微 積 分 講 義 下 載
Part A. 極限 (The Limit)
01. 函數的極限 (The Limit of a Function) - Limit_01.pdf
02. 極限的運算公式 (Basic Formulas for Limits) - Limit_02.pdf
03. 夾擠定理 (The Squeeze Theorem) - Limit_03.pdf
04. 單邊極限 (One-Sided Limits) - Limit_04.pdf
05. 重要的極限公式 (Two Important Limits) - Limit_05.pdf
06. 無窮大的極限值與鉛直漸近線 (Infinite Limits and Vertical Asymptotes) - Limit_06.pdf
07. 無窮遠處的極限與水平漸近線 (Limits at Infinity and Horizontal Asymptotes) - Limit_07.pdf
08. 連續函數 (Continuous Functions) - Limit_08.pdf
09. 連續函數的運算 (Formulas for Continuous Functions) - Limit_09.pdf
10. 中間值定理 (The Intermediate Value Theorem) - Limit_10.pdf
All. 極限(全) - Limit_all.pdf
Part B. 導數 (The Derivative)
01. 切線 (The Tangent Line) - Derivative_01.pdf
02. 變化率 (The Rate of Change) - Derivative_02.pdf
03. 導函數 (The Derivative as a Function) - Derivative_03.pdf
04. 基本的微分公式 (Basic Differentiation Formulas) - Derivative_04.pdf
05. 法線 (The Normal Line) - Derivative_05.pdf
06. 微分的乘法與除法公式 (Product and Quotient Rules) - Derivative_06.pdf
07. 三角函數的導數 (Derivatives of Trigonometric Functions) - Derivative_07.pdf
08. 高階導數 (Higher Derivatives) - Derivative_08.pdf
09. 鏈鎖律 (The Chain Rule) - Derivative_09.pdf
10. 鏈鎖律的應用 (Applications of the Chain Rule) - Derivative_10.pdf
11. 隱函數微分法 (Implicit Differentiation) - Derivative_11.pdf
All. 導數(全) - Derivative_all.pdf
Part C. 導數的應用 (Applications of the Derivative)
01. 線性估計 (Linear Approximations) - AppDer_01.pdf
02. 微分量 (Differentials) - AppDer_02.pdf
03. 函數的極值 (Extreme Values of Functions) - AppDer_03.pdf
04. 費馬引理與臨界點 (Fermat's Theorem and Critical Points) - AppDer_04.pdf
05. 均值定理 (The Mean Value Theorem) - AppDer_05.pdf
06. 遞增與遞減函數 (Increasing and Decreasing Functions) - AppDer_06.pdf
07. 一階導數判別法 (First Derivative Test) - AppDer_07.pdf
08. 圖形的凹性與反曲點 (Concavity and Inflection Points) - AppDer_08.pdf
09. 二階導數判別法 (Second Derivative Test) - AppDer_09.pdf
10. 反導函數與不定積分 (Antiderivatives and Indefinite Integrals) - AppDer_10.pdf
11. 不定積分的基本公式 (Formulas for Indefinite Integrals) - AppDer_11.pdf
All. 導數的應用(全) - AppDer_all.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) - Integral_02.pdf
03. 定積分 (The Definite Integral) - Integral_03.pdf
04. 定積分的基本性質 (The Properties of the Definite Integral) - Integral_04.pdf
05. 微積分第一基本定理 (First Fundamental Theorem of Calculus) - Integral_05.pdf
06. 微積分第二基本定理 (Second Fundamental Theorem of Calculus) - Integral_06.pdf
07. 代換積分法 (The Substitution Rule) - Integral_07.pdf
08. 奇偶函數的定積分 (The Definite Integrals of Odd and Even Functions) - Integral_08.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.pdf
02. 反函數 (Inverse Functions) [精華版(ET)] - TransFunct(ET)_02.pdf
03. 反函數的基本性質 (Properties of Inverse Functions) [精華版(ET)] - TransFunct(ET)_03.pdf
04. 自然指數函數 (The Natural Exponential Function) [精華版(ET)] - TransFunct(ET)_04.pdf
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.pdf
06. 自然對數函數 (The Natural Logarithmic Function) [精華版(ET)] - TransFunct(ET)_06.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.pdf
08. 三角函數的積分公式 (Integrals of Trigonometric Functions) [精華版(ET)] - TransFunct(ET)_08.pdf
09. 一般型指數函數的導數 (Derivatives of General Exponential Functions) [精華版(ET)] - TransFunct(ET)_09.pdf
10. 一般型對數函數的導數 (Derivatives of General Logarithmic Functions) [精華版(ET)] - TransFunct(ET)_10.pdf
11. 對數微分法 (Logarithmic Differentiation) [精華版(ET)] - TransFunct(ET)_11.pdf
12. 反三角函數 (Inverse Trigonometric Functions) [精華版(ET)] - TransFunct(ET)_12.pdf
13. 反三角函數的導數 (Derivatives of Inverse Trigonometric Functions) [精華版(ET)] - TransFunct(ET)_13.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.pdf
