**Calculus Second Edition **

**Additional Textbook Resources**

### GENERAL INFORMATION

### TEACHER RESOURCES

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**Chapter 1: A Beginning Look at Calculus**

Opening | 1.OP | Chapter Opening |

Section 1.1 | 1.1.1 | Applying Rates and Distance |

Section 1.2 | 1.2.1 | Piecewise Functions and Continuity |

1.2.2 | End Behavior and Horizontal 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 | |

Section 1.5 | 1.5.1 | Area and Slope |

**Chapter 2: Rates, Sums, Limits, and Continuity**

Opening | 2.OP | Chapter Opening |

Section 2.1 | 2.1.1 | Area Under the Curve Using Trapezoids |

2.1.2 | Methods to Easily Calculate Area | |

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 | |

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 |

**Chapter 3: Slope and Curve Analysis**

Opening | 3.OP | Chapter 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 I |

3.3.2 | The Shape of a Curve | |

3.3.3 | Curve Sketching: Derivatives | |

3.3.4 | The First and Second Derivative Tests | |

Section 3.4 | 3.4.1 | Conditions for Differentiability |

3.4.2 | Curve Constructor: Part II | |

3.4.3 | Differentiability of Specific Functions | |

3.4.4 | Intersection of Tangents |

**Chapter 4: The Fundamental Theorem of Calculus**

Opening | 4.OP | Chapter Opening |

Section 4.1 | 4.1.1 | Definite Integrals |

4.1.2 | Numerical Cases of Definite Integrals | |

4.1.3 | 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 | |

Section 4.3 | 4.3.1 | Fast Times: Parts 1 & 2 |

4.3.2 | Fast Times: Parts 3 & 4 | |

4.3.3 | Fast Times: Part 5 | |

Section 4.4 | 4.4.1 | Area Between Curves |

4.4.2 | More Area Between Curves | |

4.4.3 | Multiple Methods for Finding Area Between Curves | |

Section 4.5 | 4.5.1 | Newton’s Method |

**Chapter 5: Optimization and Derivative Tools**

Opening | 5.OP | Chapter Opening |

Section 5.1 | 5.1.1 | Distance, Velocity, and Acceleration Functions |

5.1.2 | Optimization | |

5.1.3 | Using the 1st and 2nd Derivatives | |

5.1.4 | Applying the 1st and 2nd Derivative Test | |

Section 5.2 | 5.2.1 | The Product Rule |

5.2.2 | Chain Rule and Application: Part I | |

5.2.3 | Chain Rule and Application: Part II | |

5.2.4 | Quotient Rule: Two Proofs | |

5.2.5 | More Trigonometric Derivatives: tan x, cot x, sec x, and csc x | |

Section 5.3 | 5.3.1 | Optimization Problems: Part I |

5.3.2 | Optimization Problems: Part II | |

5.3.3 | Optimization Problems: Part III | |

Section 5.4 | 5.4.1 | Chain Rule Extension of the Fundamental Theorem of Calculus |

Section 5.5 | 5.5.1 | Finding Limits of Indeterminate Forms |

5.5.2 | Using l’Hôpital’s RuleI |

**Chapter 6: More Derivative Tools**

Opening | 6.OP | Chapter 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 | Inverse Trigonometric Derivatives: The Formulas | |

6.3.3 | Derivatives of Natural Logarithms | |

6.3.4 | Derivatives of Inverse Functions | |

Section 6.4 | 6.4.1 | Mean Value |

6.4.2 | The Mean Value Theorem | |

6.4.3 | Mean Value Theorem: Applications | |

Section 6.5 | 6.5.1 | Improper Integrals |

**Chapter 7: Related Rates and Integration Tools**

Opening | 7.OP | Chapter 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 Right Triangle | |

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 | The Soda Lab: Newton’s Law of Cooling | |

7.3.3 | Slope Fields with Parallel Tangents | |

7.3.4 | Slope Fields with Non-Parallel Tangents | |

7.3.5 | 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 |

**Chapter 8: Volume**

Opening | 8.OP | Chapter 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 | Revolving the Same Region about Various Lines | |

8.1.6 | Mixture of 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 Find Volume | |

Section 8.3 | 8.3.1 | Cross Sections Lab: General Case |

8.3.2 | Comparing the Disk and Shell Methods | |

8.3.3 | Cross Section Problems | |

Section 8.4 | 8.4.1 | Arc Length |

**Chapter 9: Pre-Calculus Review**

Opening | 9.OP | Chapter 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 | Parametric Equations Using a Graphing Calculator | |

