微 积 分 习 题 下 载
Part A. 极限 (The Limit)
01. 函数的极限 (The Limit of a Function) - Limit_01_Ex.pdf
02. 极限的运算公式 (Basic Formulas for Limits) - Limit_02_Ex.pdf
03. 夹挤定理 (The Squeeze Theorem) - Limit_03_Ex.pdf
04. 单边极限 (One-Sided Limits) - Limit_04_Ex.pdf
05. 重要的极限公式 (Two Important Limits) - Limit_05_Ex.pdf
06. 无穷大的极限值与铅直渐近线 (Infinite Limits and Vertical Asymptotes) - Limit_06_Ex.pdf
07. 无穷远处的极限与水平渐近线 (Limits at Infinity and Horizontal Asymptotes) - Limit_07_Ex.pdf
08. 连续函数 (Continuous Functions) - Limit_08_Ex.pdf
09. 连续函数的运算 (Formulas for Continuous Functions) - Limit_09_Ex.pdf
10. 中间值定理 (The Intermediate Value Theorem) - Limit_10_Ex.pdf
11. 綜合練習 - Limit_11_Ex.pdf
All. 极限(全) - Limit_all_Ex.pdf
Part B. 导数 (The Derivative)
01. 切线 (The Tangent Line) - Derivative_01_Ex.pdf
02. 变化率 (The Rate of Change) - Derivative_02_Ex.pdf
03. 导函数 (The Derivative as a Function) - Derivative_03_Ex.pdf
04. 基本的微分公式 (Basic Differentiation Formulas) - Derivative_04_Ex.pdf
05. 法线 (The Normal Line) - Derivative_05_Ex.pdf
06. 微分的乘法与除法公式 (Product and Quotient Rules) - Derivative_06_Ex.pdf
07. 三角函数的导数 (Derivatives of Trigonometric Functions) - Derivative_07_Ex.pdf
08. 高阶导数 (Higher Derivatives) - Derivative_08_Ex.pdf
09. 链锁律 (The Chain Rule) - Derivative_09_Ex.pdf
10. 链锁律的应用 (Applications of the Chain Rule) - Derivative_10_Ex.pdf
11. 隐函数微分法 (Implicit Differentiation) - Derivative_11_Ex.pdf
12. 綜合練習 - Derivative_12_Ex.pdf
All. 导数(全) - Derivative_all_Ex.pdf
Part C. 导数的应用 (Applications of the Derivative)
01. 线性估计 (Linear Approximations) - AppDer_01_Ex.pdf
02. 微分量 (Differentials) - AppDer_02_Ex.pdf
03. 函数的极值 (Extreme Values of Functions) - AppDer_03_Ex.pdf
04. 费马引理与临界点 (Fermat's Theorem and Critical Points) - AppDer_04_Ex.pdf
05. 均值定理 (The Mean Value Theorem) - AppDer_05_Ex.pdf
06. 递增与递减函数 (Increasing and Decreasing Functions) - AppDer_06_Ex.pdf
07. 一阶导数判别法 (First Derivative Test) - AppDer_07_Ex.pdf
08. 图形的凹性与反曲点 (Concavity and Inflection Points) - AppDer_08_Ex.pdf
09. 二阶导数判别法 (Second Derivative Test) - AppDer_09_Ex.pdf
10. 反导函数与不定积分 (Antiderivatives and Indefinite Integrals) - AppDer_10_Ex.pdf
11. 不定积分的基本公式 (Formulas for Indefinite Integrals) - AppDer_11_Ex.pdf
12. 綜合練習 - AppDer_12_Ex.pdf
All. 导数的应用(全) - AppDer_all_Ex.pdf
Part D. 积分 (The Integral)
01. 精彩选辑 - 无
02. 曲线下的面积 (The Area under a Curve) - 无
03. 定积分 (The Definite Integral) - Integral_03_Ex.pdf
04. 定积分的基本性质 (The Properties of the Definite Integral) - Integral_04_Ex.pdf
05. 微积分第一基本定理 (First Fundamental Theorem of Calculus) - Integral_05_Ex.pdf
06. 微积分第二基本定理 (Second Fundamental Theorem of Calculus) - Integral_06_Ex.pdf
07. 代换积分法 (The Substitution Rule) - Integral_07_Ex.pdf
08. 奇偶函数的定积分 (The Definite Integrals of Odd and Even Functions) - Integral_08_Ex.pdf
09. 綜合練習 - Integral_09_Ex.pdf
All. 积分(全) - Integral_all_Ex.pdf
Part E. 积分的应用 (Applications of the Integral)