All. 超越函數(全) [精華版(ET)] - TransFunct(ET)_all.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.pdf
02. 反函數 (Inverse Functions) [傳統版(Classical)] - TransFunct(Classical)_02.pdf
03. 反函數的基本性質 (Properties of Inverse Functions) [傳統版(Classical)] - TransFunct(Classical)_03.pdf
04. 自然對數函數 (The Natural Logarithmic Function) [傳統版(Classical)] - TransFunct(Classical)_04.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.pdf
06. 對數律 (Laws of Logarithms) [傳統版(Classical)] - TransFunct(Classical)_06.pdf
07. 歐拉數 (Euler's Number) [傳統版(Classical)] - TransFunct(Classical)_07.pdf
08. 三角函數的積分公式 (Integrals of Trigonometric Functions) [傳統版(Classical)] - TransFunct(Classical)_08.pdf
09. 自然指數函數 (The Natural Exponential Function) [傳統版(Classical)] - TransFunct(Classical)_09.pdf
10. 自然指數函數的導數 (Derivatives of the Natural Exponential Function) [傳統版(Classical)] - TransFunct(Classical)_10.pdf
11. 一般型指數函數 (General Exponential Functions) [傳統版(Classical)] - TransFunct(Classical)_11.pdf
12. 一般型指數函數的導數 (Derivatives of General Exponential Functions) [傳統版(Classical)] - TransFunct(Classical)_12.pdf
13. 對數微分法 (Logarithmic Differentiation) [傳統版(Classical)] - TransFunct(Classical)_13.pdf
14. 一般型對數函數 (General Logarithmic Functions) [傳統版(Classical)] - TransFunct(Classical)_14.pdf
15. 一般型對數函數的導數 (Derivatives of General Logarithmic Functions) [傳統版(Classical)] - TransFunct(Classical)_15.pdf
16. 反三角函數 (Inverse Trigonometric Functions) [傳統版(Classical)] - TransFunct(Classical)_16.pdf
17. 反三角函數的導數 (Derivatives of Inverse Trigonometric Functions) [傳統版(Classical)] - TransFunct(Classical)_17.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.pdf
All. 超越函數(全) [傳統版(Classical)] - TransFunct(Classical)_all.pdf
Part G. 積分技巧 (Techniques of Integration)
01. 分部積分法(I) (Integration by Parts (I)) - TechInt_01.pdf
02. 分部積分法(II) (Integration by Parts (II)) - TechInt_02.pdf
03. 三角函數的積分(I) (Trigonometric Integrals (I)) - TechInt_03.pdf
04. 三角函數的積分(II) (Trigonometric Integrals (II)) - TechInt_04.pdf
05. 三角函數的積分(III) (Trigonometric Integrals (III)) - TechInt_05.pdf
06. 三角代換法(I) (Trigonometric Substitution (I)) - TechInt_06.pdf
07. 三角代換法(II) (Trigonometric Substitution (II)) - TechInt_07.pdf
08. 部分分式積分法 (I) (Integration by Partial Fractions (I)) - TechInt_08.pdf
09. 部分分式積分法 (II) (Integration by Partial Fractions (II)) - TechInt_09.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.pdf
02. 不定型式與羅必達法則(II) (Indeterminate Forms and L'Hôpital's Rule (II)) - FurApp_02.pdf
03. 不定型式與羅必達法則(III) (Indeterminate Forms and L'Hôpital's Rule (III)) - FurApp_03.pdf
04. 第一類型瑕積分 (Improper Integrals of Type I) - FurApp_04.pdf
05. 瑕積分的審斂法 (Tests for Improper Integrals) - FurApp_05.pdf
Part I. 數列與級數 (Sequences and Series)
01. 無窮數列 (Infinite Sequences) - Series_01.pdf
02. 數列的收斂定理 (Convergence Theorems for Sequences) - Series_02.pdf
03. 無窮級數 (Infinite Series) - Series_03.pdf
04. 積分審斂法 (The Integral Test) - Series_04.pdf
05. 比較審斂法 (The Comparison Test) - Series_05.pdf
06. 極限比較審斂法 (The Limit Comparison Test) - Series_06.pdf
07. 交錯級數 (Alternating Series) - Series_07.pdf
08. 絕對與條件收斂 (Absolute and Conditional Convergence) - Series_08.pdf
09. 比值審斂法 (The Ratio Test) - Series_09.pdf
10. 根值審斂法 (The Root Test) - Series_10.pdf
Part J. 冪級數 (Power Series)
01. 冪級數 (Power Series) - PowerSeries_01.pdf
02. 函數的冪級數表示法 (Representations of Functions as Power Series) - PowerSeries_02.pdf
03. 逐項微分與積分公式 (Term-by-Term Differentiation and Integration) - PowerSeries_03.pdf
04. 泰勒與馬克勞林級數 (Taylor and Maclaurin Series) - PowerSeries_04.pdf
05. 重要的馬克勞林級數 (Some Important Maclaurin Series) - PowerSeries_05.pdf
All. 冪級數(全) - PowerSeries_all.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。