(高等数学英文课件)1.5 Tangent Lines

高等数学-微积分第1章（英文讲稿）C alc u lus (Fifth Edition)高等数学- Calculus微积分（双语讲稿）Chapter 1 Functions and Models1.1 Four ways to represent a function1.1.1 ☆Definition(1-1) function: A function f is a rule that assigns to each element x in a set A exactly one element, called f(x), in a set B. see Fig.2 and Fig.3Conceptions: domain; range (See fig. 6 p13); independent variable; dependent variable. Four possible ways to represent a function: 1)Verbally语言描述(by a description in words); 2) Numerically数据表述(by a table of values); 3) Visually 视觉图形描述(by a graph);4)Algebraically 代数描述(by an explicit formula).1.1.2 A question about a Curve represent a function and can’t represent a functionThe way ( The vertical line test ) : A curve in the xy-plane is the graph of a function of x if and only if no vertical line intersects the curve more than once. See Fig.17 p 171.1.3 ☆Piecewise defined functions (分段定义的函数)Example7 (P18)1－x if x ≤1f(x)＝﹛x2if x＞1Evaluate f(0)，f(1)，f(2) and sketch the graph.Solution：1.1.4 About absolute value (分段定义的函数)⑴∣x∣≥0；⑵∣x∣≤0Example8 (P19)Sketch the graph of the absolute value function f(x)＝∣x∣.Solution：1.1.5☆☆Symmetry ，(对称) Even functions and Odd functions (偶函数和奇函数)⑴Symmetry See Fig.23 and Fig.24⑵①Even functions: If a function f satisfies f(－x)＝f(x) for every number x in its domain，then f is call an even function. Example f(x)＝x2 is even function because: f(－x)＝ (－x)2＝x2＝f(x)②Odd functions: If a function f satisfie s f(－x)＝－f(x) for every number x in its domain，thenf is call an odd function. Example f(x)＝x3 is even function because: f(－x)＝(－x)3＝－x3＝－f(x)③Neither even nor odd functions:1.1.6☆☆Increasing and decreasing function (增函数和减函数)⑴Definition(1-2) increasing and decreasing function:① A function f is called increasing on an interval I if f(x1)＜f(x2) whenever x1＜x2 in I. ①A function f is called decreasing on an interval I if f(x1)＞f(x2) whenever x1＜x2 in I.See Fig.26. and Fig.27. p211.2 Mathematical models: a catalog of essential functions p251.2.1 A mathematical model p25A mathematical model is a mathematical description of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reduction.1.2.2 Linear models and Linear function P261.2.3 Polynomial P27A function f is called a polynomial ifP(x) ＝a n x n＋a n－1x n－1＋…＋a2x2＋a1x＋a0Where n is a nonnegative integer and the numbers a0，a1，a2，…，a n－1，a n are constants called the coefficients of the polynomial. The domain of any polynomial is R＝(－∞,＋∞).if the leading coefficient a n≠0, then the degree of the polynomial is n. For example, the function P(x) ＝5x6＋2x5－x4＋3x－9⑴Quadratic function example: P(x) ＝5x2＋2x－3 二次函数（方程）⑵Cubic function example: P(x) ＝6x3＋3x2－1 三次函数（方程）1.2.4Power functions幂函数P30A function of the form f(x) ＝x a，Where a is a constant, is called a power function. We consider several cases：⑴a＝n where n is a positive integer ，(n＝1，2，3，…，)⑵a＝1/n where n is a positive integer，(n＝1，2，3，…，) The function f(x) ＝x1/n⑶a＝n－1 the graph of the reciprocal function f(x) ＝x－1 反比函数1.2.5Rational function有理函数P 32A rational function f is a ratio of two polynomials:f(x)＝P(x) /Q(x)1.2.6Algebraic function代数函数P32A function f is called algebraic function if it can be constructed using algebraic operations ( such as addition，subtraction，multiplication，division，and taking roots) starting with polynomials. Any rational function is automatically an algebraic function. Examples: P 321.2.7Trigonometric functions 三角函数P33⑴f(x)＝sin x⑵f(x)＝cos x⑶f(x)＝tan x＝sin x / cos x1.2.8Exponential function 指数函数P34The exponential functions are the functions the form f(x) ＝a x Where the base a is a positive constant.1.2.9Transcendental functions 超越函数P35These are functions that are not a algebraic. The set of transcendental functions includes the trigonometric，inverse trigonometric，exponential，and logarithmic functions，but it also includes a vast number of other functions that have never been named. In Chapter 11 we will study transcendental functions that are defined as sums of infinite series.1.2 Exercises P 35-381.3 New functions from old functions1.3.1 Transformations of functions P38⑴Vertical and Horizontal shifts (See Fig.1 p39)①y＝f(x)＋c，（c＞0）shift the graph of y＝f(x) a distance c units upward.②y＝f(x)－c，（c＞0）shift the graph of y＝f(x) a distance c units downward.③y＝f(x＋c)，（c＞0）shift the graph of y＝f(x) a distance c units to the left.④y＝f(x－c)，（c＞0）shift the graph of y＝f(x) a distance c units to the right.