| Week |
Course Content |
| Week 1 |
課程說明
The Limit of a Function
Calculating Limits Using the Limit Laws |
| Week 2 |
The Precise Definition of a Limit.
Continuity.
Derivatives and Rates of Change. |
| Week 3 |
The Derivative as a Function.
Differentiation Formulas.
Derivatives of Trigonometric Functions. |
| Week 4 |
The Chain Rule
Implicit Differentiation.
Rates of Change in the Natural and Social Sciences, and Related Rates |
| Week 5 |
Linear Approximations and Differentials.
Maximum and Minimum Values.
The Mean Value Theorem. |
| Week 6 |
期中考一
What Derivatives Tell Us About the Shape of a Graph.
Limits at Infinity; Horizontal Asymptotes. |
| Week 7 |
Summary of Curve Sketching and Graphing with Calculus and Technology.
Optimization Problems.
Antiderivatives. |
| Week 8 |
The Area and Distance Problems.
The Definite Integral.
The Fundamental Theorem of Calculus. |
| Week 9 |
Indefinite Integrals and the Net Change Theorem.
The Substitution Rule.
Areas Between Curves. |
| Week 10 |
Volumes.
Volumes by Cylindrical Shells.
Average Value of a Function. |
| Week 11 |
期中考二
Inverse Functions.
The Natural Logarithmic Function.
The Natural Exponential Function. |
| Week 12 |
General Logarithm and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions. |
| Week 13 |
Hyperbolic Functions
Indeterminate Forms and l’Hospital’s Rule
Integration by Parts |
| Week 14 |
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions |
| Week 15 |
Improper Integrals
Arc Length
Area of a Surface of Revolution |
| Week 16 |
期末考 |
| Week 17 |
課程含自主學習：由教學影片預習
Curves Defined by Parametric Equations
Calculus with Parametric Curves |
| Week 18 |
課程含自主學習：由教學影片預習
Polar Coordinates
Calculus in Polar Coordinates |