Description
Precalculus: Mathematics for Calculus 8th Edition by James Stewart, ISBN-13: 978-0357753637
[PDF eBook eTextbook] – Available Instantly
- Publisher: Cengage Learning; 8th edition (January 31, 2023)
- Language: English
- 1072 pages
- ISBN-10: 0357753631
- ISBN-13: 978-0357753637
Gain a strong foundation in the principles of mathematical thinking as you prepare for success in future calculus studies with PRECALCULUS: MATHEMATICS FOR CALCULUS, 8th Edition by the best-selling author team Stewart/Redlin/Watson. This latest edition offers updates within a clear, simple writing style that overcomes typical barriers to understanding. Comprehensive and evenly paced, this edition introduces both problem solving and mathematical modeling early and emphasizes these principles throughout with helpful practice and revised learning features. This edition provides complete coverage of the function concept and integrates the use of graphing technology to help you develop insights that help you better understand today’s mathematical ideas. New review helps you further master the fundamentals.
Table of Contents:
Cover Page
Title Page
Copyright Page
About the Authors
About the Cover
Preface
Acknowledgments
A Tribute to Lothar Redlin
To the Student
Abbreviations
Technology in the Eighth Edition
. Prologue: Principles of Problem Solving
1. Understand the Problem
2. Think of a Plan
Try to Recognize Something Familiar
Try to Recognize Patterns
Use Analogy
Introduce Something Extra
Take Cases
Work Backward
Establish Subgoals
Indirect Reasoning
Mathematical Induction
3. Carry out the Plan
4. Look Back
Problems
1. Fundamentals
1.1. Real Numbers
Real Numbers
Properties of Real Numbers
Addition and Subtraction
Multiplication and Division
The Real Line
Sets and Intervals
Absolute Value and Distance
1.1. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.2. Exponents and Radicals
Integer Exponents
Rules for Working with Exponents
Scientific Notation
Radicals
Rational Exponents
Rationalizing the Denominator; Standard Form
1.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.3. Algebraic Expressions
Adding and Subtracting Polynomials
Multiplying Algebraic Expressions
Special Product Formulas
Factoring Common Factors
Factoring Trinomials
Special Factoring Formulas
Factoring by Grouping Terms
1.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.4. Rational Expressions
The Domain of an Algebraic Expression
Simplifying Rational Expressions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Compound Fractions
Rationalizing the Denominator or the Numerator
Avoiding Common Errors
1.4. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.5. Equations
Solving Linear Equations
Formulas: Solving for One Variable in Terms of Others
Solving Quadratic Equations
Other Types of Equations
1.5. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.6. Complex Numbers
Arithmetic Operations on Complex Numbers
Square Roots of Negative Numbers
Complex Solutions of Quadratic Equations
1.6. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
1.7. Modeling with Equations
Making and Using Models
Problems About Interest
Problems About Area or Length
Problems About Mixtures
Problems About the Time Needed to Do a Job
Problems About Distance, Rate, and Time
1.7. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.8. Inequalities
Solving Linear Inequalities
Solving Nonlinear Inequalities
Absolute-Value Inequalities
Modeling with Inequalities
1.8. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.9. The Coordinate Plane; Graphs of Equations; Circles
The Coordinate Plane
The Distance and Midpoint Formulas
Graphs of Equations in Two Variables
Intercepts
Circles
Symmetry
1.9. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.10. Lines
The Slope of a Line
Point-Slope Form of the Equation of a Line
Slope-Intercept Form of the Equation of a Line
Vertical and Horizontal Lines
General Equation of a Line
Parallel and Perpendicular Lines
1.10. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.11. Solving Equations and Inequalities Graphically
Using Graphing Devices
Solving Equations Graphically
Solving Inequalities Graphically
1.11. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
1.12. Modeling Variation
Direct Variation
Inverse Variation
Combining Different Types of Variation
1.12. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Matching
Test
Focus on Modeling. Fitting Lines to Data
Problems
2. Functions
2.1. Functions
Functions All around Us
Definition of Function
Evaluating a Function
The Domain of a Function
Four Ways to Represent a Function
2.1. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
2.2. Graphs of Functions
Graphing Functions by Plotting Points
Graphing Functions with Graphing Devices
Graphing Piecewise-Defined Functions
Which Graphs Represent Functions? The Vertical Line Test
Which Equations Represent Functions?
