder
圓柱面 cylindrical surface
準線 directrix
拋物柱面 parabolic cylinder
二次曲面 quadric surface
橢圓錐面 elliptic cone
橢球面 ellipsoid
單葉雙曲面 hyperboloid of one sheet
雙葉雙曲面 hyperboloid of two sheets
旋轉(zhuǎn)橢球面 ellipsoid of revolution
橢圓拋物面 elliptic paraboloid
旋轉(zhuǎn)拋物面 paraboloid of revolution
雙曲拋物面 hyperbolic paraboloid
馬鞍面 saddle surface
橢圓柱面 elliptic cylinder
雙曲柱面 hyperbolic cylinder
拋物柱面 parabolic cylinder
空間曲線 space curve
空間曲線的一般方程 general form equations of a space curve
空間曲線的參數(shù)方程 parametric equations of a space curve
螺轉(zhuǎn)線 spiral
螺矩 pitch
投影柱面 projecting cylinder
投影 projection
平面的點法式方程 point normal form equation of a plane
法向量 normal vector
平面的一般方程 general form equation of a plane
兩平面的夾角 angle between two planes
點到平面的距離 distance from a point to a plane
空間直線的一般方程 general equation of a line in space
方向向量 direction vector
直線的點向式方程 point direction form equations of a line
方向數(shù) direction number
直線的參數(shù)方程 parametric equations of a line
兩直線的夾角 angle between wo lines
垂直 perpendicular
直線與平面的夾角 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
系數(shù)行列式 coefficient determinant

第八章 多元函數(shù)微分法及其應用 Chapter8 Differentiation of Functions of Several Variables and Its Application

元函數(shù) function of one variable
多元函數(shù) function of several variables
內(nèi)點 interior point
外點 exterior point
邊界點 frontier point boundary point
聚點 point of accumulation
開集 open set
閉集 closed set
連通集 connected set
開區(qū)域 open region
閉區(qū)域 closed region
有界集 bounded set
無界集 unbounded set
n維空間 n-dimensional space
重極限 double limit
多元函數(shù)的連續(xù)性 continuity of function of several
連續(xù)函數(shù) continuous function
不連續(xù)點 discontinuity point
一致連續(xù) uniformly continuous
偏導數(shù) partial derivative
對自變量x的偏導數(shù) partial derivative with respect to independent variable x
高階偏導數(shù) partial derivative of higher order
一階偏導數(shù) second order partial derivative
混合偏導數(shù) hybrid partial derivative
全微分 total differential
偏增量 partial increment
偏微分 partial differential
全增量 total increment
可微分 differentiable
必要條件 necessary condition
充分條件 sufficient condition
疊加原理 superposition principle
全導數(shù) total derivative
中間變量 intermediate variable
隱函數(shù)存在定理 theorem of the existence of implicit function
曲線的切向量 tangent vector of a curve
法平面 normal plane
向量方程 vector equation
向量值函數(shù) vector-valued function
切平面 tangent plane
法線 normal line
方向?qū)?shù) directional derivative
梯度 gradient
數(shù)量場 scalar field
梯度場 gradient field
向量場 vector field
勢場 potential field
引力場 gravitational field
引力勢 gravitational potential
曲面在一點的切平面 tangent plane to a surface at a point
曲線在一點的法線 normal line to a surface at a point
無條件極值 unconditional extreme values
條件極值 conditional extreme values
拉格朗日乘數(shù)法 Lagrange multiplier method
拉格朗日乘子 Lagrange multiplier
經(jīng)驗公式 empirical formula
最小二乘法 method of least squares
均方誤差 mean square error

第九章 重積分 Chapter9 Multiple Integrals

重積分 double integral
可加性 additivity
累次積分 iterated integral
體積元素 volume element
重積分 triple integral
直角坐標系中的體積元素 volume element in rectangular coordinate system
柱面坐標 cylindrical coordinates
柱面坐標系中的體積元素 volume element in cylindrical coordinate system
球面坐標 spherical coordinates
球面坐標中的體積元素 volume element in spherical coordinate system
反常二重積分 improper double integral
曲面的面積 area of a surface
質(zhì)心 center of mass
靜矩 static moment
密度 density
形心 centroid
轉(zhuǎn)動慣量 moment of inertia
參變量 parametric variable

