| 週次 |
授課內容 |
| 第1週 |
Functions and Limits: The Limit of a Function 1.5
Calculating Limits Using the Limit Laws 1.6
|
| 第2週 |
The Precise Definition of a Limit 1.7
|
| 第3週 |
Continuity 1.8
Derivatives: Derivatives and Rates of Change 2.1 |
| 第4週 |
The Derivative as a Function 2.2
Differentiation Formulas 2.3
Derivatives of Trigonomtric Functions
& The Chain Rule 2.4-2.5 |
| 第5週 |
Derivatives of Trigonomtric Functions
& The Chain Rule 2.4-2.5
Implicit Differentiation 2.6
|
| 第6週 |
Linear Approximations and Differentials 2.8-2.9
Applications of Differentiation: Maximum and Minimum Values 3.1 |
| 第7週 |
The Mean-Value Theorem
& How Derivatives Affect the Shape of a Graph 3.2-3.3
Limits at Infinity; Horizontal Asymptotes 3.4 |
| 第8週 |
Summary of Curve Sketching & Optimization Problems 3.5-3.7
Midterm Exam |
| 第9週 |
Newton’s Method & Antiderivatives 3.8-3.9
Integrals: Areas and Distances 4.1
The Definite Integral 4.2 |
| 第10週 |
The Fundamental Theorem of Calculus 4.3
Indefinite Integrals and the Net Change Theorem 4.4 |
| 第11週 |
The Substitution Rule 4.5
Applications of Integration: Areas Between Curves 5.1 |
| 第12週 |
Applications of Integration: Areas Between Curves 5.1
Volumes 5.2 |
| 第13週 |
Volumes by Cylindrical Shells &
Inverse Functions: Inverse Functions 5.3-6.1
The Natural Logarithmic Functions 6.2 |
| 第14週 |
The Natural Exponential Function
& General Logarithmic and Exponential Functions
& Exponential Growth and Decay 6.3-6.5
Inverse Trigonometric Functions & Hyperbolic Funcions 6.6-6.7 |
| 第15週 |
Indeterminate Forms and l’Hospital’ 6.8
Techniques of Integration: Integration by Parts
& Trigonometric Integrals 7.1-7.2 |
| 第16週 |
Trigonometric Substitution 7.3
Integration of Rational Functions by Partial Fractions 7.4 |
| 第17週 |
Approximate Integration 7.7
Improper Integrals 7.8
Final Exam |
| 第18週 |
自主學習：檢視期末試卷 |