⑵ V ertical and Horizontal Stretching and Reflecting (See Fig.2 p39)①y＝c f(x)，（c＞1）stretch the graph of y＝f(x) vertically bya factor of c②y＝(1/c) f(x)，（c＞1）compress the graph of y＝f(x) vertically by a factor of c③y＝f(x/c)，（c＞1）stretch the graph of y＝f(x) horizontally by a factor of c.④y＝f(c x)，（c＞1）compress the graph of y＝f(x) horizontally by a factor of c.⑤y＝－f(x)，reflect the graph of y＝f(x) about the x-axis⑥y＝f(－x)，reflect the graph of y＝f(x) about the y-axisExamples1: (See Fig.3 p39)y＝f( x) ＝cos x，y＝f( x) ＝2cos x，y＝f( x) ＝（1/2）cos x，y＝f( x) ＝cos（x/2），y＝f( x) ＝cos2xExamples2: (See Fig.4 p40)Given the graph y＝f( x) ＝( x)1/2，use transformations to graph y＝f( x) ＝( x)1/2－2，y＝f( x) ＝(x－2)1/2，y＝f( x) ＝－( x)1/2，y＝f( x) ＝2 ( x)1/2，y＝f( x) ＝(－x)1/21.3.2 Combinations of functions (代数组合函数)P42Algebra of functions: Two functions (or more) f and g through the way such as add, subtract, multiply and divide to combined a new function called Combination of function.☆Definition(1-2) Combination function: Let f and g be functions with domains A and B. The functions f±g，f g and f /g are defined as follows: （特别注意符号(f±g)( x) 定义的含义）①(f±g)( x)＝f(x)±g( x)，domain ＝A∩B②(f g)( x)＝f(x) g( x)，domain ＝A∩ B③(f /g)( x)＝f(x) /g( x)，domain ＝A∩ B and g( x)≠0Example 6 If f( x) ＝( x)1/2，and g( x)＝(4－x2)1/2，find functions y＝f(x)＋g( x)，y＝f(x)－g( x)，y＝f(x)g( x)，and y＝f(x) /g( x)Solution: The domain of f( x) ＝( x)1/2 is [0，＋∞)，The domain of g( x) ＝(4－x2)1/2 is interval [－2，2]，The intersection of the domains of f(x) and g( x) is[0，＋∞)∩[－2，2]＝[0，2]Thus，according to the definitions, we have(f＋g)( x)＝( x)1/2＋(4－x2)1/2，domain [0，2](f－g)( x)＝( x)1/2－(4－x2)1/2，domain [0，2](f g)( x)＝f(x) g( x) ＝( x)1/2(4－x2)1/2＝(4 x－x3)1/2domain [0，2](f /g)( x)＝f(x)/g( x)＝( x)1/2/(4－x2)1/2＝[ x/(4－x2)]1/2 domain [0，2)1.3.3☆☆Composition of functions (复合函数)P45☆Definition(1-3) Composition function: Given two functions f and g the composite func tion f⊙g (also called the composition of f and g ) is defined by(f⊙g)( x)＝f( g( x)) （特别注意符号(f⊙g)( x) 定义的含义）The domain of f⊙g is the set of all x in the domain of g such that g(x) is in the domain of f . In other words, (f⊙g)(x) is defined whenever both g(x) and f (g (x)) are defined. See Fig.13 p 44 Example7 If f (g)＝( g)1/2 and g(x)＝(4－x3)1/2find composite functions f⊙g and g⊙f Solution We have(f⊙g)(x)＝f (g (x) ) ＝( g)1/2＝((4－x3)1/2)1/2(g⊙f)(x)＝g (f (x) )＝(4－x3)1/2＝[4－((x)1/2)3]1/2＝[4－(x)3/2]1/2Example8 If f (x)＝( x)1/2 and g(x)＝(2－x)1/2find composite function s①f⊙g ②g⊙f ③f⊙f④g⊙gSolution We have①f⊙g＝(f⊙g)(x)＝f (g (x) )＝f((2－x)1/2)＝((2－x)1/2)1/2＝(2－x)1/4The domain of (f⊙g)(x) is 2－x≥0 that is x ≤2 {x ︳x ≤2 }＝(－∞，2]②g⊙f＝(g⊙f)(x)＝g (f (x) )＝g (( x)1/2 )＝(2－( x)1/2)1/2The domain of (g⊙f)(x) is x≥0 and 2－( x)1/2x ≥0 ，that is( x)1/2≤2 ，or x ≤ 4 ，so the domain of g⊙f is the closed interval[0，4]③f⊙f＝(f⊙f)(x)＝f (f(x) )＝f((x)1/2)＝((x)1/2)1/2＝(x)1/4The domain of (f⊙f)(x) is [0，∞)④g⊙g＝(g⊙g)(x)＝g (g(x) )＝g ((2－x)1/2 )＝(2－(2－x)1/2)1/2The domain of (g⊙g)(x) is x－2≥0 and 2－(2－x)1/2≥0 ，that is x ≤2 and x ≥－2，so the domain of g⊙g is the closed interval[－2，2]Notice: g⊙f⊙h＝f (g(h(x)))Example9Example10 Given F (x)＝cos2( x＋9)，find functions f，g，and h such that F (x)＝f⊙g⊙h Solution Since F (x)＝[cos ( x＋9)] 2，that is h (x)＝x＋9 g(x)＝cos x f (x)＝x2Exercise P 45-481.4 Graphing calculators and computers P481.5 Exponential functions⑴An exponential function is a function of the formf (x)＝a x See Fig.3 P56 and Fig.4Exponential functions increasing and decreasing (单调性讨论)⑵Lows of exponents If a and b are positive numbers and x and y are any real numbers. Then1) a x+y＝a x a y2) a x－y＝a x / a y3) (a x)y＝a xy4) (ab)x+y ＝a x b x⑶about the number e f (x)＝e x See Fig. 14，15 P61Some of the formulas of calculus will be greatly simplified if we choose the base a .Exercises P 62-631.6 Inverse functions and logarithms1.6.1 Definition(1-4) one-to-one function: A function f iscalled a one-to-one function if it never takes on the same value twice；that is，f (x1)≠f (x2)，whenever x1≠x2( 注解：不同的自变量一定有不同的函数值，不同的自变量有相同的函数值则不是一一对应函数) Example: f (x)＝x3is one-to-one function.f (x)＝x2 is not one-to-one function, See Fig.2,3,4 ☆☆Definition(1-5) Inverse function:Let f be a one-to-one function with domain A and range B. Then its inverse function f －1(y)has domain B and range A and is defined byf－1(y)＝x f (x)＝y for any y in Bdomain of f－1＝range of frange of f－1＝domain of f( 注解：it says : if f maps x into y, then f－1maps y back into