Chapter 1: Functions and Models

Section 
Topic 
1.1 
Four Ways to Represent a Function 1.1.36 Four Ways to Represent a Function

1.2 
Mathematical Models: A Catalog of Essential Functions 1.2.20 Mathematical Models 1.2.30 Mathematical Models

1.3 
New Functions from Old Functions 1.3.46 New Functions from Old Functions 1.3.50 New Functions from Old Functions

1.4 
Exponential Functions 1.4.30 Exponential Functions

1.5 
Inverse Functions and Logarithms 1.5.54 Inverse Functions and Logarithms 1.5.62 Inverse Functions and Logarithms



Chapter 2: Limits and Derivatives 
Section 
Topic 
2.1 
The Tangent and Velocity Problems 2.1.8 The Tangent and Velocity Problems

2.2 
The Limit of a Function 2.2.12 The Limit of a Function 2.2.20 The Limit of a Function 2.2.30 The Limit of a Function 2.2.50 The Limit of a Function

2.3 
Calculating Limits Using the Limit Laws 2.3.26 Calculating Limits Using the Limit Laws 2.3.32 Calculating Limits Using the Limit Laws 2.3.56 Calculating Limits Using the Limit Laws

2.4 
The Precise Definition of a Limit 2.4.12 The Precise Definition of a Limit 2.4.22 The Precise Definition of a Limit 2.4.28 The Precise Definition of a Limit

2.5 
Continuity 2.5.14 Continuity 2.5.34 Continuity 2.5.60 Continuity

2.6 
Limits at Infinity; Horizontal Asymptotes 2.6.24 Limits at Infinity; Horizontal Asymptotes 2.6.46 Limits at Infinity; Horizontal Asymptotes 2.6.68 Limits at Infinity; Horizontal Asymptotes

2.7 
Derivatives and Rates of Change 2.7.14 Derivatives and Rates of Change 2.7.48 Derivatives and Rates of Change 2.7.56 Derivatives and Rates of Change

2.8 
The Derivative as a Function 2.8.12 The Derivative as a Function 2.8.38 The Derivative as a Function 2.8.58 The Derivative as a Function




Chapter 3: Differentiation Rules 
Section 
Topic 
3.1 
Derivatives of Polynomial and Exponential Functions 3.1.22 Derivatives of Polynomial and Exponential Functions 3.1.28 Derivatives of Polynomial and Exponential Functions 3.1.50 Derivatives of Polynomial and Exponential Functions 3.1.54 Derivatives of Polynomial and Exponential Functions 3.1.70 Derivatives of Polynomial and Exponential Functions

3.2 
The Product and Quotient Rules 3.2.16 The Product and Quotient Rules 3.2.24 The Product and Quotient Rules 3.2.36 The Product and Quotient Rules 3.2.60 The Product and Quotient Rules

3.3 
Derivatives of Trigonometric Functions 3.3.12 Derivatives of Trigonometric Functions 3.3.26 Derivatives of Trigonometric Functions 3.3.36 Derivatives of Trigonometric Functions 
3.4 
The Chain Rule 3.4.26 The Chain Rule 3.4.38 The Chain Rule 3.4.50 The Chain Rule 3.4.84 The Chain Rule

3.5 
Implicit Differentiation 3.5.18 Implicit Differentiation 3.5.30 Implicit Differentiation 3.5.42 Implicit Differentiation 3.5.58 Implicit Differentiation

3.6 
Derivatives of Logarithmic Functions 3.6.20 Derivatives of Logarithmic Functions 3.6.26 Derivatives of Logarithmic Functions 3.6.44 Derivatives of Logarithmic Functions

3.7 
Rates of Change in the Natural and Social Sciences 3.7.10 Rates of Change in the Natural Sciences 3.7.16 Rates of Change in the Natural Sciences 3.7.22 Rates of Change in the Natural Sciences
3.7.26 Rates of Change in the Natural Sciences 3.7.32 Rates of Change in the Natural Sciences

3.8 
Exponential Growth and Decay 3.8.8 Exponential Growth and Decay 3.8.16 Exponential Growth and Decay 3.8.20 Exponential Growth and Decay

3.9 
Related Rates 3.9.16 Related Rates 3.9.20 Related Rates 3.9.26 Related Rates 3.9.44 Related Rates 3.9.50 Related Rates

3.10 
Linear Approximations and Differentials 3.10.40 Linear Approximations

3.11 
Hyperbolic Functions 3.11.16 Hyperbolic Functions
3.11.23 Hyperbolic Functions 3.11.54 Hyperbolic Functions



Chapter 4: Applications of Differentiation 
Section 
Topic 
4.1 
Maximum and Minimum Values 4.1.36 Maximum and Minimum Values 4.1.42 Maximum and Minimum Values 4.1.60 Maximum and Minimum Values 4.1.72 Maximum and Minimum Values

4.2 
The Mean Value Theorem 
4.3 
How Derivatives Affect the Shape of a Graph 4.3.14 How Derivatives Affect the Shape of a Graph 4.3.44 How Derivatives Affect the Shape of a Graph 4.3.72 How Derivatives Affect the Shape of a Graph

4.4 
Indeterminate Forms and l’Hospital’s Rule 4.4.26 Indeterminate Forms and l'Hospital's Rule 4.4.52 Indeterminate Forms and l'Hospital's Rule 4.4.64 Indeterminate Forms and l'Hospital's Rule 4.4.78 Indeterminate Forms and l'Hospital's Rule

4.5 
Summary of Curve Sketching 
4.6 
Graphing With Calculus and Calculators 4.6.26 Graphing With Calculus and Calculators

4.7 
Optimization Problems 4.7.32 Optimization Problems 4.7.46 Optimization Problems 4.7.64 Optimization Problems 4.7.DrH01 Optimization Problems

4.8 
Newton’s Method 
4.9 
Antiderivatives 4.9.42 Antiderivatives 4.9.46 Antiderivatives 4.9.78 Antiderivatives



Chapter 5: Integrals 
Section 
Topic 
5.1 
Areas and Distances 5.1.6 Areas and Distances 5.1.20 Areas and Distances 5.1.31 Areas and Distances 
5.2 
The Definite Integral 5.2.20 The Definite Integral 5.2.24 The Definite Integral 5.2.39 The Definite Integral 5.2.48 The Definite Integral

5.3 
The Fundamental Theorem of Calculus 5.3.2 The Fundamental Theorem of Calculus 5.3.12 The Fundamental Theorem of Calculus 5.3.18 The Fundamental Theorem of Calculus 5.3.28 The Fundamental Theorem of Calculus 5.3.42 The Fundamental Theorem of Calculus 5.3.48 The Fundamental Theorem of Calculus 5.3.72 The Fundamental Theorem of Calculus

5.4 
Indefinite Integrals and the Net Change Theorem 5.4.6 Indefinite Integrals and the Net Change Theorem 5.4.14 Indefinite Integrals and the Net Change Theorem 5.4.28 Indefinite Integrals and the Net Change Theorem 5.4.40 Indefinite Integrals and the Net Change Theorem 5.4.50 Indefinite Integrals and the Net Change Theorem 5.4.66 Indefinite Integrals and the Net Change Theorem

5.5 
The Substitution Rule 5.5.22 The Substitution Rule 5.5.24 The Substitution Rule 5.5.56 The Substitution Rule 5.5.66 The Substitution Rule 5.5.84 The Substitution Rule
