| 週次 |
授課內容 |
| 第1週 |
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 The Tangent and Velocity Problems |
| 第2週 |
1.5 The Limit of a Function
1.6 Calculating Limits Using the Limit Laws
1.7 The Precise Definition of a Limit
1.8 Continuity |
| 第3週 |
2.1 Derivatives and Rates of Change
2.2 The Derivative as a Function
2.3 Differentiation Formulas |
| 第4週 |
2.4 Derivatives of Trigonometric Functions
2.5 The Chain Rule
2.6 Implicit Differentiation |
| 第5週 |
2.7 Rates of Change in the Natural and Social Sciences
2.8 Related Rates
2.9 Linear Approximations and Differentials |
| 第6週 |
3.1 Maximum and Minimum Values
3.2 The Mean Value Theorem
3.3 How Derivatives Affect the Shape of a Graph |
| 第7週 |
3.4 Limits at Infinity; Horizontal Asymptotes
3.5 Summary of Curve Sketching
3.6 Graphing with Calculus and Calculators |
| 第8週 |
期中考 |
| 第9週 |
3.7 Optimization Problems
3.8 Newton’s Method
3.9 Antiderivatives |
| 第10週 |
4.1 Areas and Distances
4.2 The Definite Integral
4.3 The Fundamental Theorem of Calculus |
| 第11週 |
4.4 Indefinite Integrals and the Net Change Theorem
4.5 The Substitution Rule
5.1 Areas Between Curves |
| 第12週 |
5.2 Volumes
5.3 Volumes by Cylindrical Shells
5.5 Average Value of a Function |
| 第13週 |
6.1 Inverse Functions
6.2 Exponential Functions and Their Derivatives
6.3 Logarithmic Functions |
| 第14週 |
6.4 Derivatives of Logarithmic
6.5 Exponential Growth and Decay
6.6 Inverse Trigonometric Functions
|
| 第15週 |
6.7 Hyperbolic Functions
6.8 Indeterminate Forms and l’Hospital’s Rule |
| 第16週 |
期末考
|
自主學習
內容 |
02.閱覽產業及學術相關多媒體資料
自主學習 - Inverse Function online course
|