| 課程大綱 Syllabus |
學生學習目標
Learning Objectives |
單元學習活動
Learning Activities |
學習成效評量
Evaluation |
備註
Notes |
序
No. | 單元主題
Unit topic |
內容綱要
Content summary |
| 1 | Limits and Their Properties I |
1.Linear Models and Rates of Change
2.Functions and Their Graphs
3.Inverse Functions
4.Exponential and Logarithmic Functions |
1. 了解何謂函數及反函數
2. 了解指數函數及對數函數之定義、圖形及其相關性質 |
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| 2 | Limits and Their Properties II |
1. Finding Limits Graphically and Numerically
2. Evaluating Limits Analytically
3. Continuity and One-Sided Limits
4. Infinite Limits |
1. 了解各種求極限之方法
2. 了解函數之連續性意義
3. 了解單邊極限及無窮極限之意義及求法 |
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| 3 | Differentiation I |
1. The Derivative and the Tangent Line Problem
2. Basic Differentiation Rules and Rate of Change
3. Product and Quotient Rules and Higher-Order Derivatives |
1. 了解導函數之意義
2. 掌握基本的微分方法及技巧
3. 了解微分在變化率上的應用
4. 熟練積函數及商函數之微分方法
5. 了解高階導函數之定義 |
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| 4 | Differentiation II |
1. Chain Rule
2. Implicit Differentiation |
1. 了解並熟練微分的鏈鎖規則
2. 學會隱函數微分方法 |
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| 5 | Differentiation III |
1.Derivatives of Inverse Functions
2.Related Rates |
1. 學會反函數的微方法則
2. 了解相關變率的意義及其應用方法 |
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| 6 | Applications of Differentiation I |
1. Extrema on an Interval
2. Rolle's Theorem and the Mean Value Theorem
3. Increasing and Decreasing Functions and the First Derivative Test |
1. 了解函數之極值的意義
2. 了解Rolle's Theorem 及 Mean Value Theorem
3. 了解一階導函數測試法並能運用於函數極值之尋找 |
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| 7 | Applications of Differentiation II |
1. Concavity and the Second Derivative Test
2. Limits at Infinity |
1. 了解函數凹向性之意義並能用二階導函數測試法來判斷函數之凹向性
2. 了解在無窮遠處函數之極限求法及其在坐標平面上之幾何意義 |
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| 8 | Applications of Differentiation III |
1. Optimization Problems and Differentials
2. Differentials |
1. 學會利用微分來解決最佳化問題
2. 了解微分算子之意義及其如何應用 |
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| 9 | 期中考 |
檢視學生於期中考前所學之學習成效 |
對於函數/極限/微分及其應用，都能了解其涵意並能確實回答試題問題。 |
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| 10 | Integration I |
1. Antiderivatives and indefinite integration
2. Area |
1. 了解反導函數及不定積分的意義
2. 了解積分與面積間的關係 |
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| 11 | Integration II |
1. Riemann Sums and Definite integrals
2. Fundamental Theorem of Calculus |
1. 能了解黎曼和與定積分間的關聯
2. 能解決常見定積分問題
3. 能理解微積分基本定理並了解其應用 |
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| 12 | Integration III |
1. Integration by Substitution
2. The Natural Logarithmic Function: Integration |
1. 能學會以替代法來解決積分問題
2. 能以自然對數函數來解決倒數函數積分問題 |
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| 13 | Integration IV |
1. Inverse Trigonometric Function: Integration
2. Hyperbolic Functions |
1. 能學會以反三角函數來解決積分問題
2. 了解Hyperbolic Functions之意義及其如何微分、積分 |
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| 14 | Applications of Integration I |
1. Area of a Region Between Two Curves
2. Volume: The Disk Method |
1. 了解如何以積分來計算兩曲線間所圍面積
2. 了解如何以圓盤法來計算旋轉體之體積 |
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| 15 | Applications of Integration II |
1. Volume: The Shell Method
2. Arc Length and Surfaces of Revolution |
1. 了解如何以剝殼法來計算旋轉體之體積
2. 了解如何以積分來計算曲線弧長及旋轉體之表面積 |
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| 16 | Applications of Integration III |
1. Integration by Parts
2. Trigonometric Integrals |
1. 了解並能活用分部積分法之技巧
2. 了解如何解決常見三角函數之積分問題 |
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| 17 | Applications of Integration IV |
1. Trigonometric Substitution
2. Partial Fractions |
1. 了解三角替代法之使用時機及計算技巧
2. 了解部分分式法之使用時機及計算技巧 |
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| 18 | 期末考 |
檢視學生於期中考後至期末考前所學之學習成效 |
對於常見積分技巧能熟練應用 |
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