Calculus Third Edition Book Cover

## Additional Textbook Resources

### 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-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 Closure 1.CL Chapter Closure

Chapter 2: Rates, Sums, Limits, and Continuity
 Opening 2.OP Chapter Opening Section 2.1 2.1.1 Area Under a Curve Using Trapezoids 2.1.2 Methods to Calculate Area Under a Curve 2.1.3 Area Under a 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 Closure 2.CL Chapter Closure

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 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 Differentiability of Specific Functions 3.4.4 Intersection of Tangents Closure 3.CL Chapter Closure

Chapter 4: The Fundamental Theorem of Calculus
 Opening 4.OP Chapter Opening Section 4.1 4.1.1 Definite Integrals 4.1.2 Properties 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 Closure 4.CL Chapter Closure

Chapter 5: Derivative Tools and Applications
 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 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 The Chain Rule and Application: Part One 5.2.3 The 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 Closure 3.CL Chapter Closure Section 5.4 Mid-Course Reflection Activities

Chapter 6: More Tools and Theorems
 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 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 Closure 6.CL Chapter Closure

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 Applications: The Pythagorean Theorem 7.1.3 Related Rates Applications: Similar Triangles 7.1.4 Related Rates Applications: Choosing the Best Formula 7.1.5 Related Rates Applications: 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 Closure 7.CL Chapter Closure

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 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 Closure 8.CL Chapter Closure

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 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 Closure 9.CL Chapter Closure

Chapter 10: Convergence of Series
 Opening 10.OP 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 Closure 10.CL Chapter Closure

Chapter 11: Polar and Parametric Functions
 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 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 Closure 11.CL Chapter Closure

Chapter 12: Approximating Functions and Error
 Opening 12.OP Chapter 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 10.4.1 Evaluating Indeterminate Forms Using Taylor Series Closure 12.CL Chapter Closure

### RESOURCE PAGES

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Chapter 1: A Beginning Look at Calculus
Chapter 3: Slope and Curve Analysis
Chapter 4: The Fundamental Theorem of Calculus
Chapter 5: Derivative Tools and Applications
Chapter 6: More Tools and Theorems
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 Functions

### ETOOLS/VIDEOS

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General eTools
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: Derivative Tools and Applications

Chapter 6: More Tools and Theorems

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 Functions
Chapter 12: Approximating Functions and Error
Lesson Videos

### SUPPORT MATERIALS

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