Which Relations Represent Functions?
2.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
2.3. Getting Information from the Graph of a Function
Values of a Function; Domain and Range
Comparing Function Values: Solving Equations and Inequalities Graphically
Increasing and Decreasing Functions
Local Maximum and Minimum Values of a Function
2.3. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
2.4. Average Rate of Change of a Function
Average Rate of Change
Linear Functions Have Constant Rate of Change
2.4. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
2.5. Linear Functions and Models
Linear Functions
Slope and Rate of Change
Making and Using Linear Models
2.5. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
2.6. Transformations of Functions
Vertical Shifting
Horizontal Shifting
Reflecting Graphs
Vertical Stretching and Shrinking
Horizontal Stretching and Shrinking
Even and Odd Functions
2.6. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
2.7. Combining Functions
Sums, Differences, Products, and Quotients
Composition of Functions
Applications of Composition
2.7. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
2.8. One-to-One Functions and Their Inverses
One-to-One Functions: The Horizontal Line Test
The Inverse of a Function
Finding the Inverse of a Function
Graphing the Inverse of a Function
Applications of Inverse Functions
2.8. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Matching
Test
Focus on Modeling. Modeling with Functions
Problems
3. Polynomial and Rational Functions
3.1. Quadratic Functions and Models
Graphing Quadratic Functions Using the Vertex Form
Maximum and Minimum Values of Quadratic Functions
Modeling with Quadratic Functions
3.1. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
3.2. Polynomial Functions and Their Graphs
Polynomial Functions
Graphing Basic Polynomial Functions
Graphs of Polynomial Functions: End Behavior
Using Zeros to Graph Polynomials
Shape of the Graph Near a Zero
Local Maxima and Minima of Polynomials
3.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
3.3. Dividing Polynomials
Long Division of Polynomials
Synthetic Division
The Remainder and Factor Theorems
3.3. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
3.4. Real Zeros of Polynomials
Rational Zeros of Polynomials
Descartes’s Rule of Signs
Upper and Lower Bounds Theorem
Using Algebra and Graphing Devices to Solve Polynomial Equations
3.4. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
3.5. Complex Zeros and the Fundamental Theorem of Algebra
The Fundamental Theorem of Algebra and Complete Factorization
Zeros and Their Multiplicities
Complex Zeros Occur in Conjugate Pairs
Linear and Quadratic Factors
3.5. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
3.6. Rational Functions
The Rational Function f(x) = 1/x
Vertical and Horizontal Asymptotes
Finding Vertical and Horizontal Asymptotes of Rational Functions
Graphing Rational Functions
Common Factors in Numerator and Denominator
Slant Asymptotes and End Behavior
Applications
3.6. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
3.7. Polynomial and Rational Inequalities
Polynomial Inequalities
Rational Inequalities
3.7. Exercises
Concepts
Skills
Skills Plus
Applications
Properties and Formulas
Concept Check
Exercises
Matching
Test
Focus on Modeling. Fitting Polynomial Curves to Data
Problems
4. Exponential and Logarithmic Functions
4.1. Exponential Functions
Exponential Functions
Graphs of Exponential Functions
Compound Interest
4.1. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
4.2. The Natural Exponential Function
The Number e
The Natural Exponential Function
Continuously Compounded Interest
4.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
4.3. Logarithmic Functions
Logarithmic Functions
Graphs of Logarithmic Functions
Common Logarithms
Natural Logarithms
4.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
4.4. Laws of Logarithms
Laws of Logarithms
Expanding and Combining Logarithmic Expressions
Change of Base Formula
4.4. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
4.5. Exponential and Logarithmic Equations
Exponential Equations
Logarithmic Equations
Compound Interest
4.5. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
4.6. Modeling with Exponential Functions
Exponential Growth (Doubling Time)
Exponential Growth (Relative Growth Rate)
Logistic Growth
Radioactive Decay
Newton’s Law of Cooling
4.6. Exercises
Applications
4.7. Logarithmic Scales
The pH Scale
