Description
By connecting applications, modeling, and visualization, Gary Rockswold motivates students to learn mathematics in the context of their experiences. In order to both learn and retain the material, students must see a connection between the concepts and their real-lives. In this new edition, connections are taken to a new level with “See the Concept” features, where students make important connections through detailed visualizations that deepen understanding.
Rockswold is also known for presenting the concept of a function as a unifying theme, with an emphasis on the rule of four (verbal, graphical, numerical, and symbolic representations). A flexible approach allows instructors to strike their own balance of skills, rule of four, applications, modeling, and technology.
Table of Contents
1. Introduction to Functions and Graphs
1.1 Numbers, Data, and Problem Solving
1.2 Visualizing and Graphing Data
Checking Basic Concepts for Sections 1.1 and 1.2
1.3 Functions and Their Representations
1.4 Types of Functions and Their Rates of Change
Checking Basic Concepts for Sections 1.3 and 1.4
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Extended and Discovery Exercises
2. Linear Functions and Equations
2.1 Equations of Lines
2.2 Linear Equations
Checking Basic Concepts for Sections 2.1 and 2.2
2.3 Linear Inequalities
2.4 More Modeling with Functions
Checking Basic Concepts for Sections 2.3 and 2.4
2.5 Absolute Value Equations and Inequalities
Checking Basic Concepts for Section 2.5
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Extended and Discovery Exercises
Chapters 1-2 Cumulative Review Exercises
3. Quadratic Functions and Equations
3.1 Quadratic Functions and Models
3.2 Quadratic Equations and Problem Solving
Checking Basic Concepts for Sections 3.1 and 3.2
3.3 Complex Numbers
3.4 Quadratic Inequalities
Checking Basic Concepts for Sections 3.3 and 3.4
3.5 Transformations of Graphs
Checking Basic Concepts for Section 3.5
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Extended and Discovery Exercises
4. More Nonlinear Functions and Equations
4.1 More Nonlinear Functions and Their Graphs
4.2 Polynomial Functions and Models
Checking Basic Concepts for Sections 4.1 and 4.2
4.3 Division of Polynomials
4.4 Real Zeros of Polynomial Functions
Checking Basic Concepts for Sections 4.3 and 4.4
4.5 The Fundamental Theorem of Algebra
4.6 Rational Functions and Models
Checking Basic Concepts for Sections 4.5 and 4.6
4.7 More Equations and Inequalities
4.8 Radical Equations and Power Functions
Checking Basic Concepts for Sections 4.7 and 4.8
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Extended and Discovery Exercises
Chapters 1-4 Cumulative Review Exercises
5. Exponential and Logarithmic Functions
5.1 Combining Functions
5.2 Inverse Functions and Their Representations
Checking Basic Concepts for Sections 5.1 and 5.2
5.3 Exponential Functions and Models
5.4 Logarithmic Functions and Models
Checking Basic Concepts for Sections 5.3 and 5.4
5.5 Properties of Logarithms
5.6 Exponential and Logarithmic Equations
Checking Basic Concepts for Sections 5.5 and 5.6
5.7 Constructing Nonlinear Models
Checking Basic Concepts for Section 5.7
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Extended and Discovery Exercises
6. Trigonometric Functions
6.1 Angles and Their Measure
6.2 Right Triangle Trigonometry
Checking Basic Concepts for Sections 6.1 and 6.2
6.3 The Sine and Cosine Functions and Their Graphs
6.4 Other Trigonometric Functions and Their Graphs
Checking Basic Concepts for Sections 6.3 and 6.4
6.5 Graphing Trigonometric Functions
6.6 Inverse Trigonometric Functions
Checking Basic Concepts for Sections 6.5 and 6.6
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Extended and Discovery Exercises
Chapters 1-6 Cumulative Review Exercises
7. Trigonometric Identities and Equations
7.1 Fundamental Identities
7.2 Verifying Identities
Checking Basic Concepts for Sections 7.1 and 7.2
7.3 Trigonometric Equations
7.4 Sum and Difference Identities
Checking Basic Concepts for Sections 7.3 and 7.4
7.5 Multiple-Angle Identities
Checking Basic Concepts for Section 7.5
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Extended and Discovery Exercises
8. Further Topics in Trigonometry
8.1 Law of Sines
8.2 Law of Cosines
Checking Basic Concepts for Sections 8.1 and 8.2
8.3 Vectors
8.4 Parametric Equations
Checking Basic Concepts for Sections 8.3 and 8.4
8.5 Polar Equations
8.6 Trigonometric Form and Roots of Complex Numbers
Checking Basic Concepts for Sections 8.5 and 8.6
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Extended and Discovery Exercises
Chapters 1-8 Cumulative Review Exercises
9. Systems of Equations and Inequalities
9.1 Functions and Systems of Equations in Two Variables
9.2 Systems of Inequalities in Two Variables
Checking Basic Concepts for Sections 9.1 and 9.2
9.3 Systems of Linear Equations in Three Variables
9.4 Solutions to Linear Systems Using Matrices
Checking Basic Concepts for Sections 9.3 and 9.4
9.5 Properties and Applications of Matrices
9.6 Inverses of Matrices
Checking Basic Concepts for Sections 9.5 and 9.6
9.7 Determinants
Checking Basic Concepts for Section 9.7
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Extended and Discovery Exercises
Chapters 1-9 Cumulative Review Exercises
10. Conic Sections
10.1 Parabolas
10.2 Ellipses
Checking Basic Concepts for Sections 10.1 and 10.2
10.3 Hyperbolas
Checking Basic Concepts for Section 10.3
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Extended and Discovery Exercises
11. Further Topics in Algebra
11.1 Sequences
11.2 Series
Checking Basic Concepts for Sections 11.1 and 11.2
11.3 Counting
11.4 The Binomial Theorem
Checking Basic Concepts for Sections 11.3 and 11.4
11.5 Mathematical Induction
11.6 Probability
Checking Basic Concepts for Sections 11.5 and 11.6
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Extended and Discovery Exercises
Chapters 1-11 Cumulative Review Exercises
R. Reference: Basic Concepts from Algebra and Geometry
R.1 Formulas from Geometry
R.2 Integer Exponents
R.3 Polynomial Expressions
R.4 Factoring Polynomials
R.5 Rational Expressions
R.6 Radical Notation and Rational Exponents
R.7 Radical Expressions
Appendix A: Using the Graphing Calculator
Appendix B: A Library of Functions
Appendix C: Partial Fractions
Appendix D: Percent Change and Exponential Functions
Appendix E: Rotation of Axes
Bibliography
Answers to Selected Exercises
Photo Credits
Index of Applications
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Gary K Rockswold
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