Opening

Chapter 1 Opening

Section 1.1

1.1.1 

Applying Rates and Distance

Section 1.2

1.2.1

Piecewise-Defined Functions and Continuity

1.2.2

End Behavior and Asymptotes

1.2.3

Holes, Vertical Asymptotes, and Approach Statements

1.2.4

Composite Functions and Inverse Functions

1.2.5

Attributes of Even and Odd Functions

1.2.6

Design a Flag

Section 1.3

1.3.1

Finite Differences

1.3.2

Slope Statements and Finite Differences of Non-Polynomials

1.3.3

The Slope Walk

Section 1.4

1.4.1

Distance and Velocity

1.4.2

Average Velocity on a Position Graph

1.4.3

Average Velocity on a Velocity Graph

1.4.4

Acceleration

Section 1.5

1.5.1

Area and Slope

Opening

Chapter 2 Opening

Section 2.1

2.1.1

Area Under the Curve Using Trapezoids

2.1.2

Methods to Calculate Area Under a Curve

2.1.3

Area Under the Curve as a Riemann Sum

Section 2.2

2.2.1

Introduction to Limits as Predictions

2.2.2

Intuitive Ideas of Continuity

2.2.3

Definition of Continuity

2.2.4

Evaluating Limits

2.2.5s

Squeezing Limits

Section 2.3

2.3.1

Ramp Lab

2.3.2

Sudden Impact

2.3.3

Local Linearity

Section 2.4

2.4.1

Improving Approximation

Opening

Chapter 3 Opening

Section 3.1

3.1.1

The Power Rule

3.1.2

Secants to Tangents, AROC to IROC

Section 3.2

3.2.1

Definition of a Derivative

3.2.2

Derivatives Using Multiple Strategies

3.2.3

Derivatives of Sine and Cosine

Section 3.3

3.3.1

Curve Constructor: Part One

3.3.2

The Shape of a Curve

3.3.3

Curve Sketching: Derivatives

3.3.4

Ways to Describe f' and f"

Section 3.4

3.4.1

Conditions for Differentiability

3.4.2

Curve Constructor: Part Two

3.4.3

Differentiablility of Specific Functions

3.4.4

Intersection of Tangents

Opening

Chapter 4 Opening

Section 4.1

4.1.1

Definite Integrals

4.1.2

Numerical Cases of Definite Integrals

4.1.3

More Properties of Definite Integrals

Section 4.2

4.2.1 

Deriving “Area Functions”