The Richter Scale
The Decibel Scale
4.7. Exercises
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Matching
Chapter 4 Test
Focus on Modeling. Fitting Exponential and Power Curves to Data
Problems
5. Trigonometric Functions: Unit Circle Approach
5.1. The Unit Circle
The Unit Circle
Terminal Points on the Unit Circle
The Reference Number
5.1. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
5.2. Trigonometric Functions of Real Numbers
The Trigonometric Functions
Values of the Trigonometric Functions
Fundamental Identities
5.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
5.3. Trigonometric Graphs
Graphs of Sine and Cosine
Graphs of Transformations of Sine and Cosine
Using Graphing Devices to Graph Trigonometric Functions
5.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
5.4. More Trigonometric Graphs
Graphs of Tangent, Cotangent, Secant, and Cosecant
Graphs of Transformations of Tangent and Cotangent
Graphs of Transformations of Secant and Cosecant
5.4. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
5.5. Inverse Trigonometric Functions and Their Graphs
The Inverse Sine Function
The Inverse Cosine Function
The Inverse Tangent Function
The Inverse Secant, Cosecant, and Cotangent Functions
5.5. Exercises
Concepts
Skills
Discuss ▪ Discover ▪ Prove ▪ Write
5.6. Modeling Harmonic Motion
Simple Harmonic Motion
Damped Harmonic Motion
Phase and Phase Difference
5.6. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties & Formulas
Concept Check
Exercises
Matching
Test
Focus on Modeling. Fitting Sinusoidal Curves to Data
Problems
6. Trigonometric Functions: Right Triangle Approach
6.1. Angle Measure
Angle Measure
Angles in Standard Position
Length of a Circular Arc
Area of a Circular Sector
Circular Motion
6.1. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
6.2. Trigonometry of Right Triangles
Trigonometric Ratios
Special Triangles; Calculators
Applications of Trigonometry of Right Triangles
6.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
6.3. Trigonometric Functions of Angles
Trigonometric Functions of Angles
Evaluating Trigonometric Functions at Any Angle
Trigonometric Identities
Areas of Triangles
6.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
6.4. Inverse Trigonometric Functions and Right Triangles
The Inverse Sine, Inverse Cosine, and Inverse Tangent Functions
Solving for Angles in Right Triangles
Evaluating Expressions Involving Inverse Trigonometric Functions
6.4. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
6.5. The Law of Sines
The Law of Sines
The Ambiguous Case
6.5. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
6.6. The Law of Cosines
The Law of Cosines
Navigation: Heading and Bearing
The Area of a Triangle
6.6. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Matching
Test
Focus on Modeling. Surveying
Problems
7. Analytic Trigonometry
7.1. Trigonometric Identities
Simplifying Trigonometric Expressions
Proving Trigonometric Identities
7.1. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
7.2. Addition and Subtraction Formulas
Addition and Subtraction Formulas
Expressions Involving Trigonometric Functions of a Sum
Expressions of the Form A sin x + B cos x
7.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
7.3. Double-Angle, Half-Angle, and Product-Sum Formulas
Double-Angle Formulas
Half-Angle Formulas
Expressions Involving Inverse Trigonometric Functions
Product-Sum Formulas
7.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
7.4. Basic Trigonometric Equations
Basic Trigonometric Equations
Solving Trigonometric Equations by Factoring
7.4. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
7.5. More Trigonometric Equations
Solving Trigonometric Equations by Using Identities
Equations with Trigonometric Functions of Multiples of Angles
7.5. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Matching
Test
Focus on Modeling. Traveling and Standing Waves
Problems
8. Polar Coordinates, Parametric Equations, and Vectors
8.1. Polar Coordinates
Definition of Polar Coordinates
Relationship between Polar and Rectangular Coordinates
Polar Equations
8.1. Exercises
Concepts
Skills
Discuss ▪ Discover ▪ Prove ▪ Write
8.2. Graphs of Polar Equations
Graphing Polar Equations
Symmetry
Graphing Polar Equations with Graphing Devices
8.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
8.3. Polar Form of Complex Numbers; De Moivre’s Theorem
Graphing Complex Numbers
Polar Form of Complex Numbers
De Moivre’s Theorem
nth Roots of Complex Numbers
