【正文】 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(dāng)且僅當(dāng) 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(fù)合函數(shù) posite function中間變量 intermediate variable函數(shù)的運(yùn)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(dāng)x趨于x0時(shí)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(zhǔn)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(diǎn) discontinuity point第一類間斷點(diǎn) discontinuity point of the first kind第二類間斷點(diǎn) 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(diǎn)定理 the zero point theorem介值定理 intermediate value theorem第二章 導(dǎo)數(shù)與微分Chapter2 Derivative and Differential速度 velocity勻速運(yùn)動(dòng) uniform motion平均速度 average velocity瞬時(shí)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(dǎo)數(shù) derivative可導(dǎo) derivable函數(shù)的變化率問題 problem of the change rate of a function導(dǎo)函數(shù) derived function左導(dǎo)數(shù) lefthand derivative右導(dǎo)數(shù) righthand derivative單側(cè)導(dǎo)數(shù) onesided derivatives在閉區(qū)間【a,b】上可導(dǎo) 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?zhǔn)椒▌t chain rule隱函數(shù) implicit function顯函數(shù) explicit function二階函數(shù) second derivative三階導(dǎo)數(shù) third derivative高階導(dǎo)數(shù) nth derivative萊布尼茨公式 Leibniz formula對數(shù)求導(dǎo)法 log derivative參數(shù)方程 parametric equation相關(guān)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(dǎo)數(shù)的應(yīng)用Chapter3 MeanValue Theorem of Differentials and the Application of Derivatives羅馬定理 Rolle’s theorem費(fèi)馬引理 Fermat’s lemma拉格朗日中值定理 Lagrange’s mean value theorem駐點(diǎn) stationary point穩(wěn)定點(diǎn) stable point臨界點(diǎn) 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(dá)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(xiàng) remainder term拉格朗日余項(xiàng) 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(diǎn) 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(biāo)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 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 integvals牛頓－萊布尼茨公式 NewtonLeibniz 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(yīng)用Chapter6 Applications of the Definite Integrals元素法 the element method面積元素 element of area平面圖形的面積 ar