Section 9.3 | 9.3.1 | Introduction to Vectors |

9.3.2 | Vector Operations | |

Section 9.4 | 9.4.1 | Polar Graphs |

9.4.2 | Polar Curves Using a Graphing Calculator | |

9.4.3 | Polar Families |

**Chapter 10: Convergence of Series**

Opening | 10.OP | Chapter Opening |

Section 10.1 | 10.1.1 | Convergence of Series |

10.1.2 | Divergence Test | |

10.1.3 | Alternating Series Test | |

10.1.4 | Integral Test for Convergence | |

10.1.5 | P-Series Test for Convergence | |

10.1.6 | Direct Comparison Test for Convergence | |

10.1.7 | Limit Comparison Test for Convergence | |

10.1.8 | Ration Test for Convergence | |

Section 10.2 | 10.2.1 | Catching Cooties 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 |

**Chapter 11: Polar and Parametric Equations**

Opening | 11.OP | Chapter 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 | Velocity Vectors and Slope |

11.2.2 | Acceleration Vectors | |

11.2.3 | Slope of a Tangent Vector | |

11.2.4 | Arclength of Parametric Curves | |

Section 11.3 | 11.3.1 | Derivative of Polar Curves |

11.3.2 | More Slopes of Polar Curves | |

Section 11.4 | 11.4.1 | Battling Robots |

**Chapter 12: Approximating Functions and Error**

Opening | 12.OP | Chapter Opening |

Section 12.1 | 12.1.1 | Approximating with Polynomial Functions |

12.1.2 | Constructing Maclaurin Polynomials | |

12.1.3 | Constructing Taylor Polynomials | |

12.1.4 | Taylor Series | |

12.1.5 | Substitution with Taylor Polynomials | |

Section 12.2 | 12.2.1 | Error of Taylor Polynomials |

12.2.2 | Error Formula | |

12.2.3 | Interval of Convergence for Taylor Series | |

12.2.4 | Indeterminate Forms Using Taylor Series |

**Index**[ Open All | Close All ]

**Chapter 1: A Beginning Look at Calculus**

**Chapter 2: Rates, Sums, Limits, and Continuity****Chapter 3: Slope and Curve Analysis**

**Chapter 4: The Fundamental Theorem of Calculus**

**Chapter 5: Optimization and Derivative Tools**

**Chapter 6: More Derivative Tools**

**Chapter 7: Related Rates and Integration Tools**

**Chapter 8: Volume**

**Chapter 9: Pre-Calculus Review**

**Chapter 10: Convergence of Series****Chapter 11: Polar and Parametric Equations**

**Chapter 12: Approximating Functions and Error**

Additional problems and lessons needed to align to the AP Calculus Curriculum Framework for 2016-2017

### ETOOLS

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**General eTools**

- Algebra Tiles (CPM)
- Desmos Graphing Calculator (Desmos)
- Desmos Accessibility

**Chapter 1: A Beginning Look at Calculus**

- Lesson 1.2.1: 1-15 Student eTool (Desmos)
- Lesson 1.2.1: 1-18 Student eTool (Desmos)
- Lesson 1.2.2: 1-31 Student eTool (Desmos)
- Lesson 1.2.2: 1-32 Student eTool (Desmos)

**Chapter 2: Rates, Sums, Limits, and Continuity**

- Lesson 2.1.2: 2-17 Student eTool (Desmos)
- Lesson 2.1.3: 2-29 Student eTool (Desmos)
- Lesson 2.4.1: 2-132 Student eTool (Desmos)

**Chapter 3: Slope and Curve Analysis**

**Chapter 4: The Fundamental Theorem of Calculus****Chapter 5: Optimization and Derivative Tools****Chapter 6: More Derivative Tools****Chapter 7: Related Rates and Integration Tools****Chapter 8: Volume****Chapter 9: Pre-Calculus Review****Chapter 10: Convergence of Series**

**Chapter 11: Polar and Parametric Equations**

- Lesson 11.4.1: Robot Battle eTool (Desmos)

**Chapter 12: Approximating Functions and Error***Calculus*: Course Overview PDF*Calculus*: Development of Major Content Strands PDF

If you have adopted the CPM curriculum and do not have a teacher edition, please contact our Business Office at (209) 745-2055 for information to obtain a copy.