Table of Contents
Preface
Acknowledgments
To the Student
About the Author
Applications Index
P. Prerequisites: Fundamental Concepts of Algebra
P.1 Algebraic Expressions, Mathematical Models, and Real Numbers
P.2 Basic Rules of Algebra
P.3 Exponents and Scientific Notation
P.4 Radicals and Rational Exponents
P.5 Polynomials
Mid-Chapter Check Point
P.6 Factoring Polynomials
P.7 Rational Expressions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER P TEST
1. Functions and Graphs
1.1 Graphs and Graphing Utilities
1.2 Basics of Functions and Their Graphs
1.3 More on Functions and Their Graphs
1.4 Linear Functions and Slope
1.5 More on Slope
Mid-Chapter Check Point
1.6 Transformations of Functions
1.7 Combinations of Functions; Composite Functions
1.8 Inverse Functions
1.9 Distance and Midpoint Formulas; Circles
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 1 TEST
2. Equations and Inequalities
2.1 Linear Equations and Rational Equations
2.2 Models and Applications
2.3 Complex Numbers
2.4 Quadratic Equations
Mid-Chapter Check Point
2.5 Other Types of Equations
2.6 Linear Inequalities and Absolute Value Inequalities
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 2 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-2)
3. Polynomial and Rational Functions
3.1 Quadratic Functions
3.2 Polynomial Functions and Their Graphs
3.3 Dividing Polynomials; Remainder and Factor Theorems
3.4 Zeros of Polynomial Functions
Mid-Chapter Check Point
3.5 Rational Functions and Their Graphs
3.6 Polynomial and Rational Inequalities
3.7 Modeling Using Variation
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 3 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-3)
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Properties of Logarithms
Mid-Chapter Check Point
4.4 Exponential and Logarithmic Equations
4.5 Exponential Growth and Decay; Modeling Data
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 4 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-4)
5. Trigonometric Functions
5.1 Angles and Radian Measure
5.2 Right Triangle Trigonometry
5.3 Trigonometric Functions of Any Angle
5.4 Trigonometric Functions of Real Numbers; Periodic Functions
Mid-Chapter Check Point
5.5 Graphs of Sine and Cosine Functions
5.6 Graphs of Other Trigonometric Functions
5.7 Inverse Trigonometric Functions
5.8 Applications of Trigonometric Functions
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 5 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-5)
6. Analytic Trigonometry
6.1 Verifying Trigonometric Identities
6.2 Sum and Difference Formulas
6.3 Double-Angle, Power-Reducing, and Half-Angle Formulas
Mid-Chapter Check Point
6.4 Product-to-Sum and Sum-to-Product Formulas
6.5 Trigonometric Equations
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 6 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-6)
7. Additional Topics in Trigonometry
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Polar Coordinates
7.4 Graphs of Polar Equations
Mid-Chapter Check Point
7.5 Complex Numbers in Polar Form; DeMoivre's Theorem
7.6 Vectors
7.7 The Dot Product
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 7 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-7)
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Partial Fractions
8.4 Systems of Nonlinear Equations in Two Variables
Mid-Chapter Check Point
8.5 Systems of Inequalities
8.6 Linear Programming
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 8 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-8)
9. Matrices and Determinants
9.1 Matrix Solutions to Linear Systems
9.2 Inconsistent and Dependent Systems and Their Applications
9.3 Matrix Operations and Their Applications
Mid-Chapter Check Point
9.4 Multiplicative Inverses of Matrices and Matrix Equations
9.5 Determinants and Cramer's Rule
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 9 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-9)
10. Conic Sections and Analytic Geometry
10.1 The Ellipse
10.2 The Hyperbola
10.3 The Parabola
Mid-Chapter Check Point
10.4 Rotation of Axes
10.5 Parametric Equations
10.6 Conic Sections in Polar Coordinates
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 10 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-10)
11. Sequences, Induction, and Probability
11.1 Sequences and Summation Notation
11.2 Arithmetic Sequences
11.3 Geometric Sequences and Series
Mid-Chapter Check Point
11.4 Mathematical Induction
11.5 The Binomial Theorem
11.6 Counting Principles, Permutations, and Combinations
11.7 Probability
SUMMARY, REVIEW, AND TEST
REVIEW EXERCISES
CHAPTER 11 TEST
CUMULATIVE REVIEW EXERCISES (CHAPTERS 1-11)
Appendix: Where Did That Come From? Selected Proofs
Answers to Selected Exercises
Subject Index
Photo Credits
