微 积 分 讲 义 下 载
微 积 分 讲 义 下 载
01. 函数的极限 (The Limit of a Function) - Limit_01.pdf
02. 极限的运算公式 (Basic Formulas for Limits) - Limit_02.pdf
03. 夹挤定理 (The Squeeze Theorem) - Limit_03.pdf
04. 单边极限 (One-Sided Limits) - Limit_04.pdf
05. 重要的极限公式 (Two Important Limits) - Limit_05.pdf
06. 无穷大的极限值与铅直渐近线 (Infinite Limits and Vertical Asymptotes) - Limit_06.pdf
07. 无穷远处的极限与水平渐近线 (Limits at Infinity and Horizontal Asymptotes) - Limit_07.pdf
08. 连续函数 (Continuous Functions) - Limit_08.pdf
09. 连续函数的运算 (Formulas for Continuous Functions) - Limit_09.pdf
10. 中间值定理 (The Intermediate Value Theorem) - Limit_10.pdf
All. 极限(全) - Limit_all.pdf
01. 切线 (The Tangent Line) - Derivative_01.pdf
02. 变化率 (The Rate of Change) - Derivative_02.pdf
03. 导函数 (The Derivative as a Function) - Derivative_03.pdf
04. 基本的微分公式 (Basic Differentiation Formulas) - Derivative_04.pdf
05. 法线 (The Normal Line) - Derivative_05.pdf
06. 微分的乘法与除法公式 (Product and Quotient Rules) - Derivative_06.pdf
07. 三角函数的导数 (Derivatives of Trigonometric Functions) - Derivative_07.pdf
08. 高阶导数 (Higher Derivatives) - Derivative_08.pdf
09. 链锁律 (The Chain Rule) - Derivative_09.pdf
10. 链锁律的应用 (Applications of the Chain Rule) - Derivative_10.pdf
11. 隐函数微分法 (Implicit Differentiation) - Derivative_11.pdf
All. 导数(全) - Derivative_all.pdf
01. 线性估计 (Linear Approximations) - AppDer_01.pdf
02. 微分量 (Differentials) - AppDer_02.pdf
03. 函数的极值 (Extreme Values of Functions) - AppDer_03.pdf
04. 费马引理与临界点 (Fermat's Theorem and Critical Points) - AppDer_04.pdf
05. 均值定理 (The Mean Value Theorem) - AppDer_05.pdf
06. 递增与递减函数 (Increasing and Decreasing Functions) - AppDer_06.pdf
07. 一阶导数判别法 (First Derivative Test) - AppDer_07.pdf
08. 图形的凹性与反曲点 (Concavity and Inflection Points) - AppDer_08.pdf
09. 二阶导数判别法 (Second Derivative Test) - AppDer_09.pdf
10. 反导函数与不定积分 (Antiderivatives and Indefinite Integrals) - AppDer_10.pdf
11. 不定积分的基本公式 (Formulas for Indefinite Integrals) - AppDer_11.pdf
All. 导数的应用(全) - AppDer_all.pdf
01. 精彩选辑 - 无
02. 曲线下的面积 (The Area under a Curve) - Integral_02.pdf
03. 定积分 (The Definite Integral) - Integral_03.pdf
04. 定积分的基本性质 (The Properties of the Definite Integral) - Integral_04.pdf
05. 微积分第一基本定理 (First Fundamental Theorem of Calculus) - Integral_05.pdf
06. 微积分第二基本定理 (Second Fundamental Theorem of Calculus) - Integral_06.pdf
07. 代换积分法 (The Substitution Rule) - Integral_07.pdf
08. 奇偶函数的定积分 (The Definite Integrals of Odd and Even Functions) - Integral_08.pdf
All. 积分(全) - Integral_all.pdf
01. 曲线所围区域的面积(I) (The Area between Curves (I)) - AppInt_01.pdf
02. 曲线所围区域的面积(II) (The Area between Curves (II)) - AppInt_02.pdf
03. 函数的平均 (The Average of a Function) - AppInt_03.pdf
