Precalculus Third Edition Book Cover

Precalculus Third Edition Book Cover

Precalculus Third Edition

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TABLE OF CONTENTS

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Chapter 1: Preparing for Your Journey
Opening 1.OP Chapter Opening
Section 1.1 1.1.1 Interpreting Graphs
1.1.2 The Spring Problem
1.1.3 Modeling with Functions
1.1.4 Rates of Change
1.1.5 Setting Up Word Problems
1.1.6 Equivalent Expressions
Section 1.2 1.2.1 Composition of Functions
1.2.2 Inverse Functions
1.2.3 Piecewise-Defined Functions and Continuity
Section 1.3 1.3.1 Radians as a Unit of Measure
1.3.2 Radian Measure in the Unit Circle
1.3.3 Applications of Radian Measure
Closure 1.CL Chapter Closure

Chapter 2: Functions and Trigonometry
Opening 2.OP Chapter Opening
Section 2.1 2.1.1 Characteristics of Functions
2.1.2 Even and Odd Functions
2.1.3 Transformations of Functions
Section 2.2 2.2.1 Special Angles in the Unit Circle
2.2.2 Trigonometric Ratios in the Unit Circle
2.2.3 Graphs of Sine and Cosine
2.2.4 Transformations of Sine and Cosine
2.2.5 Horizontal Stretches of Sine and Cosine Graphs
Section 2.3 2.3.1 Solving Trigonometric Equations
2.3.2 Inverse Sine and Cosine
2.3.3 Graphs of Tangent and Inverse Tangent
Closure 2.CL Chapter Closure

Chapter 3: Algebra and Area Under a Curve
Opening 3.OP Chapter Opening
Section 3.1 3.1.1 Operations with Rational Expressions
3.1.2 Rewriting Expressions and Equations
3.1.3 Solving Nonlinear Systems of Equations
3.1.4 Polynomial Division
3.1.5 Solving Classic Word Problems
Section 3.2 3.2.1 Using Sigma Notation
3.2.2 Area Under a Curve: Part One
3.2.3 Area Under a Curve: Part Two
3.2.4 Area Under a Curve: Part Three
Closure 3.CL Chapter Closure

Chapter 4: Polynomial and Rational Functions
Opening 4.OP Chapter Opening
Section 4.1 4.1.1 Graphs of Polynomial Functions in Factored Form
4.1.2 Writing Equations of Polynomial Functions
4.1.3 Identifying and Using Roots of Polynomials
Section 4.2 4.2.1 Graphing Transformations of y = 1/x
4.2.2 Graphing Rational Functions
4.2.3 Graphing Reciprocal Functions
Section 4.3 4.3.1 Polynomial and Rational Inequalities
4.3.2 Applications of Polynomial and Rational Functions
Closure 4.CL Chapter Closure

Chapter 5: Exponentials and Logarithms
Opening 5.OP Chapter Opening
Section 5.1 5.1.1 Applications of Exponential Functions
5.1.2 Stretching Exponential Functions
5.1.3 The number e
Section 5.2 5.2.1 Logarithms
5.2.2 Properties of Logarithms
5.2.3 Solving Exponential and Logarithmic Equations
5.2.4 Graphing Logarithmic Functions
5.2.5 Applications of Exponentials and Logarithms
Closure 5.CL Chapter Closure

Chapter 6: Triangles and Vectors
Opening 6.OP Chapter Opening
Section 6.1 6.1.1 The Law of Sines and Area
6.1.2 Law of Cosines
6.1.3 The Ambiguous Case of the Law of Sines
Section 6.2 6.2.1 An Introduction to Vectors
6.2.2 Operations with Vectors
6.2.3 Applications of Vectors
6.2.4 The Dot Product
Closure 6.CL Chapter Closure

Chapter 7: Limits and Rates
Opening 7.OP Chapter Opening
Section 7.1 7.1.1 An Introduction to Limits
7.1.2 Working With One-Sided Limits
7.1.3 The Definition of a Limit
7.1.4 Limits and Continuity
7.1.5 Special Limits
Section 7.2 7.2.1 Rates of Change From Data
7.2.2 Slope and Rates of Change
7.2.3 Average Velocity and Rates of Change
7.2.4 Moving From AROC to IROC
7.2.5 Rate of Change Applications
Closure 7.CL Chapter Closure