x . Caution: If f were not one-to-one function，then f－1 would not be uniquely defined. )Caution: Do not mistake the－1 in f－1for an exponent. Thus f－1(x)＝1/ f(x) Because the letter x is traditionally used as the independent variable, so when we concentrate on f－1(y) rather than on f－1(y), we usually reverse the roles of x and y in Definition (1-5) and write as f－1(x)＝y f (x)＝yWe get the following cancellation equations:f－1( f(x))＝x for every x in Af (f－1(x))＝x for every x in B See Fig.7 P66Example 4 Find the inverse function of f(x)＝x3＋6Solution We first writef(x)＝y＝x3＋6Then we solve this equation for x:x3＝y－6x＝(y－6)1/3Finally, we interchange x and y：y＝(x－6)1/3That is, the inverse function is f－1(x)＝(x－6)1/3( 注解：The graph of f－1 is obtained by reflecting the graph of f about the line y＝x. ) See Fig.9、8 1.6.2 Logarithmic function If a＞0 and a≠1，the exponential function f (x)＝a x is either increasing or decreasing and so it is one-to-one function by the Horizontal Line Test. It therefore has an inverse function f－1，which is called the logarithmic function with base a and is denoted log a，If we use the formulation of an inverse function given by (See Fig.3 P56)f－1(x)＝y f (x)＝yThen we havelogx＝y a y＝xThe logarithmic function log a x＝y has domain (0,∞) and range R.Usefully equations:①log a(a x)＝x for every x∈R②a log ax＝x for every x＞01.6.3 ☆Lows of logarithms :If x and y are positive numbers, then①log a(xy)＝log a x＋log a y②log a(x/y)＝log a x－log a y③log a(x)r＝r log a x where r is any real number1.6.4 Natural logarithmsNatural logarithm isl og e x＝ln x ＝ythat is①ln x ＝y e y＝x② ln(e x)＝x x∈R③e ln x＝x x＞0 ln e＝1Example 8 Solve the equation e5－3x＝10Solution We take natural logarithms of both sides of the equation and use ②、③ln (e5－3x)＝ln10∴5－3x＝ln10x＝(5－ln10)/3Example 9 Express ln a＋(ln b)/2 as a single logarithm.Solution Using laws of logarithms we have:ln a＋(ln b)/2＝ln a＋ln b1/2＝ln(ab1/2)1.6.5 ☆Change of Base formula For any positive number a (a≠1), we havel og a x＝ln x/ ln a1.6.6 Inverse trigonometric functions⑴Inverse sine function or Arcsine functionsin－1x＝y sin y＝x and －π/2≤y≤π / 2，－1≤x≤1 See Fig.18、20 P72Example13 ① sin－1 (1/2) or arcsin(1/2) ② tan(arcsin1/3)Solution①∵sin (π/6)＝1/2，π/6 lies between －π/2 and π / 2，∴sin－1 (1/2)＝π/6② Let θ＝arcsin1/3，so sinθ＝1/3tan(arcsin1/3)＝tanθ＝s inθ/cosθ＝(1/3)/(1－s in2θ)1/2＝1/(8)1/2Usefully equations:①sin－1(sin x)＝x for －π/2≤x≤π / 2②sin (sin－1x)＝x for －1≤x≤1⑵Inverse cosine function or Arccosine functioncos－1x＝y cos y＝x and 0 ≤y≤π，－1≤x≤1 See Fig.21、22 P73Usefully equations:①cos－1(cos x)＝x for 0 ≤x≤π②cos (cos－1x)＝x for －1≤x≤1⑶Inverse Tangent function or Arctangent functiontan－1x＝y tan y＝x and －π/2＜y＜π / 2 ，x∈R See Fig.23 P73、Fig.25 P74Example 14 Simplify the expression cos(ta n－1x).Solution 1 Let y＝tan－1 x，Then tan y＝x and －π/2＜y＜π / 2 ，We want find cos y but since tan y is known, it is easier to find sec y first:sec2y＝1 ＋tan2y sec y＝(1 ＋x2 )1/2∴cos(ta n－1x)＝cos y ＝1/ sec y＝(1 ＋x2)－1/2Solution 2∵cos(ta n－1x)＝cos y∴cos(ta n－1x)＝(1 ＋x2)－1/2⑷Other Inverse trigonometric functionscsc－1x＝y∣x∣≥1csc y＝x and y∈(0，π / 2]∪(π，3π / 2]sec－1x＝y∣x∣≥1sec y＝x and y∈[0，π / 2)∪[π，3π / 2]cot－1x＝y x∈R cot y＝x and y∈(0，π)Exercises P 74-85Key words and PhrasesCalculus 微积分学Set 集合Variable 变量Domain 定义域Range 值域Arbitrary number 独立变量Independent variable 自变量Dependent variable 因变量Square root 平方根Curve 曲线Interval 区间Interval notation 区间符号Closed interval 闭区间Opened interval 开区间Absolute 绝对值Absolute value 绝对值Symmetry 对称性Represent of a function 函数的表述（描述）Even function 偶函数Odd function 奇函数Increasing Function 增函数Increasing Function 减函数Empirical model 经验模型Essential Function 基本函数Linear function 线性函数Polynomial function 多项式函数Coefficient 系数Degree 阶Quadratic function 二次函数（方程）Cubic function 三次函数（方程）Power functions 幂函数Reciprocal function 反比函数Rational function 有理函数Algebra 代数Algebraic function 代数函数Integer 整数Root function 根式函数（方程）Trigonometric function 三角函数Exponential function 指数函数Inverse function 反函数Logarithm function 对数函数Inverse trigonometric function 反三角函数Natural logarithm function 自然对数函数Chang of base of formula 换底公式Transcendental function 超越函数Transformations of functions 函数的变换Vertical shifts 垂直平移Horizontal shifts 水平平移Stretch 伸张Reflect 反演Combinations of functions 函数的组合Composition of functions 函数的复合Composition function 复合函数Intersection 交集Quotient 商Arithmetic 算数。