All. 积分的应用(全)- AppInt_all.pdf
01. 一对一函数 (One-to-One Functions) [精华版(ET)] - TransFunct(ET)_01.pdf
02. 反函数 (Inverse Functions) [精华版(ET)] - TransFunct(ET)_02.pdf
03. 反函数的基本性质 (Properties of Inverse Functions) [精华版(ET)] - TransFunct(ET)_03.pdf
04. 自然指数函数 (The Natural Exponential Function) [精华版(ET)] - TransFunct(ET)_04.pdf
05. 自然指数函数的基本公式 (Formulas for the Natural Exponential Function) [精华版(ET)] - TransFunct(ET)_05.pdf
06. 自然对数函数 (The Natural Logarithmic Function) [精华版(ET)] - TransFunct(ET)_06.pdf
07. 自然对数函数的基本公式 (Formulas for the Natural Logarithmic Function) [精华版(ET)] - TransFunct(ET)_07.pdf
08. 三角函数的积分公式 (Integrals of Trigonometric Functions) [精华版(ET)] - TransFunct(ET)_08.pdf
09. 一般型指数函数的导数 (Derivatives of General Exponential Functions) [精华版(ET)] - TransFunct(ET)_09.pdf
10. 一般型对数函数的导数 (Derivatives of General Logarithmic Functions) [精华版(ET)] - TransFunct(ET)_10.pdf
11. 对数微分法 (Logarithmic Differentiation) [精华版(ET)] - TransFunct(ET)_11.pdf
12. 反三角函数 (Inverse Trigonometric Functions) [精华版(ET)] - TransFunct(ET)_12.pdf
13. 反三角函数的导数 (Derivatives of Inverse Trigonometric Functions) [精华版(ET)] - TransFunct(ET)_13.pdf
14. 反三角函数相关的不定积分 (Indefinite Integrals involving Inverse Trigonometric Functions) [精华版(ET)] - TransFunct(ET)_14.pdf
All. 超越函数(全) [精华版(ET)] - TransFunct(ET)_all.pdf
01. 一对一函数 (One-to-One Functions) [传统版(Classical)] - TransFunct(Classical)_01.pdf
02. 反函数 (Inverse Functions) [传统版(Classical)] - TransFunct(Classical)_02.pdf
03. 反函数的基本性质 (Properties of Inverse Functions) [传统版(Classical)] - TransFunct(Classical)_03.pdf
04. 自然对数函数 (The Natural Logarithmic Function) [传统版(Classical)] - TransFunct(Classical)_04.pdf
05. 自然对数函数的基本公式 (Formulas for the Natural Logarithmic Function) [传统版(Classical)] - TransFunct(Classical)_05.pdf
06. 对数律 (Laws of Logarithms) [传统版(Classical)] - TransFunct(Classical)_06.pdf
07. 欧拉数 (Euler's Number) [传统版(Classical)] - TransFunct(Classical)_07.pdf
08. 三角函数的积分公式 (Integrals of Trigonometric Functions) [传统版(Classical)] - TransFunct(Classical)_08.pdf
09. 自然指数函数 (The Natural Exponential Function) [传统版(Classical)] - TransFunct(Classical)_09.pdf
10. 自然指数函数的导数 (Derivatives of the Natural Exponential Function) [传统版(Classical)] - TransFunct(Classical)_10.pdf
11. 一般型指数函数 (General Exponential Functions) [传统版(Classical)] - TransFunct(Classical)_11.pdf
12. 一般型指数函数的导数 (Derivatives of General Exponential Functions) [传统版(Classical)] - TransFunct(Classical)_12.pdf
13. 对数微分法 (Logarithmic Differentiation) [传统版(Classical)] - TransFunct(Classical)_13.pdf
14. 一般型对数函数 (General Logarithmic Functions) [传统版(Classical)] - TransFunct(Classical)_14.pdf
