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莊重老師真心告白 |
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課程介紹 |
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第一章 Functions and Models
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
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第二章 Limits and derivatives
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws |
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2.4 The Precise Definition of a Limit |
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2.5 Continuity |
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2.6 Limits at Infinity; Horizontal Asymptotes |
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2.7 Derivatives and Rates of Change
(本影片內容有部分錯誤，詳見YouTube留言) |
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2.8 The Derivative as a Function |
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第三章 Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions |
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3.2 The Product and Quotient Rules |
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3.3 Derivatives of Trigonometric Functions |
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3.4 The Chain Rule
(本影片內容有部分錯誤，詳見YouTube留言) |
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3.5 Implicit Differentiation |
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3.6 Derivatives of Logarithmic Functions |
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3.9 Related Rates |
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3.10 Linear Approximations and Differentials |
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第四章 Applications of Differentiation
4.1 Maximum and Minimum Values |
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4.2 The Mean Value Theorem |
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4.3 How Derivatives Affect the Shape of a Graph
4.5 Summary of Curve Sketching |
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4.4 Indeterminate Forms and L’Hospital’s Rule |
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4.7 Optimization Problems |
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4.9 Antiderivatives |
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第五章 Integrals
5.1 Areas and Distances |
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5.2 The Definite Integral |
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5.3 The Fundamental Theorem of Calculus |
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5.4 Indefinite Integrals and the Net Change Theorem |
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5.5 The Substitution Rule |
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第六章 Applications of Integration
6.1 Areas between Curves |
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6.2 Volumes
6.3 Volumes by Cylindrical Shells |
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6.5 Average Value of a Function |
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第七章 Techniques of Integration
7.1 Integration by Parts |
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7.2 Trigonometric Integrals |
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7.3 Trigonometric Substitution |
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7.4 Integration of Rational Functions by Partial Fractions |
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7.7 Approximate Integration |
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7.8 Improper Integrals |
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第八章 Further Applications of Integration
8.1 Arc Length |
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8.2 Area of a Surface of Revolution |
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8.5 Probability |
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第十章 Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations |
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10.2 Calculus with Parametric Curves |
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