| ◆標記為自修內容不授課 |
| Ch1. Functions and Models |
| ◆ 1.3 New Functions from Old Functions |
| 1.4 Exponential Functions |
| 1.5 Inverse Functions and Logarithms |
| Ch2. Limits and Derivatives |
| 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 |
| Ch3. Differentiation Rules |
| 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 |
| Ch4. Applications of Differentiation |
| 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 |
| Ch5. Integrals |
| 5.1 Areas and Distances |
| 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 |
| Ch6. Applications of Integration |
| 6.1 Areas Between Curves |
| 6.2 Volumes |
| 6.3 Volumes by Cylindrical Shells |
| 6.5 Average Value of a Function |
| Ch7. Techniques of Integration |
| 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 |
| Ch8. Further Applications of Integration |
| 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 |
| Ch10. Parametric Equations and Polar Coordinates |
| 10.1 Curves Defined by Parametric Equations |
| 10.2 Calculus with Parametric Curves |
