Chapter 2 |
Limits and Rates of Change |
2.1 |
The Tangent and Velocity Problems |
2.2 |
Limit of a Function |
2.3 |
Calculating Limits using the Limit Laws |
2.5 |
Continuity |
2.6 |
Tangents, Velocities, and Other Rates of Change |
Chapter 3 |
Derivatives |
3.1 |
Derivatives |
3.2 |
The Derivative as a Function |
3.3 |
Differentiation Formulas |
3.5 |
Derivatives of Trigonometric Functions |
3.6 |
The Chain Rule |
3.7 |
Implicit Differntiation |
3.8 |
Higher Derivatives |
3.9 |
Related Rates |
3.10 |
Linear Approximations and Differentials |
Chapter 4 |
Applications of Derivatives |
4.1 |
Maximum and Minimum Values |
4.2 |
The Mean Value Theorem |
4.3 |
How Derivatives Affect the Shape of a Graph |
4.4 |
Limits at Infinity; Horizontal Asymptotes |
4.5 |
Summary of Curve Sketching |
4.7 |
Optimization Problems |
4.9 |
Newton's Method |
4.10 |
Antiderivatives |
Chapter 5 |
Integrals |
5.1 |
Areas and Distances |
5.2 |
Definite Integrals |
8.7 |
Numerical Integration (Trapezoidal Rule only) |
5.3 |
The Fundamental Theorem of Calculus |
5.4 |
Indefinite Integrals and Total Change Theorem |
5.5 |
The Substitution Rule |
Chapter 6 |
Applications of Integration |
6.1 |
Area Between Curves |
6.2 |
Volumes |
|
(Prepared Summer 2000 by Leung, Bergman, Wenger) |
