Contents

1. Title Page
2. Contents
3. Preface
   1. A Message to the Student
   2. Important Information
   3. Schedule
   4. Habits for Success
4. 1 Algebraic Expressions, Equations, and Inequalities
   1. 1.1 Real Numbers and Algebraic Expressions
   2. 1.2 Properties of Exponents and Radicals
   3. 1.3 Polynomials and Factoring
   4. 1.4 Rational Expressions
   5. 1.5 Complex Numbers
   6. 1.6 Linear Equations in One Variable
   7. 1.7 Linear Inequalities in One Variable
   8. 1.8 Polynomial and Polynomial-Like Equations in One Variable
   9. 1.9 Rational and Radical Equations in One Variable
5. 2 Equations and Inequalities in Two Variables
   1. 2.1 The Cartesian Coordinate System
   2. 2.2 Circles
   3. 2.3 Linear Equations in Two Variables
   4. 2.4 Slope and Forms of Linear Equations
   5. 2.5 Parallel and Perpendicular Lines
   6. 2.6 Linear Inequalities in Two Variables
6. 3 Relations, Functions, and Their Graphs
   1. 3.1 Relations and Functions
   2. 3.2 Linear Functions
   3. 3.3 Quadratic Functions
   4. 3.4 Other Common Functions
   5. 3.5 Variation and Multivariable Functions
   6. 3.6 Mathematical Models
7. 4 Working with Functions
   1. 4.1 Transformations of Functions
   2. 4.2 Properties of Functions
   3. 4.3 Combining Functions
   4. 4.4 Inverses of Functions
8. 5 Polynomial and Rational Functions
   1. 5.1 Polynomial Functions and Polynomial Inequalities
   2. 5.2 Polynomial Division and the Division Algorithm
   3. 5.3 Locating Real Zeros of Polynomial Functions
   4. 5.4 The Fundamental Theorem of Algebra
   5. 5.5 Rational Functions and Rational Inequalities
9. 6 Exponential and Logarithmic Functions
   1. 6.1 Exponential Functions and Their Graphs
   2. 6.2 Exponential Models
   3. 6.3 Logarithmic Functions and Their Graphs
   4. 6.4 Logarithmic Properties and Models
   5. 6.5 Exponential and Logarithmic Equations
10. 7 Trigonometric Functions
    1. 7.1 Radian and Degree Measure
    2. 7.2 Trigonometric Functions and Right Triangles
    3. 7.3 Trigonometric Functions and the Unit Circle
    4. 7.4 Graphs of Sine and Cosine Functions
    5. 7.5 Graphs of Other Trigonometric Functions
    6. 7.6 Inverse Trigonometric Functions
11. 8 Trigonometric Identities and Equations
    1. 8.1 Fundamental Trigonometric Identities
    2. 8.2 Sum and Di˙erence Identities
    3. 8.3 Product-Sum Identities
    4. 8.4 Trigonometric Equations
12. 9 Additional Topics in Trigonometry
    1. 9.1 The Law of Sines
    2. 9.2 The Law of Cosines
    3. 9.3 Polar Coordinates and Polar Equations
    4. 9.4 Parametric Equations
    5. 9.5 Trigonometric Form of Complex Numbers
    6. 9.6 Vectors in the Cartesian Plane
    7. 9.7 The Dot Product
    8. 9.8 Hyperbolic Functions
13. 10 Conic Sections
    1. 10.1 Ellipses
    2. 10.2 Parabolas
    3. 10.3 Hyperbolas
    4. 10.4 Rotation of Conic Sections
    5. 10.5 Polar Equations of Conic Sections
14. 11 Systems of Equations and Inequalities
    1. 11.1 Solving Systems of Linear Equations by Substitution and Elimination
    2. 11.2 Matrix Notation and Gauss-Jordan Elimination
    3. 11.3 Determinants and Cramer's Rule
    4. 11.4 Basic Matrix Operations
    5. 11.5 Inverses of Matrices
    6. 11.6 Partial Fraction Decomposition
    7. 11.7 Systems of Linear Inequalities and Linear Programming
    8. 11.8 Systems of Nonlinear Equations and Inequalities
15. 12 Sequences, Series, Combinatorics, and Probability
    1. 12.1 Sequences and Series
    2. 12.2 Arithmetic Sequences and Series
    3. 12.3 Geometric Sequences and Series
    4. 12.4 Mathematical Induction
    5. 12.5 Combinatorics
    6. 12.6 Probability
16. 13 An Introduction to Limits, Continuity, and the Derivative
    1. 13.1 Rates of Change and Tangents
    2. 13.2 Limits in the Plane
    3. 13.3 The Mathematical Definition of Limit
    4. 13.4 Determining Limits of Functions
    5. 13.5 Continuity
    6. 13.6 The Derivative