微积分英文词汇，高数名词中英文对照，高等数学术语英语翻译一览V、X、Z:Value Of fun CtiO n :函数值VariabIe :变数VeCtOr :向量Velocity :速度VertiCaI asymptote :垂直渐近线Volume :体积X-axis : X 轴x-coord in ate : X 坐标x-intercept : X 截距Zero VeCtOr :函数的零点Zeros of a polyno mial : 多项式的零点T:Tangentfun Cti on :正切函数Tangentline :切线Tangent pla ne :切平面Tangent VeCtOr :切向量Total differe ntial :全微分TrigOnO metric fun Cti on :三角函数TrigOnO metric in tegrals :三角积分TrigOnO metric SUbStitUti ons :三角代换法TriPe in tegrals :三重积分S:SaddIe poi nt :鞍点SCaIar :纯量SeCan t li ne :割线SeCOnd derivative :二阶导数SeCOnd DeriVatiVe TeSt :二阶导数试验法SeC ond PartiaI derivative :二阶偏导数SeCtOr :扇形SeqUe nce :数歹USerieS :级数Set :集合Shell method :剥壳法SinefUn Cti on :正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称R:Radius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、Q:Parabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation ：线性近似Linear equation ：线性方程式Linearfunction ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/ 高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面D:Decreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function of a constant function directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数 partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数 second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程partial ：偏微分方程 Differentiation ：求导法 implicit ：隐求导法 partial：偏微分法 term by term ：逐项求导法 Directional derivatives ：方向导数Discontinuity ：不连续性 Disk method ：圆盘法：复合函数之导数：常数函数之导数DiSta nce :距离DiVerge nce :发散Domai n :定义域Dot PrOduCt :点积Double in tegral :二重积分Cha nge Of VariabIe in :二重积分之变数变换in polar coord in ates :极坐标二重积分C:Calculus :微积分differe ntial :微分学in tegral :积分学CarteSian coordinates :笛卡儿坐标JIl 一般指直角坐标CarteSia n coord in ates SyStem : 笛卡儿坐标系CaUCh's Mean VaIUe TheOrem :柯西均值定理Chai n Rule :连锁律Change of VariabIeS :变数变换CirCIe :圆CirCUIar cyli nder :圆柱Closed in terval :圭寸闭区间COeffiCie nt :系数Compositi on of fun Cti on :函数之合成Compo Undin terest :复禾UCon CaVity :凹性Conchoid :蚌线Cone :圆锥Con Sta nt fun ctio n :常数函数Con Sta nt of in tegrati on :积分常数COntin Uity :连续性at a poi nt :在一点处之连续性of a fun ctio n :函数之连续性on an in:在区间之连续性tervalfrom the left :左连续from the right : 右连续Con ti nu ous fun Cti on :连续函数Convergence :收敛in terval of :收敛区间radius of :收敛半径Conv erge nt SeqUe nce :收敛数列SerieS :收敛级数Coord in ate : S :坐标CarteSian :笛卡儿坐标cyli ndrical :柱面坐标polar ：极坐标rectangular ：直角坐标spherical ：球面坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平面Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder ：圆柱Cylindrical Coordinates ：圆柱坐标A、B:Absolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：用微分逼近linear ：线性逼近法by Simpson's Rule ：Simpson 法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：面积under a curve ：曲线下方之面积between curves ：曲线间之面积in polar coordinates ：极坐标表示之面积of a sector of a circle ：扇形之面积of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线horizontal ：水平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：二项级数。

高数名词中英文对照来源：微积分英文词汇,高数名词中英文对照,高等数学术语英语翻译一览关键词：微积分英文,高等数学英文翻译,高数英语词汇来源：上海外教网| 发布日期：2008-05-16 17:12V、X、Z:Value of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点T:Tangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分S:Saddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称R:Radius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、Q:Parabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面D:Decreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程partial ：偏微分方程Differentiation ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in ：二重积分之变数变换in polar coordinates ：极坐标二重积分C:Calculus ：微积分differential ：微分学integral ：积分学Cartesian coordinates ：笛卡儿坐标一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cauch’s Mean Value Theorem ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线Cone ：圆锥Constant function ：常数函数Constant of integration ：积分常数Continuity ：连续性at a point ：在一点处之连续性of a function ：函数之连续性on an interval ：在区间之连续性from the left ：左连续from the right ：右连续Continuous function ：连续函数Convergence ：收敛interval of ：收敛区间radius of ：收敛半径Convergent sequence ：收敛数列series ：收敛级数Coordinate：s：坐标Cartesian ：笛卡儿坐标cylindrical ：柱面坐标polar ：极坐标rectangular ：直角坐标spherical ：球面坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平面Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder：圆柱Cylindrical Coordinates ：圆柱坐标A、B:Absolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：用微分逼近linear ：线性逼近法by Simpson’s Rule ：Simpson法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：面积under a curve ：曲线下方之面积between curves ：曲线间之面积in polar coordinates ：极坐标表示之面积of a sector of a circle ：扇形之面积of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线horizontal ：水平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：二项级数。