01. 曲线所围区域的面积(I) (The Area between Curves (I)) - AppInt_01_Ex.pdf
02. 曲线所围区域的面积(II) (The Area between Curves (II)) - AppInt_02_Ex.pdf
03. 函数的平均 (The Average of a Function) - AppInt_03_Ex.pdf
04. 綜合練習 - AppInt_04_Ex.pdf
All. 积分的应用(全) - AppInt_all_Ex.pdf
Part F. 超越函数：精华版 (Transcendental Functions: Early Transcendentals)
01. 一对一函数 (One-to-One Functions) [精华版(ET)] - TransFunct(ET)_01_Ex.pdf
02. 反函数 (Inverse Functions) [精华版(ET)] - TransFunct(ET)_02_Ex.pdf
03. 反函数的基本性质 (Properties of Inverse Functions) [精华版(ET)] - TransFunct(ET)_03_Ex.pdf
04. 自然指数函数 (The Natural Exponential Function) [精华版(ET)] - 无
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_Ex.pdf
06. 自然对数函数 (The Natural Logarithmic Function) [精华版(ET)] - TransFunct(ET)_06_Ex.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_Ex.pdf
08. 三角函数的积分公式 (Integrals of Trigonometric Functions) [精华版(ET)] - TransFunct(ET)_08_Ex.pdf
09. 一般型指数函数的导数 (Derivatives of General Exponential Functions) [精华版(ET)] - TransFunct(ET)_09_Ex.pdf
10. 一般型对数函数的导数 (Derivatives of General Logarithmic Functions) [精华版(ET)] - TransFunct(ET)_10_Ex.pdf
11. 对数微分法 (Logarithmic Differentiation) [精华版(ET)] - TransFunct(ET)_11_Ex.pdf
12. 反三角函数 (Inverse Trigonometric Functions) [精华版(ET)] - TransFunct(ET)_12_Ex.pdf
13. 反三角函数的导数 (Derivatives of Inverse Trigonometric Functions) [精华版(ET)] - TransFunct(ET)_13_Ex.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_Ex.pdf
15. 综合练习 [精华版(ET)] - TransFunct(ET)_15_Ex.pdf
All. 超越函数(全) [精华版(ET)] - TransFunct(ET)_all_Ex.pdf
Part F*. 超越函数：传统版 (Transcendental Functions: Classical)
01. 一对一函数 (One-to-One Functions) [传统版(Classical)] - TransFunct(Classical)_01_Ex.pdf
02. 反函数 (Inverse Functions) [传统版(Classical)] - TransFunct(Classical)_02_Ex.pdf
03. 反函数的基本性质 (Properties of Inverse Functions) [传统版(Classical)] - TransFunct(Classical)_03_Ex.pdf
04. 自然对数函数 (The Natural Logarithmic Function) [传统版(Classical)] - TransFunct(Classical)_04_Ex.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_Ex.pdf
06. 对数律 (Laws of Logarithms) [传统版(Classical)] - TransFunct(Classical)_06_Ex.pdf
07. 欧拉数 (Euler's Number) [传统版(Classical)] - 无
08. 三角函数的积分公式 (Integrals of Trigonometric Functions) [传统版(Classical)] - TransFunct(Classical)_08_Ex.pdf
09. 自然指数函数 (The Natural Exponential Function) [传统版(Classical)] - TransFunct(Classical)_09_Ex.pdf
10. 自然指数函数的导数 (Derivatives of the Natural Exponential Function) [传统版(Classical)] - TransFunct(Classical)_10_Ex.pdf
11. 一般型指数函数 (General Exponential Functions) [传统版(Classical)] - 无
12. 一般型指数函数的导数 (Derivatives of General Exponential Functions) [传统版(Classical)] - TransFunct(Classical)_12_Ex.pdf
13. 对数微分法 (Logarithmic Differentiation) [传统版(Classical)] - TransFunct(Classical)_13_Ex.pdf
14. 一般型对数函数 (General Logarithmic Functions) [传统版(Classical)] - TransFunct(Classical)_14_Ex.pdf
15. 一般型对数函数的导数 (Derivatives of General Logarithmic Functions) [传统版(Classical)] - TransFunct(Classical)_15_Ex.pdf
