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上學期：單變數微積分 |
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章節 |
週次 |
課次 |
課程進度 |
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1. Functions and Models |
第一週 9/14-9/18 |
1 |
[1.5] Exponential Functions [1.6] Inverse Functions and Logarithms |
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2. Limits and Derivatives |
2 |
[2.1] The Tangent and Velocity Problems [2.2] The Limit of a Function |
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第二週 9/21-9/25 |
1 |
[2.3] Calculating Limits Using the Limit Laws [2.4] The Precise Definition of a Limit |
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2 |
[2.5] Continuity [2.6] Limits at Infinity; Horizontal Asymptotes [2.7] Derivatives and Rates of Change |
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第三週 9/28-10/2 |
1 |
[2.8] The Derivative as a Function [3.1] Derivatives of Polynomials and Exponential Functions |
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3. Differentiation Rules |
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2 |
[3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions |
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第四週 10/5-10/9 |
1 |
[3.4] The Chain Rule [3.5] Implicit Differentiation |
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2 |
[3.6] Derivatives of Logarithmic Functions [3.7] Rates of Change in the Natural and Social Sciences（※） [3.8] Exponential Growth and Decay |
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第五週 10/12-10/16 |
1 |
[3.9] Related Rates [3.10] Linear Approximations and Differentials [3.11] Hyperbolic Functions（※） |
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4. Applications of Differentiation |
2 |
[4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem |
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第六週 10/19-10/23 |
1 |
[4.3] How Derivatives Affect the Shape of a Graph [4.4] Indeterminate Forms and L’Hospital’s Rule |
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2 |
緩衝時間 |
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第七週 10/26-10/30 |
1 |
[4.5] Summary of Curve Sketching [4.6] Graphing with Calculus and Calculators [4.7] Optimization Problems |
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2 |
[4.8] Newton’s Method（※） [4.9] Antiderivatives [5.1] Areas and Distances |
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5. Integrals |
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第八週 11/2-11/6 |
1 |
[5.2] The Definite Integral [5.3] The Fundamental Theorem of Calculus |
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2 |
[5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule |
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6. Applications of Integration |
第九週 11/9-11/13 |
1 |
[6.1] Areas between Curves [6.2] Volumes |
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2 |
緩衝時間\停課 |
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11/14(六)13:30～16:00期中考 考試範圍1.5～5.5 (英文命題) |
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第十週 11/16-11/20 |
1 |
[6.3] Volumes by Cylindrical Shells [6.4] Work（※） |
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2 |
[6.5] Average Value of a Function [7.1] Integration by Parts |
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7. Techniques of Integration |
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第十一週 11/23-11/27 |
1 |
[7.2] Trigonometric Integrals |
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2 |
[7.3] Trigonometric Substitution |
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第十二週 11/30-12/4 |
1 |
[7.4] Integration of Rational Functions by Partial Fractions |
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2 |
[7.5] Strategy for Integration [7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration |
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第十三週 12/7-12/11 |
1 |
[7.8] Improper Integrals |
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2 |
緩衝時間 |
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8. Further Applications of Integration |
第十四週 12/14-12/18 |
1 |
[8.1] Arc Length [8.2] Area of a Surface of Revolution |
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9. Differential Equations |
2 |
[9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method |
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第十五週 12/21-12/25 |
1 |
[9.3] Separable Equations [9.4] Models for Population Growth |
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2 |
[9.5] Linear Equations [9.6] Predator-Prey Systems （※） |
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10. Parametric Equations and Polar Coordinates |
第十六週 12/28-1/1 |
1 |
[10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves |
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2 |
1/1(五) 元旦放假 |
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第十七週 1/4-1/8 |
1 |
[10.3] Polar Coordinates [10.4] Areas and Lengths in Polar Coordinates |
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2 |
緩衝時間 |
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1/10(日)13:30～16:00期末考 考試範圍6.1～10.4 (英文命題) |
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