Calculus Second Edition Book Cover

 Calculus Second Edition Book Cover

Calculus Second Edition

Additional Textbook Resources

GENERAL INFORMATION

TEACHER RESOURCES


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 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
 
 

RESOURCE PAGES

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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 LESSONS

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


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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: 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

SUPPORT MATERIALS

Calculus: Course Overview PDF
Calculus: Development of Major Content Strands PDF

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