第十章 曲線積分與曲面積分 Chapter10 Line (Curve)Integrals and Surface Integrals

對弧長的曲線積分 line integrals with respect to arc length
第一類曲線積分 line integrals of the first type
對坐標的曲線積分 line integrals with respect to x, y, and z
第二類曲線積分 line integrals of the second type
有向曲線弧 directed arc
單連通區(qū)域 simple connected region
復連通區(qū)域 complex connected region
格林公式 Green formula
第一類曲面積分 surface integrals of the first type
對面的曲面積分 surface integrals with respect to area
有向曲面 directed surface
對坐標的曲面積分 surface integrals with respect to coordinate elements
第二類曲面積分 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
環(huán)流量 circulation
旋度 rotation, curl

第十一章 無窮級數(shù) Chapter11 Infinite Series

一般項 general term
部分和 partial sum
余項 remainder term
等比級數(shù) geometric series
幾何級數(shù) geometric series
公比 common ratio
調(diào)和級數(shù) harmonic series
柯西收斂準則 Cauchy convergence criteria, Cauchy criteria for convergence
正項級數(shù) series of positive terms
達朗貝爾判別法 d'Alembert's ratio test
柯西判別法 Cauchy test
交錯級數(shù) alternating series
絕對收斂 absolutely convergent
條件收斂 conditionally convergent
柯西乘積 Cauchy product
函數(shù)項級數(shù) series of functions
發(fā)散點 point of divergence
收斂點 point of convergence
收斂域 convergence domain
和函數(shù) sum function
冪級數(shù) power series
冪級數(shù)的系數(shù) coefficients of power series
阿貝爾定理 Abel Theorem
收斂半徑 radius of convergence
收斂區(qū)間 interval of convergence
泰勒級數(shù) Taylor series
麥克勞林級數(shù) Maclaurin series
項展開式 binomial expansion
近似計算 approximate calculation
舍入誤差 round-off error, rounding error
歐拉公式 Euler' s formula
魏爾斯特拉絲判別法 Weierstrass test
三角級數(shù) trigonometric series
振幅 amplitude
角頻率 angular frequency
初相 initial phase
矩形波 square wave
諧波分析 harmonic analysis
直流分量 direct component
基波 fundamental wave
二次諧波 second harmonic
三角函數(shù)系 trigonometric function system
傅立葉系數(shù) Fourier coefficient
傅立葉級數(shù) Fourier series
周期延拓 periodic prolongation
正弦級數(shù) sine series
余弦級數(shù) cosine series
奇延拓 odd prolongation
偶延拓 even prolongation
傅立葉級數(shù)的復數(shù)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 differential equation
常微分方程 ordinary differential equation
偏微分方程 prial differential equation, PDE
微分方程的階 order of 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
初始條件 initial condition
微分方程的特解 particular solution of a differential equation
初值問題 initial value problem
微分方程的積分曲線 integral curve of a differential equation
可分離變量的微分方程 variable separable differential equation
隱式解 implicit solution
隱式通解 implicit general solution
衰變系數(shù) decay coefficient
衰變 decay
齊次方程 homogeneous equation
一階線性方程 linear differential equation of first order
非齊次 non-homogeneous
齊次線性方程 homogeneous linear equation
非齊次線性方程 non-homogeneous linear equation
常數(shù)變易法 method of variation of constant
暫態(tài)電流 transient state current
穩(wěn)態(tài)電流 steady state current
伯努利方程 Bernoulli equation
全微分方程 total differential equation
積分因子 integrating factor
高階微分方程 differential equation of higher order
懸鏈線 catenary
高階線性 微分方程 linear differential equation of higher order
自由振動的微分方程 differential equation of free vibration
強迫振動的微分方程 differential equation of forced oscillation
串聯(lián)電路的振蕩方程 oscillation equation of series circuit
二階線性微分方程 second order linear differential equation
線性相關 linearly dependence
線性無關 linearly independence
二階常系數(shù)齊次線性微分方程 second order homogeneous linear differential equation with constant coefficient
一階變系數(shù)齊次線性微分方程 second order homogeneous linear differential equation with variable coefficient
特征方程 characteristic equation
無阻尼自由振動的微分方程 differential equation of free vibration with zero damping
固有頻率 natural frequency
簡諧振動 simple harmonic oscillation, simple harmonic vibration
微分算子 differential operator
待定系數(shù)法 method of undetermined coefficient
共振現(xiàn)象 resonance phenomenon
歐拉方程 Euler equation
冪級數(shù)解法 power series solution
數(shù)值解法 numeral solution
勒讓德方程 Legendre equation
微分方程組 system of differential equations
常系數(shù)線性微分方程組 system of linear differential equations with constant coefficient