| 週次 |
授課內容 |
| 第1週 |
課程說明
The Limit of a Function
Calculating Limits Using the Limit Laws |
| 第2週 |
The Precise Definition of a Limit.
Continuity.
Derivatives and Rates of Change. |
| 第3週 |
The Derivative as a Function.
Differentiation Formulas.
Derivatives of Trigonometric Functions. |
| 第4週 |
The Chain Rule
Implicit Differentiation.
Rates of Change in the Natural and Social Sciences, and Related Rates |
| 第5週 |
Linear Approximations and Differentials.
Maximum and Minimum Values.
The Mean Value Theorem. |
| 第6週 |
Mid-term 1
What Derivatives Tell Us About the Shape of a Graph.
Limits at Infinity; Horizontal Asymptotes. |
| 第7週 |
Summary of Curve Sketching and Graphing with Calculus and Technology.
Optimization Problems.
Antiderivatives. |
| 第8週 |
The Area and Distance Problems.
The Definite Integral.
The Fundamental Theorem of Calculus. |
| 第9週 |
Indefinite Integrals and the Net Change Theorem.
The Substitution Rule.
Areas Between Curves. |
| 第10週 |
Volumes.
Volumes by Cylindrical Shells.
Average Value of a Function. |
| 第11週 |
Mid-term 2
Inverse Functions.
The Natural Logarithmic Function.
The Natural Exponential Function. |
| 第12週 |
General Logarithm and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions. |
| 第13週 |
Hyperbolic Functions
Indeterminate Forms and l’Hospital’s Rule
Integration by Parts |
| 第14週 |
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions |
| 第15週 |
Improper Integrals
Arc Length
Area of a Surface of Revolution |
| 第16週 |
Final Exam
課程含自主學習：由教學影片預習
Curves Defined by Parametric Equations
Calculus with Parametric Curves
Self-study by recorded lecture video (自主學習：由教學影片)
Polar Coordinates
Calculus in Polar Coordinates |
自主學習
內容 |
02.閱覽產業及學術相關多媒體資料
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