用書:Calculus(Early Transcendentals), James Stewart, 9th Edition
(◆ 標示之章節,由老師決定是否講授,不列入微積分會考範圍)
1. | Functions and Models -- 3 hours |
◆ | 1.3 New Functions from Old Functions |
1.4 Exponential Functions | |
1.5 Inverse Functions and Logarithms | |
2. | Limits and Derivatives -- 8hours |
2.2 The Limit of a Function | |
2.3 Calculating Limits Using the Limit Laws | |
2.4 The Precise Definition of a Limit | |
2.5 Continuity | |
2.6 Limits at Infinity; Horizontal Asymptotes | |
2.7 Derivatives and Rates of Change | |
2.8 The Derivative as a Function | |
3. | Differentiation Rules -- 8 hours |
3.1 Derivatives of Polynomials and Exponential Functions | |
3.2 The Product and Quotient Rules | |
3.3 Derivatives of Trigonometric Functions | |
3.4 The Chain Rule | |
3.5 Implicit Differentiation | |
3.6 Derivatives of Logarithmic and Inverse Trigonometric Functions | |
◆ | 3.7 Rates of Change in the Natural and Social Sciences |
◆ | 3.8 Exponential Growth and Decay |
◆ | 3.9 Related Rates |
3.10 Linear Approximations and Differentials | |
◆ | 3.11 Hyperbolic Functions |
4. | Applications of Differentiation -- 7 hours |
4.1 Maximum and Minimum Values | |
4.2 The Mean Value Theorem | |
4.3 What Derivatives Tell Us about the Shape of a Graph | |
4.4 Indeterminate Forms and L’Hospital’s Rule | |
4.5 Summary of Curve Sketching | |
4.7 Optimization Problems | |
◆ | 4.8 Newtons Method |
4.9 Antiderivatives | |
5. | Integrals -- 6 hours |
5.1 The Areas and Distance Problems | |
5.2 The Definite Integral | |
5.3 The Fundamental Theorem of Calculus | |
5.4 Indefinite Integrals and the Net Change Theorem | |
5.5 The Substitution Rule | |
6. | Applications of Integration -- 3 hours |
6.1 Areas Between Curves | |
6.2 Volumes | |
6.3 Volumes by Cylindrical Shells | |
6.5 Average Value of a Function | |
7. | Techniques of Integration -- 7 hours |
7.1 Integration by Parts | |
7.2 Trigonometric Integrals | |
7.3 Trigonometric Substitution | |
7.4 Integration of Rational Functions by Partial Fractions | |
◆ | 7.5 Strategy for Integration |
◆ | 7.7 Approximate Integration |
7.8 Improper Integrals | |
8. | Further Applications of Integration -- 3 hours |
8.1 Arc Length | |
8.2 Area of a Surface of Revolution | |
◆ | 8.3 Applications to Physics and Engineering |
◆ | 8.4 Applications to Economics and Biology |
◆ | 8.5 Probability |
10. | Parametric Equations and Polar Coordinates -- 4 hours |
10.1 Curves Defined by Parametric Equations | |
10.2 Calculus with Parametric Curves | |
說明:
- 第一學期課程規劃 47小時,其餘時間由任課老師運用:演習課,考試,進度調整。
- 常微分方程因時間因素省略,在二年級由其他課程搭配。
- 課程內之定理與性質,強調在說明與講述其內容。
- 學期末有一次期末會考,題型為選擇、填空或計算/證明題;以鑑別基本觀念與計算能力為準。會考成績為微積分獎給獎依據。