4.2.2

Indefinite and Definite Integrals

4.2.3

The Fundamental Theorem of Calculus

4.2.4

The Fundamental Theorem of Calculus

4.2.5

Integrals as Accumulators

Section 4.3

4.3.1

Fast Times: Parts One & Two

4.3.2

Fast Times: Parts Three & Four

4.3.3 

Fast Times: Part Five

Section 4.4

4.4.1

Area Between Curves

4.4.2

More Area Between Curves

4.4.3

Multiple Methods for Calculating Area Between Curves

Section 4.5

4.5.1

Newton's Method

Opening

Chapter 5 Opening

Section 5.1

5.1.1

Distance, Velocity, and Acceleration Functions

5.1.2

Optimization

5.1.3

Using the Frist and Second Derivatives

5.1.4

Applying the First and Second Derivative Tests

Section 5.2

5.2.1

The Product Rule

5.2.2

Chain Rule and Application: Part One

5.2.3

Chain Rule and Application: Part Two

5.2.4

The Quotient Rule

5.2.5

More Trigonometric Derivatives

Section 5.3

5.3.1

Optimization Problems: Part One

5.3.2

Optimization Problems: Part Two

5.3.3

Optimization Problems: Part Three

Section 5.4

5.4.1

Chain Rule Extension of the Fundamental Theorem of Calculus

Section 5.5

5.5.1

Evaluating LImits of Indeterminate Forms

5.5.2

Using l'Hôpital's Rule

Opening

Chapter 6 Opening

Section 6.1

6.1.1

Exponential Functions

6.1.2

Derivatives of Exponential Functions

6.1.3

Derivatives Using Multiple Tools

6.1.4

Integrals of Exponential Functions

Section 6.2

6.2.1

Implicit Differentiation

6.2.2

Implicit Differentiation Practice

Section 6.3

6.3.1

Inverse Trigonometric Derivatives

6.3.2

Derivatives of Natural Logarithms

6.3.3

Derivatives of Inverse Functions

Section 6.4

6.4.1

Mean Value

6.4.2

Mean Value Theorem

6.4.3

Mean Value Theorem: Applications

Section 6.5

6.5.1

Improper Integrals

Opening

Chapter 7 Opening

Section 7.1

7.1.1

Related Rates Introduction

7.1.2

Related Rates Application: The Pythagorean Theorem

7.1.3

Related Rates Application: Similar Triangles

7.1.4

Related Rates Application: Choosing the Best Formula

7.1.5

Related Rates Application: Trigonometry

Section 7.2

7.2.1

Undoing the Chain Rule

7.2.2

Integration With u-Substitution

7.2.3

Definite Integrals and u-Substitution

7.2.4

Varied Integration Techniques

Section 7.3

7.3.1

Solving Differential Equations

7.3.2

Newton’s Law of Cooling

7.3.3

Solving Separable Differential Equations

7.3.4

Slope Fields with Parallel Tangents

7.3.5

Plotting Slope Efficiently

7.3.6

Differential Equation and Slope Field Applications

Section 7.4

7.4.1

Euler’s Method

7.4.2

Integration by Parts

7.4.3

Integration by Parts with Substitution

7.4.4

Integration by Partial Fractions

Opening

Chapter 8 Opening

Section 8.1

8.1.1

Volumes by Slicing

8.1.2

The Disk Method

8.1.3

The Washer Method

8.1.4

Revolution about Horizontal and Vertical Lines

8.1.5

Changing the Axis of Rotation

8.1.6

Disk and Washer Problems

Section 8.2

8.2.1

Shell Lab

8.2.2

Comparing the Disk and Shell Methods

8.2.3

Using an Appropriate Method to Calculate Volume

Section 8.3

8.3.1

Cross-Sections Lab: General Case

8.3.2

Cross-Sections Lab: Functions Given

8.3.3

Cross-Section Problems

Section 8.4

8.4.1

Arc Length

Opening

Chapter 9 Opening

Section 9.1

9.1.1

Infinite Geometric Series

9.1.2

More Infinite Geometric Series

9.1.3

Convergence and Divergence

Section 9.2

9.2.1

Parametric Equations

9.2.2

Converting Between Parametric and Rectilinear Form

Section 9.3

9.3.1

Introduction to Vectors

9.3.2

Vector Operations

Section 9.4

9.4.1

Graphs of Polar Equations

9.4.2

Converting Between Polar and Rectilinear Form

9.4.3

Polar Families

Opening

Chapter Opening

Section 10.1

10.1.1

Convergence of Series

10.1.2

The Divergence Test

10.1.3

The Alternating Series Test

10.1.4

The Integral Test

10.1.5

The p-Series Test

10.1.6

The Comparison Test

10.1.7

The Limit Comparison Test

10.1.8

The Ratio Test

Section 10.2

10.2.1

The Cootie Lab

10.2.2

More Logistic Differential Equations

Section 10.3

10.3.1

Power Series Convergence

10.3.2

Using Polynomials to Approximate Curves

Section 10.4

10.4.1

Absolute Convergence

10.4.2

Regrouping and Rearranging Series

Opening

Chapter 11 Opening

Section 11.1

11.1.1

Area Bounded by a Polar Curve

11.1.2

More Polar Area

11.1.3

Area Between Polar Curves

Section 11.2

11.2.1

Applied Calculus in Component Form

11.2.2

Second Derivatives in Component Form

11.2.3

Total Distance and Arc Length

Section 11.3

11.3.1

Slopes of Polar Curves

11.3.2

More Slopes of Polar Curves

Section 11.4

11.4.1

Battling Robots

Opening

Chapter 12 Opening

Section 12.1

12.1.1

Approximating with Polynomial Functions

12.1.2

Taylor Polynomials About x = 0

12.1.3

Taylor Polynomials About x = c

12.1.4

Taylor Series

12.1.5

Building Taylor Series Using Substitution

Section 12.2

12.2.1

Interval of Convergence Using Technology

12.2.2

Interval of Convergence Analytically

Section 12.3

12.3.1

Error Bound for Alternating Taylor Polynomials

12.3.2

Lagrange Error Bound

Section 12.4

12.4.1

Evaluating Indeterminate Forms Using Taylor Series