一階導數英語怎麼說及英文翻譯

『壹』 微積分裡面專有名詞中英文對照

absolutely convergent 絕對收斂
absolute value 絕對值
algebraic function 代數函數
analytic geometry 解析幾何
antiderivative 不定積分
approximate integration 近似積分
approximation 近似法、逼近法
arbitrary constant 任意常數
arithmetic series/progression (AP)算數級數
asymptotes (vertical and horizontal)(垂直/水平)漸近線
average rate of change 平均變化率
base 基數
binomial theorem 二項式定理，二項展開式
Cartesian coordinates 笛卡兒坐標(一般指直角坐標)
Cartesian coordinates system 笛卡兒坐標系
Cauch』s Mean Value Theorem 柯西均值定理
chain rule 鏈式求導法則
calculus 微積分學
closed interval integral 閉區間積分
coefficient 系數
composite function 復合函數
conchoid 蚌線
continuity (函數的)連續性
concavity (函數的)凹凸性
conditionally convergent 有條件收斂
continuity 連續性
critical point 臨界點
cubic function 三次函數
cylindrical coordinates 圓柱坐標
decreasing function 遞減函數
decreasing sequence 遞減數列
definite integral 定積分
derivative 導數
determinant 行列式
differential coefficient 微分系數
differential equation 微分方程
directional derivative 方向導數
discontinuity 不連續性
discriminant (二次函數)判別式
disk method 圓盤法
divergence 散度
divergent 發散的
domain 定義域
dot proct 點積
double integral 二重積分
ellipse 橢圓
ellipsoid 橢圓體
epicycloid 外擺線
Euler's method (BC)歐拉法
expected valued 期望值
exponential function 指數函數
extreme value heorem 極值定理
factorial 階乘
finite series 有限級數
fundamental theorem of calculus 微積分基本定理
geometric series/progression (GP)幾何級數
gradient 梯度
Green formula 格林公式
half-angle formulas 半形公式
harmonic series 調和級數
helix 螺旋線
higher derivative 高階導數
horizontal asymptote 水平漸近線
horizontal line 水平線
hyperbola 雙曲線
hyper boloid 雙曲面
implicit differentiation 隱函數求導
implicit function 隱函數
improper integral 廣義積分、瑕積分
increment 增量
increasing function 增函數
indefinite integral 不定積分
independent variable 自變數
inequality 不等式
ndeterminate form 不定型
infinite point 無窮極限
infinite series 無窮級數
infinite series 無限級數
inflection point (POI) 拐點
initial condition 初始條件
instantaneous rate of change 瞬時變化率
integrable 可積的
integral 積分
integrand 被積分式
integration 積分
integration by part 分部積分法
intercept 截距
intermediate value of Theorem ：中間值定理
inverse function 反函數
irrational function 無理函數
iterated integral 逐次積分
Laplace transform 拉普拉斯變換
law of cosines 餘弦定理
least upper bound 最小上界
left-hand derivative 左導數
left-hand limit 左極限
L'Hospital's rule 洛必達法則
limacon 蚶線
linear approximation 線性近似法
linear equation 線性方程式
linear function 線性函數
linearity 線性
linearization 線性化
local maximum 極大值
local minimum 極小值
logarithmic function 對數函數
MacLaurin series 麥克勞林級數
maximum 最大值
mean value theorem (MVT)中值定理
minimum 最小值
method of lagrange multipliers 拉格朗日乘數法
molus 絕對值
multiple integral 多重積分
multiple 倍數
multiplier 乘子
octant 卦限
open interval integral 開區間積分
optimization 優化法，極值法
origin 原點
orthogonal 正交
parametric equation (BC)參數方程
partial derivative 偏導數
partial differential equation 偏微分方程
partial fractions 部分分式
piece-wise function 分段函數
parabola 拋物線
parabolic cylinder 拋物柱面
paraboloid ：拋物面
parallelepiped 平行六面體
parallel lines 並行線
parameter ：參數
partial integration 部分積分
partiton ：分割
period ：周期
periodic function 周期函數
perpendicular lines 垂直線
piecewise defined function 分段定義函數
plane 平面
point of inflection 反曲點
point-slope form 點斜式
polar axis 極軸
polar coordinates 極坐標
polar equation 極坐標方程
pole 極點
polynomial 多項式
power series 冪級數
proct rule 積的求導法則
quadrant 象限
quadratic functions 二次函數
quotient rule 商的求導法則
radical 根式
radius of convergence 收斂半徑
range 值域
(related) rate of change with time (時間)變化率
rational function 有理函數
reciprocal 倒數
remainder theorem 余數定理
Riemann sum 黎曼和
Riemannian geometry 黎曼幾何
right-hand limit 右極限
Rolle's theorem 羅爾(中值)定理
root 根
rotation 旋轉
secant line 割線
second derivative 二階導數
second derivative test 二階導數試驗法
second partial derivative 二階偏導數
series 級數
shell method (積分)圓筒法
sine function 正弦函數
singularity 奇點
slant 母線
slant asymptote 斜漸近線
slope 斜率
slope-intercept equation of a line 直線的斜截式
smooth curve 平滑曲線
smooth surface 平滑曲面
solid of revolution 旋轉體
symmetry 對稱性
substitution 代入法、變數代換
tangent function 正切函數
tangent line 切線
tangent plane 切(平)面
tangent vector 切矢量
taylor's series 泰勒級數
three-dimensional analytic geometry 空間解析幾何
total differentiation 全微分
trapezoid rule 梯形(積分)法則