8.3. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
8.4. Plane Curves and Parametric Equations
Plane Curves and Parametric Equations
Eliminating the Parameter
Finding Parametric Equations for a Curve
Using Graphing Devices to Graph Parametric Curves
8.4. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
8.5. Vectors
Geometric Description of Vectors
Vectors in the Coordinate Plane
Using Vectors to Model Velocity and Force
8.5. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
8.6. The Dot Product
The Dot Product of Vectors
The Component of u along v
The Projection of u onto v
Work
8.6. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Chapter 8. Test
Focus on Modeling. The Path of a Projectile
Problems
9. Systems of Equations and Inequalities
9.1. Systems of Linear Equations in Two Variables
Systems of Linear Equations and Their Solutions
Substitution Method
Elimination Method
Graphical Method
The Number of Solutions of a Linear System in Two Variables
Modeling with Linear Systems
9.1. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
9.2. Systems of Linear Equations in Several Variables
Solving a Linear System
The Number of Solutions of a Linear System
Modeling Using Linear Systems
9.2. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
9.3. Matrices and Systems of Linear Equations
Matrices
The Augmented Matrix of a Linear System
Elementary Row Operations
Gaussian Elimination
Gauss-Jordan Elimination
Inconsistent and Dependent Systems
Modeling with Linear Systems
9.3. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
9.4. The Algebra of Matrices
Equality of Matrices
Addition, Subtraction, and Scalar Multiplication of Matrices
Multiplication of Matrices
Properties of Matrix Multiplication
Applications of Matrix Multiplication
9.4. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
9.5. Inverses of Matrices and Matrix Equations
The Inverse of a Matrix
Finding the Inverse of a 2 × 2 Matrix
Finding the Inverse of an n × n Matrix
Matrix Equations
Modeling with Matrix Equations
9.5. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
9.6. Determinants and Cramer’s Rule
Determinant of a 2 × 2 Matrix
Determinant of an n × n Matrix
Row and Column Transformations
Cramer’s Rule
Areas of Triangles Using Determinants
9.6. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
9.7. Partial Fractions
Distinct Linear Factors
Repeated Linear Factors
Irreducible Quadratic Factors
Repeated Irreducible Quadratic Factors
9.7. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
9.8. Systems of Nonlinear Equations
Substitution and Elimination Methods
Graphical Method
9.8. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
9.9. Systems of Inequalities
Graphing an Inequality
Systems of Inequalities
Systems of Linear Inequalities
Application: Feasible Regions
9.9. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Test
Focus on Modeling. Linear Programming
Problems
10. Conic Sections
10.1. Parabolas
Geometric Definition of a Parabola
Equations and Graphs of Parabolas
Applications
10.1. Exercises
Concepts
Skills
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
10.2. Ellipses
Geometric Definition of an Ellipse
Equations and Graphs of Ellipses
Eccentricity of an Ellipse
10.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
10.3. Hyperbolas
Geometric Definition of a Hyperbola
Equations and Graphs of Hyperbolas
10.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
10.4. Shifted Conics
Shifting Graphs of Equations
Shifted Ellipses
Shifted Parabolas
Shifted Hyperbolas
The General Equation of a Shifted Conic
10.4. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
10.5. Rotation of Axes
Rotation of Axes
General Equation of a Conic
The Discriminant
10.5. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
10.6. Polar Equations of Conics
A Unified Geometric Description of Conics
Polar Equations of Conics
10.6. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Matching
Test
Focus on Modeling. Conics in Architecture
Problems
11. Sequences and Series
11.1. Sequences and Summation Notation
Sequences
Recursively Defined Sequences
The Partial Sums of a Sequence
Sigma Notation
11.1. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
11.2. Arithmetic Sequences
Arithmetic Sequences
Partial Sums of Arithmetic Sequences
11.2. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
11.3. Geometric Sequences
Geometric Sequences
Partial Sums of Geometric Sequences
What Is an Infinite Series?
