【正文】 Equation) ……………159 高階線性微分方程(Linear Differential Equation of Higher Order) …159 常系數(shù)齊次線性微分方程(Homogeneous LinearDifferential Equation with Constant Coefficient) …………………163 常系數(shù)非齊次線性微分方程(Non HomogeneousDifferential Equation with Constant Coefficient) …………………164 歐拉方程(Euler Equation) …………………………………………164 微分方程的冪級數(shù)解法(Power Series Solution to Differential Equation) ……………………………………………164第三部分 常用數(shù)學符號的英文表達Part 3 English Expression of the Mathematical Symbol in Common Use第一部分 英漢微積分詞匯Part1 EnglishChinese Calculus Vocabulary第一章 函數(shù)與極限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補集 plement 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)間 infinite interval領域 neighborhood領域的中心 centre of a neighborhood領域的半徑 radius of a neighborhood左領域 left neighborhood右領域 right neighborhood映射 mappingX到Y(jié)的映射 mapping of X ontoY滿射 surjection單射 injection一一映射 onetoone mapping雙射 bijection算子 operator變化 transformation函數(shù) function逆映射 inverse mapping復合映射 posite mapping自變量 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 onevalued 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) posite 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 onesided 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等階無窮小 equivalent infinitesimal函數(shù)的連續(xù)性 continuity of a function增量 increment函數(shù)在x0連續(xù) the function is continuous at x0左連續(xù) left continuous右連續(xù) right continuous區(qū)間上的連續(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)間 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) lefthand derivative右導數(shù) righthand derivative單側(cè)導數(shù) onesided 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二階函數(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 rata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 MeanValue 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 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, cancave up凹向下的，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) mximum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曲率園 circle of curvature曲率中心 center of curvature曲率半徑 radius of curvature漸屈線 evolut