16. 反三角函数 (Inverse Trigonometric Functions) [传统版(ET)] - TransFunct(Classical)_16_Ex.pdf
17. 反三角函数的导数 (Derivatives of Inverse Trigonometric Functions) [传统版(Classical)] - TransFunct(Classical)_17_Ex.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_Ex.pdf
19. 综合练习 [传统版(Classical)] - TransFunct(Classical)_19_Ex.pdf
All. 超越函数(全) [传统版(Classical)] - TransFunct(Classical)_all_Ex.pdf
Part G. 积分技巧 (Techniques of Integration)
01. 分部积分法(I) (Integration by Parts (I)) - TechInt_01_Ex.pdf
02. 分部积分法(II) (Integration by Parts (II)) - TechInt_02_Ex.pdf
03. 三角函数的积分(I) (Trigonometric Integrals (I)) - TechInt_03_Ex.pdf
04. 三角函数的积分(II) (Trigonometric Integrals (II)) - TechInt_04_Ex.pdf
05. 三角函数的积分(III) (Trigonometric Integrals (III)) - TechInt_05_Ex.pdf
06. 三角代换法(I) (Trigonometric Substitution (I)) - TechInt_06_Ex.pdf
07. 三角代换法(II) (Trigonometric Substitution (II)) - TechInt_07_Ex.pdf
08. 部分分式积分法 (I) (Integration by Partial Fractions (I)) - TechInt_08_Ex.pdf
09. 部分分式积分法 (I) (Integration by Partial Fractions (I)) - TechInt_09_Ex.pdf
10. 綜合練習 - TechInt_10_Ex.pdf
All. 积分技巧(全) - TechInt_all_Ex.pdf
Part H. 进阶的应用 (Further Applications)
01. 不定型式与罗必达法则(I) (Indeterminate Forms and L'Hôpital's Rule (I)) - FurApp_01_Ex.pdf
02. 不定型式与罗必达法则(II) (Indeterminate Forms and L'Hôpital's Rule (II)) - FurApp_02_Ex.pdf
03. 不定型式与罗必达法则(III) (Indeterminate Forms and L'Hôpital's Rule (III)) - FurApp_03_Ex.pdf
04. 第一类型瑕积分 (Improper Integrals of Type I) - FurApp_04_Ex.pdf
05. 瑕积分的审敛法 (Tests for Improper Integrals) - FurApp_05_Ex.pdf
06. 第二类型瑕积分 (Improper Integrals of Type II) - FurApp_06_Ex.pdf
07. 綜合練習 - FurApp_07_Ex.pdf
All. 进阶的应用(全) - FurApp_all_Ex.pdf
Part I. 数列与级数 (Sequences and Series)
01. 无穷数列 (Infinite Sequences) - Series_01_Ex.pdf
02. 数列的收敛定理 (Convergence Theorems for Sequences) - Series_02_Ex.pdf
03. 无穷级数 (Infinite Series) - Series_03_Ex.pdf
04. 积分审敛法 (The Integral Test) - Series_04_Ex.pdf
05. 比较审敛法 (The Comparison Test) - Series_05_Ex.pdf
06. 极限比较审敛法 (The Limit Comparison Test) - Series_06_Ex.pdf
07. 交错级数 (Alternating Series) - Series_07_Ex.pdf
08. 绝对与条件收敛 (Absolute and Conditional Convergence) - Series_08_Ex.pdf
09. 比值审敛法 (The Ratio Test) - Series_09_Ex.pdf
10. 根值审敛法 (The Root Test) - Series_10_Ex.pdf
11. 綜合練習 - Series_11_Ex.pdf
All. 数列与级数(全) - Series_all_Ex.pdf
Part J. 幂级数 (Power Series)
01. 幂级数 (Power Series) - PowerSeries_01_Ex.pdf
02. 函数的幂级数表示法 (Representations of Functions as Power Series) - PowerSeries_02_Ex.pdf
03. 逐项微分与积分公式 (Term-by-Term Differentiation and Integration) - PowerSeries_03_Ex.pdf
04. 泰勒与马克劳林级数 (Taylor and Maclaurin Series) - PowerSeries_04_Ex.pdf
05. 重要的马克劳林级数 (Some Important Maclaurin Series) - PowerSeries_05_Ex.pdf
06. 綜合練習 - PowerSeries_06_Ex.pdf
All. 幂级数(全) - PowerSeries_all_Ex.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。