微积分英文词汇,高数名词中英文对照,高等数学术语英语翻译一览关键词：微积分英文,高等数学英文翻译,高数英语词汇来源：上海外教网| 发布日期：2008-05-16 17:12V、X、Z:Value of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点T:Tangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分S:Saddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称R:Radius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、Q:Parabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面D:Decreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程partial ：偏微分方程Differentiation ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in ：二重积分之变数变换in polar coordinates ：极坐标二重积分C:Calculus ：微积分differential ：微分学integral ：积分学Cartesian coordinates ：笛卡儿坐标一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cauch’s Mean Value Theorem ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线Cone ：圆锥Constant function ：常数函数Constant of integration ：积分常数Continuity ：连续性at a point ：在一点处之连续性of a function ：函数之连续性on an interval ：在区间之连续性from the left ：左连续from the right ：右连续Continuous function ：连续函数Convergence ：收敛interval of ：收敛区间radius of ：收敛半径Convergent sequence ：收敛数列series ：收敛级数Coordinate：s：坐标Cartesian ：笛卡儿坐标cylindrical ：柱面坐标polar ：极坐标rectangular ：直角坐标spherical ：球面坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平面Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder：圆柱Cylindrical Coordinates ：圆柱坐标A、B:Absolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：用微分逼近linear ：线性逼近法by Simpson’s Rule ：Simpson法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：面积under a curve ：曲线下方之面积between curves ：曲线间之面积in polar coordinates ：极坐标表示之面积of a sector of a circle ：扇形之面积of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线horizontal ：水平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：二项级数微积分词汇第一章函数与极限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函数当x趋于x0时的极限limit of functions 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作者：新少年特工2007-10-8 18:37 回复此发言--------------------------------------------------------------------------------2 高等数学-翻译等阶无穷小equivalent infinitesimal函数的连续性continuity of a function增量increment函数在x0连续the function is continuous at x0左连续left continuous右连续right continuous区间上的连续函数continuous function函数在该区间上连续function 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在闭区间【a,b】上可导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 constantValue of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点T:Tangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分S:Saddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称R:Radius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、Q:Parabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、O:Maximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的L:Laplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数I:Implicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分H:Higher mathematics 高等数学/高数E、F、G、H:Ellipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面D:Decreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程partial ：偏微分方程Differentiation ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分。

高等数学中定义定理的英文表达Value of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点TTangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分SSaddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称RRadius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、QParabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、OMaximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的LLaplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数IImplicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分HHigher mathematics 高等数学/高数E、F、G、HEllipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面DDecreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程partial ：偏微分方程Differentiation ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in ：二重积分之变数变换in polar coordinates ：极坐标二重积分CCalculus ：微积分differential ：微分学integral ：积分学Cartesian coordinates ：笛卡儿坐标图片一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cauch’s Mean Value Theorem ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线Cone ：圆锥Constant function ：常数函数Constant of integration ：积分常数Continuity ：连续性at a point ：在一点处之连续性of a function ：函数之连续性on an interval ：在区间之连续性from the left ：左连续from the right ：右连续Continuous function ：连续函数Convergence ：收敛interval of ：收敛区间radius of ：收敛半径Convergent sequence ：收敛数列series ：收敛级数Coordinate：s：坐标Cartesian ：笛卡儿坐标cylindrical ：柱面坐标polar ：极坐标rectangular ：直角坐标spherical ：球面坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平面Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder：圆柱Cylindrical Coordinates ：圆柱坐标A、BAbsolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：用微分逼近linear ：线性逼近法by Simpson’s Rule ：Simpson法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：面积under a curve ：曲线下方之面积between curves ：曲线间之面积in polar coordinates ：极坐标表示之面积of a sector of a circle ：扇形之面积of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线horizontal ：水平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：二项级数。