Infinite Geometric Series
11.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
11.4. Mathematical Induction
Conjecture and Proof
Mathematical Induction
11.4. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
11.5. The Binomal Theorem
Expanding ( a + b ) n
The Binomial Coefficients
The Binomial Theorem
Proof of the Binomial Theorem
11.5. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Test
Focus on Modeling. Modeling with Recursive Sequences
Problems
12. Limits: A Preview of Calculus
12.1. Finding Limits Numerically and Graphically
Definition of Limit
Estimating Limits Numerically and Graphically
Limits That Fail to Exist
One-Sided Limits
12.1. Exercises
Concepts
Skills
Discuss ▪ Discover ▪ Prove ▪ Write
12.2. Finding Limits Algebraically
Limit Laws
Applying the Limit Laws
Finding Limits Using Algebra and the Limit Laws
Using Left- and Right-Hand Limits
12.2. Exercises
Concepts
Skills
Skills Plus
Discuss ▪ Discover ▪ Prove ▪ Write
12.3. Tangent Lines and Derivatives
Tangent Lines
Derivatives
Instantaneous Rates of Change
12.3. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
12.4. Limits at Infinity; Limits of Sequences
Limits at Infinity
Limits of Sequences
12.4. Exercises
Concepts
Skills
Skills Plus
Applications
Discuss ▪ Discover ▪ Prove ▪ Write
12.5. Areas
The Area Problem
Definition of Area
12.5. Exercises
Concepts
Skills
Discuss ▪ Discover ▪ Prove ▪ Write
Properties and Formulas
Concept Check
Exercises
Test
Focus on Modeling. Interpretations of Area
Problems
SSM
Chapter 1. Fundamentals
1.1. Real Numbers
1.2. Exponents and Radicals
1.3. Algebraic Expressions
1.4. Rational Expressions
1.5. Equations
1.6. Complex Numbers
1.7. Modeling with Equations
1.8. Inequalities
1.9. The Coordinate Plane; Graphs of Equations; Circles
1.10. Lines
1.11. Solving Equations and Inequalities Graphically
1.12. Modeling Variation
Chapter 1 Review
Chapter 1 Test
Focus on Modeling. Fitting Lines to Data
Chapter 2. Functions
2.1. Functions
2.2. Graphs of Functions
2.3. Getting Information from the Graph of a Function
2.4. Average Rate of Change of a Function
2.5. Linear Functions and Models
2.6. Transformations of Functions
2.7. Combining Functions
2.8. One-to-One Functions and Their Inverses
Chapter 2. Review
Chapter 2. Test
Focus on Modeling. Modeling with Functions
Chapter 3. Polynomial and Rational Functions
3.1. Quadratic Functions and Models
3.2. Polynomial Functions and Their Graphs
3.3. Dividing Polynomials
3.4. Real Zeros of Polynomials
3.5. Complex Zeros and The Fundamental Theorem of Algebra
3.6. Rational Functions
3.7. Polynomial and Rational Inequalities
Chapter 3 Review
Chapter 3 Test
Focus On Modeling – Fitting Polynomial Curves to Data
Chapter 4. Exponential and Logarithmic Functions
4.1. Exponential Functions
4.2. The Natural Exponential Function
4.3. Logarithmic Functions
4.4. Laws of Logarithms
4.5. Exponential and Logarithmic Equations
4.6. Modeling with Exponential Functions
4.7. Logarithmic Scales
Chapter 4. Review
Chapter 4 Test
Focus on Modeling. Fitting Exponential and Power Curves to Data
Chapter 5. Trigonometric Functions: Unit Circle Approach
5.1. The Unit Circle
5.2. Trigonometric Functions of Real Numbers
5.3. Trigonometric Graphs
5.4. More Trigonometric Graphs
5.5. Inverse Trigonometric Functions and Their Graphs
5.6. Modeling Harmonic Motion
Chapter 5. Review
Chapter 5. Test
Focus on Modeling. Fitting Sinusoidal Curves to Data
Chapter 6. Trigonometric Functions: Right Triangle Approach
6.1. Angle Measure
6.2. Trigonometry of Right Triangles
6.3. Trigonometric Functions of Angles
6.4. Inverse Trigonometric Functions and Right Triangles
6.5. The Law of Sines
6.6. The Law of Cosines
Chapter 6. Review
Chapter 6. Test
Focus on Modeling. Surveying
Chapter 7. Analytic Trigonometry
7.1. Trigonometric Identities
7.2. Addition and Subtraction Formulas
7.3. Double-Angle, Half-Angle, and Product-Sum Formulas
7.4. Basic Trigonometric Equations
7.5. More Trigonometric Equations
Chapter 7. Review
Chapter 7. Test
Focus on Modeling. Traveling and Standing Waves
Chapter 8. Polar Coordinates, Parametric Equations, Vectors
8.1. Polar Coordinates
8.2. Graphs of Polar Equations
8.3. Polar Form of Complex Numbers; De Moivre’s Theorem
8.4. Plane Curves and Parametric Equations
8.5. Vectors
8.6. The Dot Product
Chapter 8 Review
Chapter 8 Test
Focus on Modeling. The Path of a Projectile
