微 積 分 習 題 下 載
Part A. 極限 (The Limit)
01. 函數的極限 (The Limit of a Function) - Limit_01_Ex.pdf
02. 極限的運算公式 (Basic Formulas for Limits) - Limit_02_Ex.pdf
03. 夾擠定理 (The Squeeze Theorem) - Limit_03_Ex.pdf
04. 單邊極限 (One-Sided Limits) - Limit_04_Ex.pdf
05. 重要的極限公式 (Two Important Limits) - Limit_05_Ex.pdf
06. 無窮大的極限值與鉛直漸近線 (Infinite Limits and Vertical Asymptotes) - Limit_06_Ex.pdf
07. 無窮遠處的極限與水平漸近線 (Limits at Infinity and Horizontal Asymptotes) - Limit_07_Ex.pdf
08. 連續函數 (Continuous Functions) - Limit_08_Ex.pdf
09. 連續函數的運算 (Formulas for Continuous Functions) - Limit_09_Ex.pdf
10. 中間值定理 (Formulas for Continuous Functions) - Limit_10_Ex.pdf
11. 綜合練習 - Limit_11_Ex.pdf
Part B. 導數 (The Derivative)
01. 切線 (The Tangent Line) - Derivative_01_Ex.pdf
02. 變化率 (The Rate of Change) - Derivative_02_Ex.pdf
03. 導函數 (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. 法線 (The Normal Line) - Derivative_05_Ex.pdf
06. 微分的乘法與除法公式 (Product and Quotient Rules) - Derivative_06_Ex.pdf
07. 三角函數的導數 (Derivatives of Trigonometric Functions) - Derivative_07_Ex.pdf
08. 高階導數 (Higher Derivatives) - Derivative_08_Ex.pdf
09. 鏈鎖律 (The Chain Rule) - Derivative_09_Ex.pdf
10. 鏈鎖律的應用 (Applications of the Chain Rule) - Derivative_10_Ex.pdf
11. 隱函數微分法 (Implicit Differentiation) - Derivative_11_Ex.pdf
12. 綜合練習 - Derivative_12_Ex.pdf
All. 導數(全) - Derivative_all_Ex.pdf
Part C. 導數的應用 (Applications of the Derivative)
01. 線性估計 (Linear Approximations) - AppDer_01_Ex.pdf
02. 微分量 (Differentials) - AppDer_02_Ex.pdf
03. 函數的極值 (Extreme Values of Functions) - AppDer_03_Ex.pdf
04. 費馬引理與臨界點 (Fermat's Theorem and Critical Points) - AppDer_04_Ex.pdf
05. 均值定理 (The Mean Value Theorem) - AppDer_05_Ex.pdf
06. 遞增與遞減函數 (Increasing and Decreasing Functions) - AppDer_06_Ex.pdf
07. 一階導數判別法 (First Derivative Test) - AppDer_07_Ex.pdf
08. 圖形的凹性與反曲點 (Concavity and Inflection Points) - AppDer_08_Ex.pdf
09. 二階導數判別法 (Second Derivative Test) - AppDer_09_Ex.pdf
10. 反導函數與不定積分 (Antiderivatives and Indefinite Integrals) - AppDer_10_Ex.pdf
11. 不定積分的基本公式 (Formulas for Indefinite Integrals) - AppDer_11_Ex.pdf
Part D. 積分 (The Integral)
01. 精彩選輯 - 無
02. 曲線下的面積 (The Area under a Curve) - 無
03. 定積分 (The Definite Integral) - Integral_03_Ex.pdf
04. 定積分的基本性質 (The Properties of the Definite Integral) - Integral_04_Ex.pdf
05. 微積分第一基本定理 (First Fundamental Theorem of Calculus) - Integral_05_Ex.pdf
06. 微積分第二基本定理 (Second Fundamental Theorem of Calculus) - Integral_06_Ex.pdf
07. 代換積分法 (The Substitution Rule) - Integral_07_Ex.pdf
08. 奇偶函數的定積分 (The Definite Integrals of Odd and Even Functions) - Integral_08_Ex.pdf
09. 綜合練習 - Integral_09_Ex.pdf
Part F. 超越函數：精華版 (Transcendental Functions: Early Transcendentals)
01. 一對一函數 (One-to-One Functions) [精華版(ET)] - TransFunct(ET)_01_Ex.pdf