『貳』 微積分英文專業術語

下面提供AP最常用的微積分詞彙，如果需要翻譯，請Hi我：
antiderivative 原函數
a representation, usually in symbolic form, of any function whose derivative is a given function.

tangent 切線，斜率，正切
a line or a plane that touches a curve or a surface at a single point.

chain rule 鏈式求導法
the theorem that defines the method for taking the derivative of a composite function.

concave downward 向下開口
part of a graph resembling an upside down bowl.

concave upward 向上開口
part of a graph resembling a right side up bowl.

continuous 連續
being in immediate connection or spatial relationship.

critical point 臨界點
point on the graph where the derivative is either 0 or undefined.

cylindrical shell method 旋轉體積圓筒積分法
technique for finding the volume of a solid of revolution.

definite integral 定積分
the representation of the difference in values of a primitive of a given function evaluated at two designated points.

derivative 導數，求導，導函數
the change of a function with respect to an infinitesimally small change in the independent variable, or the slope of the point's tangent line.

differentiable 可導的，可微的
a function whose graph is curve that is smooth and contains no discontinuities or cusps.

disk method 旋轉體積圓盤法
technique for finding the volume of a solid of revolution when integrating along the axis of revolution.

extreme value theorem 極值理論
guarantees an absolute max and an absolute min

first derivative test 極值點、拐點的確定法
determines whether an inflection point is a minimum, maximum, or neither.

higher order derivatives 高階導數，高階導函數
any derivatives beyond the first derivative.

implicit differentiation 隱函數求導、微分
method for finding the derivative of an implicitly defined function or relation using the chain rule.

indefinite integral 不定積分
another way of saying antiderivative.

instantaneous rate of change 瞬時牽連變化率、相關變化率
rate of change at a particular moment.

instantaneous velocity 瞬時速度
rate at which an object is moving at a particular moment.

integration by parts 分部積分
a method of evaluating an integral by use of the formula, ∫udv = uv − ∫v.

limit 極限
value that a function approaches as the domain variable approach a specific value.

mean value theorem 中值定理
the theorem that there is a point in a continuous curve where the derivative is equal to the average derivative of the entire arc.

normal line 法線
line that is at a 90 degree angle, perpendicular to a surface.

point-slope form 直線方程點斜式
form used the most when finding the equation of a line.

riemann sum 黎曼積分
method for approximating the definite integral.

second derivative test 用二階導數檢查是否是極大值點或極小值點
determines whether a critical point is a relative minimum or maximum using the value of the second derivative at the point.

u-substitution U型變數代換
integration method that involves using the chain rule in reverse.

trigonometric substitution 三角函數變數代換
substitution of trigonometric functions for other expressions to eliminate radicals in integrals.

washer method 旋轉體積的圓筒積分法
similar to the disk method but using washers instead of disks.

『叄』 求微積分的英語詞彙,

你好,本人現在在美國讀高中正在學微積分,所以微積分的專業詞彙英文知道的比較多一些 如果中文有翻譯不對的希望你能理解
微積分 Calculus
極限 limit
積分 integration
微分 differentiation
導數 derivative
極值應該是extrema
三角函數 trig(trigonometric) functions
反三角函數 inverse trig(trigonomic) functions
微分方程 differential equations
黎曼積分 Riemann Sums
定積分 definite integrals
指數函數 exponential functions
對數函數 log(logarithmic) functions
自然對數函數 natural log functions
微積分基本定理 the Fundamental Theorem of Calculus
洛必達法則 l'hopital's rule
Rolle定理 Rolle's Theorem
u代入法 u substitution
弧線長度 arc length
正無窮大 positive infinity
負無窮大 negative infinity

例題
1. Find the volume of the solid formed by revolving the region by the graphs of y = x^2 +1, y = 0, and x = 1. About the y-axis.
求被函數y= x^2 +1, y = 0,和 x = 1所包圍的區域圍繞Y軸旋轉後形成的體積.
答案是3pi/2

2.Find the area bounded by the graphs of x =3 - y^2 and x = y + 1.
求被x = 3 - y^2 和 x = y + 1 的圖像所包圍的面積.
答案是9/2

3.A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the page are to be 3/2 inches, and the margins on the left and right are to be 1 inch. What should the dimensions of the page be so that the least amount of paper is used?
有一頁長方形的紙,上面有24平方英寸的印刷區域,紙上端和下端的空白都是3/2英寸,左邊和右邊的空白都是1英寸.求這張紙的長寬以使所用的紙最少.

我知道這些不是很多隻是微積分的一小部分,不過也是費了好大力氣寫的希望能對你有幫助吧!