 |
Chapter
1: Functions, Models and Graphs |
 |
|
| 1.1 |
Real Numbers and Number Lines |
| 1.2 |
Integer Exponents |
| 1.3 |
Fractional Exponents and Radicals |
| 1.4 |
Polynomials |
| 1.5 |
Lines and Their Graphs |
| 1.6a |
An Introduction to Functions |
| 1.6b |
Operations with Functions |
| 1.7 |
Functions and Their Graphs: A Calculator Section |
| 1.8 |
Functions and Models |
| |
Chapter 2: Limits, Slopes, and the Derivative |
|
|
| 2.1a |
Left and Right Hand Limits |
| 2.1b |
Limits |
| 2.2a |
Average Rate of Change |
| 2.2b |
Instantaneous Rate of Change and Interpreting Graphs |
| 2.3a |
Definition of the Derivative and Power Rule |
| 2.3b |
Slope and Rate of Change Considered Algebraically |
| 2.4 |
Applications: Marginal Analysis |
| 2.5a |
More About Limits |
| 2.5b |
More About Continuity |
| |
Chapter 3: Algebraic Differentiation Rules |
|
|
| 3.1 |
Product and Quotient Rules |
| 3.2 |
The Chain Rule and the General Power Rule |
| 3.3 |
Implicit Differentiation and Related Rates |
| 3.4a |
Local Extrema |
| 3.4b |
Critical Points and the First Derivatice Test |
| 3.5 |
Absolute Maximum and Minimum |
| |
Chapter 4: Applications of the Derivative |
|
|
| 4.1a |
Higher Order Derivatives and Concavity |
| 4.1b |
Higher Order Derivatives: the Second Derivative Test |
| 4.2 |
Curve Sketching: Polynomial Functions |
| 4.3 |
Curve Sketching: Rational Functions |
| 4.4 |
Business Applications |
| 4.5 |
Other Applications |
| 4.6 |
Differentials |
| |
Chapter 5: Exponential and Logarithmic Functions |
|
|
| 5.1 |
Exponential Functions |
| 5.2 |
The Algebra of the Natural Logarithm Function |
| 5.3 |
Differentiation of Logarithmic Functions |
| 5.4 |
Differentiation of Exponential Functions |
| 5.5a |
Applications of Exponential Functions: Growth and Decay |
| 5.5b |
Logarithmic Differentiation and Elasticity of Demand |
 |
