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 | |
| 10.3 Polar Coordinates | |
| 10.4 Calculus in Polar Coordinates | |
說明：
- 第一學期課程規劃 49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，題型為選擇題及計算/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。