15. 一般型对数函数的导数 (Derivatives of General Logarithmic Functions) [传统版(Classical)] - TransFunct(Classical)_15.pdf
16. 反三角函数 (Inverse Trigonometric Functions) [传统版(Classical)] - TransFunct(Classical)_16.pdf
17. 反三角函数的导数 (Derivatives of Inverse Trigonometric Functions) [传统版(Classical)] - TransFunct(Classical)_17.pdf
18. 反三角函数相关的不定积分 (Indefinite Integrals involving Inverse Trigonometric Functions) [传统版(Classical)] - TransFunct(Classical)_18.pdf
All. 超越函数(全) [传统版(Classical)] - TransFunct(Classical)_all.pdf
01. 分部积分法(I) (Integration by Parts (I)) - TechInt_01.pdf
02. 分部积分法(II) (Integration by Parts (II)) - TechInt_02.pdf
03. 三角函数的积分(I) (Trigonometric Integrals (I)) - TechInt_03.pdf
04. 三角函数的积分(II) (Trigonometric Integrals (II)) - TechInt_04.pdf
05. 三角函数的积分(III) (Trigonometric Integrals (III)) - TechInt_05.pdf
06. 三角代换法(I) (Trigonometric Substitution (I)) - TechInt_06.pdf
07. 三角代换法(II) (Trigonometric Substitution (II)) - TechInt_07.pdf
08. 部分分式积分法 (I) (Integration by Partial Fractions (I)) - TechInt_08.pdf
09. 部分分式积分法 (II) (Integration by Partial Fractions (II)) - TechInt_09.pdf
All. 积分技巧(全) - TechInt_all.pdf
01. 不定型式与罗必达法则(I) (Indeterminate Forms and L'Hôpital's Rule (I)) - FurApp_01.pdf
02. 不定型式与罗必达法则(II) (Indeterminate Forms and L'Hôpital's Rule (II)) - FurApp_02.pdf
03. 不定型式与罗必达法则(III) (Indeterminate Forms and L'Hôpital's Rule (III)) - FurApp_03.pdf
04. 第一类型瑕积分 (Improper Integrals of Type I) - FurApp_04.pdf
05. 瑕积分的审敛法 (Tests for Improper Integrals) - FurApp_05.pdf
06. 第二类型瑕积分 (Improper Integrals of Type II) - FurApp_06.pdf
All. 进阶的应用(全) - FurApp_all.pdf
01. 无穷数列 (Infinite Sequences) - Series_01.pdf
02. 数列的收敛定理 (Convergence Theorems for Sequences) - Series_02.pdf
03. 无穷级数 (Infinite Series) - Series_03.pdf
04. 积分审敛法 (The Integral Test) - Series_04.pdf
05. 比较审敛法 (The Comparison Test) - Series_05.pdf
06. 极限比较审敛法 (The Limit Comparison Test) - Series_06.pdf
07. 交错级数 (Alternating Series) - Series_07.pdf
08. 绝对与条件收敛 (Absolute and Conditional Convergence) - Series_08.pdf
09. 比值审敛法 (The Ratio Test) - Series_09.pdf
10. 根值审敛法 (The Root Test) - Series_10.pdf
All. 数列与级数(全) - Series_all.pdf
01. 幂级数 (Power Series) - PowerSeries_01.pdf
02. 函数的幂级数表示法 (Representations of Functions as Power Series) - PowerSeries_02.pdf
03. 逐项微分与积分公式 (Term-by-Term Differentiation and Integration) - PowerSeries_03.pdf
04. 泰勒与马克劳林级数 (Taylor and Maclaurin Series) - PowerSeries_04.pdf
05. 重要的马克劳林级数 (Some Important Maclaurin Series) - PowerSeries_05.pdf
All. 幂级数(全) - PowerSeries_all.pdf
注：「Part F. 超越函数：精华版 (Transcendental Functions: Early Transcendentals)」与「Part F*. 超越函数：传统版 (Transcendental Functions: Classical)」是介绍同一个主题，主要差异在于切入观点与单元顺序不同，请视自身需求择一学习。