Chapter 9. Systems of Equations and Inequalities
9.1. Systems of Linear Equations in Two Variables
9.2. Systems of Linear Equations in Several Variables
9.3. Matrices and Systems of Linear Equations
9.4. The Algebra of Matrices
9.5. Inverses of Matrices and Matrix Equations
9.6. Determinants and Cramer’s Rule
9.7. Partial Fractions
9.8. Systems of Nonlinear Equations
9.9. Systems of Inequalities
Chapter 9. Review
Chapter 9. Test
Focus on Modeling Linear Programming
Chapter 10. Conic Sections
10.1. Parabolas
10.2. Ellipses
10.3. Hyperbolas
10.4. Shifted Conics
10.5. Rotation of Axes
10.6. Polar Equations of Conics
Chapter 10. Review
Chapter 4 Test
Focus on Modeling. Conics in Architecture
Chapter 11. Sequences And Series
11.1. Sequences And Summation Notation
11.2. Arithmetic Sequences
11.3. Geometric Sequences
11.4. Mathematical Induction
11.5. The Binomial Theorem
Chapter 11. Review
Chapter 11. Test
Focus On Modeling. Modeling with Recursive Sequences
Chapter 12. Limits: A Preview of Calculus
12.1. Finding Limits Numerically and Graphically
12.2. Finding Limits Algebraically
12.3. Tangent Lines and Derivatives
12.4. Limits at Infinity; Limits of Sequences
12.5. Areas
Chapter 12. Review
Chapter 12. Test
Focus on Modeling. Interpretations of Area
Appendixes A. Geometry Review
Appendixes B. Calculations And Significant Figures
Appendixes C. Graphing with a Graphing Calculator
. Appendixs E
E.1. Three-Dimensional Coordinate Geometry
E.2. Vectors in Three Dimensions
E.3. The Cross Product
E.4. Equations Of Lines And Planes
Appendixs F. Mathematics of Finance
Appendix G. Probability and Statistics
G.1. Counting
G.2. Probability
G.3. Binomial Probability
G.4. Expected Value
G.5. Descriptive Statistics (Numerical)
G.6. Descriptive Statistics (Graphical)
G.7. Introduction to Statistical Thinking
G.8. Introduction to Inferential Statistics
Appendix G. Review
Appendix G. Test
Focus on Modeling. The Monte Carlo Method
Prologue. Principles of Problem Solving
Appendix A. Geometry Review
Appendix B. Calculations and Significant Figures
Appendix C. Graphing with a Graphing Calculator
Appendix D. Using the TI-83/84 Graphing Calculator
Appendix E. Vectors in Two and Three Dimensions
Appendix F. Sequences and Series
Appendix G. Probability and Statistics
Algebra Toolkit A. Working with Numbers
Algebra Toolkit B. Working with Expressions
Algebra Toolkit C. Working with Equations
Algebra Toolkit D. Working with Graphs
Formula Sheets
The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He conducted research at the University of London and was influenced by the famous mathematician, George Polya, at Stanford University. Dr. Stewart most recently served as a professor of mathematics at McMaster University and the University of Toronto. His research focused on harmonic analysis. Dr. Stewart authored the best-selling calculus textbook series, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of successful precalculus texts and college algebra and trigonometry texts.
The late Lothar Redlin grew up on Vancouver Island and received a bachelor of science degree from the University of Victoria and a Ph.D. from McMaster University. He subsequently did research and taught at the University of Washington and the University of Waterloo as well as California State University, Long Beach. He was most recently a professor of mathematics at The Pennsylvania State University, Abington Campus. His research focused on topology. Dr. Redlin was a valued co-author for Dr. Stewart’s best-selling calculus textbook series and his popular precalculus, college algebra and trigonometry texts.
Saleem Watson received his bachelor of science degree from Andrews University in Michigan. He completed his graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. Dr. Watson conducted subsequently research at the Mathematics Institute of the University of Warsaw in Poland. He taught mathematics at Pennsylvania State University before serving at California State University, Long Beach, where he is currently professor emeritus. Dr. Watson’s research encompasses the field of functional analysis. Dr. Watson is an important co-author for Dr. Stewart’s best-selling calculus textbook series as well as his popular precalculus, college algebra and trigonometry texts.
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