Calculus Third Edition Book Cover

Calculus Third Edition Book Cover

Calculus Third Edition

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TABLE OF CONTENTS

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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

 
 

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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

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