Chapter 8: Extending Periodic Functions
Opening 8.OP Chapter Opening
Section 8.1 8.1.1 Graphing y = asin(b(xh)) + k
8.1.2 Modeling With Periodic Functions
8.1.3 Improving the Spring Problem
Section 8.2 8.2.1 Graphing Reciprocal Trigonometric Functions
8.2.2 Trigonometric Functions, Geometrically (optional)
Section 8.3 8.3.1 Simplifying Trigonometric Expressions
8.3.2 Proving Trigonometric Identities
8.3.3 Angle Sum and Difference Identities
8.3.4 Double-Angle and Half-Angle Identities
8.3.5 Solving Complex Trigonometric Equations
Closure 8.CL Chapter Closure

Chapter 9: Matrices
Opening 9.OP Chapter Opening
Section 9.1 9.1.1 Introduction to Matrices
9.1.2 Matrix Multiplication
9.1.3 Determinants and Inverse Matrices
9.1.4 Solving Systems Using Matrix Equations
Section 9.2 9.2.1 Linear Transformations
9.2.2 Compositions of Transformations
9.2.3 Properties of Linear Transformations
Closure 9.CL Chapter Closure

Chapter 10: Conics and Parametric Functions
Opening 10.OP Chapter Opening
Section 10.1 10.1.1 Circles and Completing the Square
10.1.2 Ellipses
10.1.3 Hyperbolas
10.1.4 Parabolas
10.1.5 Identifying Conic Sections
Section 10.2 10.2.1 Parametrically-Defined Functions
10.2.2 Applications of Parametric-Defined Functions
10.2.3 Conic Sections in Parametric Form
Closure 10.CL Chapter Closure

Chapter 11: Polar Functions and Complex Numbers
Opening 11.OP Chapter Opening
Section 11.1 11.1.1 Plotting Polar Coordinates
11.1.2 Graphs of Polar Functions
11.1.3 Families of Polar Functions
11.1.4 Converting Between Polar and Rectangular Forms
Section 11.2 11.2.1 Using the Complex Plane
11.2.2 Operations with Complex Numbers Geometrically
11.2.3 Polar Form of Complex Numbers
11.2.4 Operations with Complex Numbers in Polar Form
11.2.5 Powers and Roots of Complex Numbers
Closure 11.CL Chapter Closure

Chapter 12: Series and Statistics
Opening 12.OP Chapter Opening
Section 12.1 12.1.1 Arithmetic Series
12.1.2 Geometric Series
12.1.3 Infinite Geometric Series
12.1.4 Applications of Geometric Series
12.1.5 The Sum of the Harmonic Series (optional)
Section 12.2 12.2.1 The Binomial Theorem
12.2.2 Binomial Probabilities
Section 12.3 12.3.1 Expected Value of a Discrete Random Variable
12.3.2 Expected Value and Decision Making
Closure 12.CL Chapter Closure

Chapter 13: Precalculus Finale
Opening 13.OP Chapter Opening
Section 13.1 13.1.1 A Race to Infinity
13.1.2 Limits to Infinity
13.1.3 Evaluating Limits at a Point Algebraically
13.1.4 Another Look at e
Section 13.2 13.2.1 Trapping Area With Trapezoids
13.2.2 Area as a Function
13.2.2A Going all to Pieces: Writing an Area Program
13.2.3 Rocket Launch
Section 13.3 13.3.1 Velocity and Position Graphs
13.3.2 Instantaneous Velocity
13.3.3 Slope Functions
13.3.4 The Definition of Derivative
13.3.5 Slope and Area Under a Curve
Closure 13.CL Chapter Closure

 
 

RESOURCE PAGES

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Chapter 1: Preparing for Your Journey
Chapter 2: Functions and Trigonometry
Chapter 3: Algebra and Area Under a Curve
Chapter 4: Polynomial and Rational Functions
Chapter 5: Exponentials and Logarithms
Chapter 6: Triangles and Vectors
Chapter 7: Limits and Rates
Chapter 8: Extending Periodic Functions
Chapter 9: Matrices
Chapter 10: Conics and Parametric Functions
Chapter 11: Polar Functions and Complex Numbers
Chapter 12: Series and Statistics
Chapter 13: Precalculus Finale

ETOOLS/VIDEOS

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General eTools
Chapter 1: Preparing for Your Journey
Chapter 2: Functions and Trigonometry
Chapter 3: Algebra and Area Under a Curve
Chapter 4: Polynomial and Rational Functions

Chapter 5: Exponentials and Logarithms

Chapter 6: Triangles and Vectors

Chapter 7: Limits and Rates
Chapter 8: Extending Periodic Functions
Chapter 9: Matrices

Chapter 10: Conics and Parametric Functions
Chapter 11: Polar Functions and Complex Numbers

Chapter 12: Series and Statistics

Chapter 13: Precalculus Finale

Lesson Videos
  • Lesson 3.1.1 Study Skills - Learning From Mistakes (You Tube)


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