02. 反函數 (Inverse Functions) [精華版(ET)] - TransFunct(ET)_02_Ex.pdf
03. 反函數的基本性質 (Properties of Inverse Functions) [精華版(ET)] - TransFunct(ET)_03_Ex.pdf
04. 自然指數函數 (The Natural Exponential Function) [精華版(ET)] - 無
05. 自然指數函數的基本公式 (Formulas for the Natural Exponential Function) [精華版(ET)] - TransFunct(ET)_05_Ex.pdf
06. 自然對數函數 (The Natural Logarithmic Function) [精華版(ET)] - TransFunct(ET)_06_Ex.pdf
07. 自然對數函數的基本公式 (Formulas for the Natural Logarithmic Function) [精華版(ET)] - TransFunct(ET)_07_Ex.pdf
08. 三角函數的積分公式 (Integrals of Trigonometric Functions) [精華版(ET)] - TransFunct(ET)_08_Ex.pdf
09. 一般型指數函數的導數 (Derivatives of General Exponential Functions) [精華版(ET)] - TransFunct(ET)_09_Ex.pdf
10. 一般型對數函數的導數 (Derivatives of General Logarithmic Functions) [精華版(ET)] - TransFunct(ET)_10_Ex.pdf
11. 對數微分法 (Logarithmic Differentiation) [精華版(ET)] - TransFunct(ET)_11_Ex.pdf
12. 反三角函數 (Inverse Trigonometric Functions) [精華版(ET)] - TransFunct(ET)_12_Ex.pdf
13. 反三角函數的導數 (Derivatives of Inverse Trigonometric Functions) [精華版(ET)] - TransFunct(ET)_13_Ex.pdf
14. 反三角函數相關的不定積分 (Indefinite Integrals involving Inverse Trigonometric Functions) [精華版(ET)] - TransFunct(ET)_14_Ex.pdf
15. 綜合練習 [精華版(ET)] - TransFunct(ET)_15_Ex.pdf
All. 超越函數(全) [精華版(ET)] - TransFunct(ET)_all_Ex.pdf
Part F*. 超越函數：傳統版 (Transcendental Functions: Classical)
01. 一對一函數 (One-to-One Functions) [傳統版(Classical)] - TransFunct(Classical)_01_Ex.pdf
02. 反函數 (Inverse Functions) [傳統版(Classical)] - TransFunct(Classical)_02_Ex.pdf
03. 反函數的基本性質 (Properties of Inverse Functions) [傳統版(Classical)] - TransFunct(Classical)_03_Ex.pdf
04. 自然對數函數 (The Natural Logarithmic Function) [傳統版(Classical)] - TransFunct(Classical)_04_Ex.pdf
05. 自然對數函數的基本公式 (Formulas for the Natural Logarithmic Function) [傳統版(Classical)] - TransFunct(Classical)_05_Ex.pdf
06. 對數律 (Laws of Logarithms) [傳統版(Classical)] - TransFunct(Classical)_06_Ex.pdf
07. 歐拉數 (Euler's Number) [傳統版(Classical)] - 無
08. 三角函數的積分公式 (Integrals of Trigonometric Functions) [傳統版(Classical)] - TransFunct(Classical)_08_Ex.pdf
09. 自然指數函數 (The Natural Exponential Function) [傳統版(Classical)] - TransFunct(Classical)_09_Ex.pdf
10. 自然指數函數的導數 (Derivatives of the Natural Exponential Function) [傳統版(Classical)] - TransFunct(Classical)_10_Ex.pdf
11. 一般型指數函數 (General Exponential Functions) [傳統版(Classical)] - 無
12. 一般型指數函數的導數 (Derivatives of General Exponential Functions) [傳統版(Classical)] - TransFunct(Classical)_12_Ex.pdf
13. 對數微分法 (Logarithmic Differentiation) [傳統版(Classical)] - TransFunct(Classical)_13_Ex.pdf
14. 一般型對數函數 (General Logarithmic Functions) [傳統版(Classical)] - TransFunct(Classical)_14_Ex.pdf
15. 一般型對數函數的導數 (Derivatives of General Logarithmic Functions) [傳統版(Classical)] - TransFunct(Classical)_15_Ex.pdf