高等数学术语英语翻译V、X、Z:Value of function：函数值Vector：函数值Volume：体积X-axis：x轴x-coordinate：x坐标x-intercept：x截距Zero vector：函数的零点T:Tangent function：正切函数Tangent line：切线Total differential：全微分Trigonometric function：三角函数Tripe integrals：三重积分S:Second derivative：二阶导数Second partial derivative：二阶偏导数Sequence：数列Set：集合Slope：斜率Smooth curve：平滑曲线Smooth surface：平滑曲面Solid of revolution：旋转体Space：空间Speed：速率Spherical coordinates：球面坐标Sum：和Surface：曲面Surface integral：面积分Surface of revolution：旋转曲面Symmetry：对称Sine function：正弦函数Slant asymptote：斜渐近线R:Range of a function：函数的值域Rate of change：变化率Rational function：有理函数Rational number：有理数Real number：实数Rectangular coordinates：直角坐标Revolution,solid of：旋转体Revolution,surface of：旋转曲面Root：根P、Q:Parabola：拋物线Parabolic cylinder：抛物柱面Paraboloid：抛物面Parallelepiped：平行六面体Parallel lines：并行线Parameter：参数Partial derivative：偏导数Partial differential equation：偏微分方程Partial fractions：部分分式Partial integration：部分积分Partiton：分割Period：周期Periodic function：周期函数Perpendicular lines：垂直线Plane：平面Polar coordinate：极坐标Pole：极点Polynomial：多项式Positive angle：正角Power function：幂函数Product：积M、N、O:Maximum and minimum values：极大与极小值Multiple integrals：重积分Natural num ber：自然数Normal line：法线Number：数Odd function：奇函数One-sided li mit：单边极限Open interval：开区间Ordinary differential equation：常微分方程Orthogonal：正交的Origin：原点L:Law of Cosines：余弦定理Left-hand derivative：左导数Left-hand limit：左极限Length：长度Limit：极限Linear approximation：线性近似Linear equation：线性方程式Linear function：线性函数Linearity：线性Logarithm：对数Logarithmic function：对数函数I:Implicit function：隐函数Increment：增量Indefinite integral：不定积分Independent variable：自变数Indeterminate from：不定型Inequality：不等式Infinite point：无穷极限Infinite series：无穷级数Integer：整数Integral：积分Integrand：被积分式Integration：积分Intercepts：截距Interval：区间Inverse function：反函数Inverse trigonometric function：反三角函数Iterated integral：逐次积分Intermediate value of Theorem：中间值定理H:Higher mathematics高等数学/高数E、F、G、H:Ellipse：椭圆Ellipsoid：椭圆体Equation：方程式Even function：偶函数Expected Valued：期望值Exponential Function：指数函数Extreme value：极值Focus：焦点Fractions：分式Function：函数Gradient：梯度Graph：图形Higher Derivative：高阶导数Horizontal asymptote：水平渐近线Horizontal line：水平线Hyperbola：双曲线Hyper boloid：双曲面D:Decreasing function：递减函数Decreasing sequence：递减数列Definite integral：定积分Density：密度Derivative：导数higher：高阶导数partial：偏导数Determinant：行列式Differentiable function：可导函数Differential：微分Differential equation：微分方程partial：偏微分方程Differentiation：求导法implicit：隐求导法partial：偏微分法Discontinuity：不连续性Distance：距离Divergence：发散Domain：定义域Double integral：二重积分C:Calculus：微积分differential：微分学integral：积分学Circle：圆Circular cylinder：圆柱Closed interval：封闭区间Coefficient：系数Cone：圆锥Constant function：常数函数Constant of integration：积分常数Continuity：连续性Continuous function：连续函数Convergence：收敛Convergent sequence：收敛数列Coordinate：s：坐标polar：极坐标rectangular：直角坐标spherical：球面坐标Coordinate axes：坐标轴Cosine function：余弦函数Critical point：临界点Cubic function：三次函数Curve：曲线Cylinder：圆柱A、B:Absolute convergence：绝对收敛Absolute extreme values：绝对极值Absolute maximum and minimum：绝对极大与极小Absolute value：绝对值Absolute value function：绝对值函数Acceleration：加速度Antiderivative：反导Arbitrary constant：任意常数Arc length：弧长Area：面积Asymptote：渐近线horizontal：水平渐近线slant：斜渐近线vertical：垂直渐近线Average speed：平均速率Average velocity：平均速度微积分词汇第一章函数与极限Chapter1Function 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开区间open interval闭区间closed interval映射mapping一一映射one-to-one mapping变化transformation函数function自变量independent variable因变量dependent variable函数关系function relation值域range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分段函数piecewise function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对称symmetry偶函数even function奇函数odd 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inversetrigonometric function常数函数constant function极限limit数列sequence of number 收敛convergence发散divergent子列subsequence函数的极限limits of functions左极限left limit右极限right limit单侧极限one-sided limits无穷小infinitesimal无穷大infinity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 