16. 反三角函數 (Inverse Trigonometric Functions) [傳統版(ET)] - TransFunct(Classical)_16_Ex.pdf
17. 反三角函數的導數 (Derivatives of Inverse Trigonometric Functions) [傳統版(Classical)] - TransFunct(Classical)_17_Ex.pdf
18. 反三角函數相關的不定積分 (Indefinite Integrals involving Inverse Trigonometric Functions) [傳統版(Classical)] - TransFunct(Classical)_18_Ex.pdf
19. 綜合練習 [傳統版(Classical)] - TransFunct(Classical)_19_Ex.pdf
All. 超越函數(全) [傳統版(Classical)] - TransFunct(Classical)_all_Ex.pdf
Part G. 積分技巧 (Techniques of Integration)
01. 分部積分法(I) (Integration by Parts (I)) - TechInt_01_Ex.pdf
02. 分部積分法(II) (Integration by Parts (II)) - TechInt_02_Ex.pdf
03. 三角函數的積分(I) (Trigonometric Integrals (I)) - TechInt_03_Ex.pdf
04. 三角函數的積分(II) (Trigonometric Integrals (II)) - TechInt_04_Ex.pdf
05. 三角函數的積分(III) (Trigonometric Integrals (III)) - TechInt_05_Ex.pdf
06. 三角代換法(I) (Trigonometric Substitution (I)) - TechInt_06_Ex.pdf
07. 三角代換法(II) (Trigonometric Substitution (II)) - TechInt_07_Ex.pdf
08. 部分分式積分法 (I) (Integration by Partial Fractions (I)) - TechInt_08_Ex.pdf
09. 部分分式積分法 (II) (Integration by Partial Fractions (II)) - TechInt_09_Ex.pdf
Part H. 進階的應用 (Further Applications)
01. 不定型式與羅必達法則(I) (Indeterminate Forms and L'Hôpital's Rule (I)) - FurApp_01_Ex.pdf
02. 不定型式與羅必達法則(II) (Indeterminate Forms and L'Hôpital's Rule (II)) - FurApp_02_Ex.pdf
03. 不定型式與羅必達法則(III) (Indeterminate Forms and L'Hôpital's Rule (III)) - FurApp_03_Ex.pdf
04. 第一類型瑕積分 (Improper Integrals of Type I) - FurApp_04_Ex.pdf
05. 瑕積分的審斂法 (Tests for Improper Integrals) - FurApp_05_Ex.pdf
06. 第二類型瑕積分 (Improper Integrals of Type II) - FurApp_06_Ex.pdf
Part I. 數列與級數 (Sequences and Series)
01. 無窮數列 (Infinite Sequences) - Series_01_Ex.pdf
02. 數列的收斂定理 (Convergence Theorems for Sequences) - Series_02_Ex.pdf
03. 無窮級數 (Infinite Series) - Series_03_Ex.pdf
04. 積分審斂法 (The Integral Test) - Series_04_Ex.pdf
05. 比較審斂法 (The Comparison Test) - Series_05_Ex.pdf
06. 極限比較審斂法 (The Limit Comparison Test) - Series_06_Ex.pdf
07. 交錯級數 (Alternating Series) - Series_07_Ex.pdf
08. 絕對與條件收斂 (Absolute and Conditional Convergence) - Series_08_Ex.pdf
09. 比值審斂法 (The Ratio Test) - Series_09_Ex.pdf
Part J. 冪級數 (Power Series)
01. 冪級數 (Power Series) - PowerSeries_01_Ex.pdf
02. 函數的冪級數表示法 (Representations of Functions as Power Series) - PowerSeries_02_Ex.pdf
03. 逐項微分與積分公式 (Term-by-Term Differentiation and Integration) - PowerSeries_03_Ex.pdf
04. 泰勒與馬克勞林級數 (Taylor and Maclaurin Series) - PowerSeries_04_Ex.pdf
05. 重要的馬克勞林級數 (Some Important Maclaurin Series) - PowerSeries_05_Ex.pdf
06. 綜合練習 - PowerSeries_06_Ex.pdf
All. 冪級數(全) - PowerSeries_all_Ex.pdf
註：「Part F. 超越函數：精華版 (Transcendental Functions: Early Transcendentals)」與「Part F*. 超越函數：傳統版 (Transcendental Functions: Classical)」是介紹同一個主題，主要差異在於切入觀點與單元順序不同，請視自身需求擇一學習。