order2高等数学-翻译等阶无穷小equivalent infinitesimal函数的连续性continuity of a function增量increment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Chapter2Derivative and Differential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导函数derived function切线方程tangent equation隐函数implicit function显函数explicit function高阶导数nth derivative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Chapter3MeanValue Theorem of Differentials and the Application of Derivatives临界点critical point辅助函数auxiliary function不定式indeterminate form泰勒公式Taylor formula余项remainder term拐点inflection point函数的极值extremum of function极大值local(relative)maximum极小值local(relative)minimum曲率curvature平均曲率average curvature曲率中心center of curvature第四章不定积分Chapter4Indefinite 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第五章定积分Chapter5Definite Integrals曲边梯形trapezoid with曲边curve 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反常积分improper integral第六章定积分的应用面积元素element of area极坐标polar coordinates抛物线parabola椭圆ellipse旋转体的面积volume of a solid of rotation曲线的弧长arc length of acurve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Chapter7Space Analytic Geometry and Vector Algebra相等equal平行parallel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差difference分配律distributive law球面sphere轴axis顶点vertex抛物柱面parabolic cylinder二次曲面quadric surface椭圆锥面dlliptic cone椭球面ellipsoid椭圆柱面elliptic cylinder双曲柱面hyperbolic cylinder抛物柱面parabolic cylinder空间曲线space curve投影projection垂直perpendicular第八章多元函数微分法及其应用Chapter8Differentiation of Functions of Several Variables and Its Application一元函数function of one variable多元函数function of several variables边界点frontier point,boundary point开集openset闭集closed set有界集bounded set 无界集unbounded set二重极限double limit连续函数continuous function不连续点discontinuity point偏导数partial derivative高阶偏导数partial derivative of higher order二阶偏导数second order 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全导数total derivative法线normal line梯度gradient 无条件极值unconditional extreme values条件极值conditional extreme values最小二乘法method of least squares第九章重积分Chapter9Multiple Integrals二重积分double integral可加性additivity三重积分triple integral反常二重积分improper double integral曲面的面积area of a surface质心centre of mass密度density第十二章微分方程Chapter12Differential Equation常微分方程ordinary differential equation偏微分方程partial differential equation,PDE初始条件initial condition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全微分方程total differential equation高阶微分方程differential equation of higher order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 variable coefficient微分方程组system of differential equations。

数学专有名词英文词典V、X、ZValue of function ：函数值Variable ：变数Vector ：向量Velocity ：速度Vertical asymptote ：垂直渐近线Volume ：体积X-axis ：x轴x-coordinate ：x坐标x-intercept ：x截距Zero vector ：函数的零点Zeros of a polynomial ：多项式的零点TTangent function ：正切函数Tangent line ：切线Tangent plane ：切平面Tangent vector ：切向量Total differential ：全微分Trigonometric function ：三角函数Trigonometric integrals ：三角积分Trigonometric substitutions ：三角代换法Tripe integrals ：三重积分SSaddle point ：鞍点Scalar ：纯量Secant line ：割线Second derivative ：二阶导数Second Derivative Test ：二阶导数试验法Second partial derivative ：二阶偏导数Sector ：扇形Sequence ：数列Series ：级数Set ：集合Shell method ：剥壳法Sine function ：正弦函数Singularity ：奇点Slant asymptote ：斜渐近线Slope ：斜率Slope-intercept equation of a line ：直线的斜截式Smooth curve ：平滑曲线Smooth surface ：平滑曲面Solid of revolution ：旋转体Space ：空间Speed ：速率Spherical coordinates ：球面坐标Squeeze Theorem ：夹挤定理Step function ：阶梯函数Strictly decreasing ：严格递减Strictly increasing ：严格递增Sum ：和Surface ：曲面Surface integral ：面积分Surface of revolution ：旋转曲面Symmetry ：对称RRadius of convergence ：收敛半径Range of a function ：函数的值域Rate of change ：变化率Rational function ：有理函数Rationalizing substitution ：有理代换法Rational number ：有理数Real number ：实数Rectangular coordinates ：直角坐标Rectangular coordinate system ：直角坐标系Relative maximum and minimum ：相对极大值与极小值Revenue function ：收入函数Revolution , solid of ：旋转体Revolution , surface of ：旋转曲面Riemann Sum ：黎曼和Riemannian geometry ：黎曼几何Right-hand derivative ：右导数Right-hand limit ：右极限Root ：根P、QParabola ：拋物线Parabolic cylinder ：抛物柱面Paraboloid ：抛物面Parallelepiped ：平行六面体Parallel lines ：并行线Parameter ：参数Partial derivative ：偏导数Partial differential equation ：偏微分方程Partial fractions ：部分分式Partial integration ：部分积分Partiton ：分割Period ：周期Periodic function ：周期函数Perpendicular lines ：垂直线Piecewise defined function ：分段定义函数Plane ：平面Point of inflection ：反曲点Polar axis ：极轴Polar coordinate ：极坐标Polar equation ：极方程式Pole ：极点Polynomial ：多项式Positive angle ：正角Point-slope form ：点斜式Power function ：幂函数Product ：积Quadrant ：象限Quotient Law of limit ：极限的商定律Quotient Rule ：商定律M、N、OMaximum and minimum values ：极大与极小值Mean Value Theorem ：均值定理Multiple integrals ：重积分Multiplier ：乘子Natural exponential function ：自然指数函数Natural logarithm function ：自然对数函数Natural number ：自然数Normal line ：法线Normal vector ：法向量Number ：数Octant ：卦限Odd function ：奇函数One-sided limit ：单边极限Open interval ：开区间Optimization problems ：最佳化问题Order ：阶Ordinary differential equation ：常微分方程Origin ：原点Orthogonal ：正交的LLaplace transform ：Leplace 变换Law of Cosines ：余弦定理Least upper bound ：最小上界Left-hand derivative ：左导数Left-hand limit ：左极限Lemniscate ：双钮线Length ：长度Level curve ：等高线L'Hospital's rule ：洛必达法则Limacon ：蚶线Limit ：极限Linear approximation：线性近似Linear equation ：线性方程式Linear function ：线性函数Linearity ：线性Linearization ：线性化Line in the plane ：平面上之直线Line in space ：空间之直线Lobachevski geometry ：罗巴切夫斯基几何Local extremum ：局部极值Local maximum and minimum ：局部极大值与极小值Logarithm ：对数Logarithmic function ：对数函数IImplicit differentiation ：隐求导法Implicit function ：隐函数Improper integral ：瑕积分Increasing/Decreasing Test ：递增或递减试验法Increment ：增量Increasing Function ：增函数Indefinite integral ：不定积分Independent variable ：自变数Indeterminate from ：不定型Inequality ：不等式Infinite point ：无穷极限Infinite series ：无穷级数Inflection point ：反曲点Instantaneous velocity ：瞬时速度Integer ：整数Integral ：积分Integrand ：被积分式Integration ：积分Integration by part ：分部积分法Intercepts ：截距Intermediate value of Theorem ：中间值定理Interval ：区间Inverse function ：反函数Inverse trigonometric function ：反三角函数Iterated integral ：逐次积分HHigher mathematics 高等数学/高数E、F、G、HEllipse ：椭圆Ellipsoid ：椭圆体Epicycloid ：外摆线Equation ：方程式Even function ：偶函数Expected Valued ：期望值Exponential Function ：指数函数Exponents , laws of ：指数率Extreme value ：极值Extreme Value Theorem ：极值定理Factorial ：阶乘First Derivative Test ：一阶导数试验法First octant ：第一卦限Focus ：焦点Fractions ：分式Function ：函数Fundamental Theorem of Calculus ：微积分基本定理Geometric series ：几何级数Gradient ：梯度Graph ：图形Green Formula ：格林公式Half-angle formulas ：半角公式Harmonic series ：调和级数Helix ：螺旋线Higher Derivative ：高阶导数Horizontal asymptote ：水平渐近线Horizontal line ：水平线Hyperbola ：双曲线Hyper boloid ：双曲面DDecreasing function ：递减函数Decreasing sequence ：递减数列Definite integral ：定积分Degree of a polynomial ：多项式之次数Density ：密度Derivative ：导数of a composite function ：复合函数之导数of a constant function ：常数函数之导数directional ：方向导数domain of ：导数之定义域of exponential function ：指数函数之导数higher ：高阶导数partial ：偏导数of a power function ：幂函数之导数of a power series ：羃级数之导数of a product ：积之导数of a quotient ：商之导数as a rate of change ：导数当作变率right-hand ：右导数second ：二阶导数as the slope of a tangent ：导数看成切线之斜率Determinant ：行列式Differentiable function ：可导函数Differential ：微分Differential equation ：微分方程partial ：偏微分方程Differentiation ：求导法implicit ：隐求导法partial ：偏微分法term by term ：逐项求导法Directional derivatives ：方向导数Discontinuity ：不连续性Disk method ：圆盘法Distance ：距离Divergence ：发散Domain ：定义域Dot product ：点积Double integral ：二重积分change of variable in ：二重积分之变数变换in polar coordinates ：极坐标二重积分CCalculus ：微积分differential ：微分学integral ：积分学Cartesian coordinates ：笛卡儿坐标图片一般指直角坐标Cartesian coordinates system ：笛卡儿坐标系Cauch’s Mean Value Theorem ：柯西均值定理Chain Rule ：连锁律Change of variables ：变数变换Circle ：圆Circular cylinder ：圆柱Closed interval ：封闭区间Coefficient ：系数Composition of function ：函数之合成Compound interest ：复利Concavity ：凹性Conchoid ：蚌线Cone ：圆锥Constant function ：常数函数Constant of integration ：积分常数Continuity ：连续性at a point ：在一点处之连续性of a function ：函数之连续性on an interval ：在区间之连续性from the left ：左连续from the right ：右连续Continuous function ：连续函数Convergence ：收敛interval of ：收敛区间radius of ：收敛半径Convergent sequence ：收敛数列series ：收敛级数Coordinate：s：坐标Cartesian ：笛卡儿坐标cylindrical ：柱面坐标polar ：极坐标rectangular ：直角坐标spherical ：球面坐标Coordinate axes ：坐标轴Coordinate planes ：坐标平面Cosine function ：余弦函数Critical point ：临界点Cubic function ：三次函数Curve ：曲线Cylinder：圆柱Cylindrical Coordinates ：圆柱坐标A、BAbsolute convergence ：绝对收敛Absolute extreme values ：绝对极值Absolute maximum and minimum ：绝对极大与极小Absolute value ：绝对值Absolute value function ：绝对值函数Acceleration ：加速度Antiderivative ：反导数Approximate integration ：近似积分Approximation ：逼近法by differentials ：用微分逼近linear ：线性逼近法by Simpson’s Rule ：Simpson法则逼近法by the Trapezoidal Rule ：梯形法则逼近法Arbitrary constant ：任意常数Arc length ：弧长Area ：面积under a curve ：曲线下方之面积between curves ：曲线间之面积in polar coordinates ：极坐标表示之面积of a sector of a circle ：扇形之面积of a surface of a revolution ：旋转曲面之面积Asymptote ：渐近线horizontal ：水平渐近线slant ：斜渐近线vertical ：垂直渐近线Average speed ：平均速率Average velocity ：平均速度Axes, coordinate ：坐标轴Axes of ellipse ：椭圆之轴Binomial series ：二项级数。