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Chapter 1: Equations and Inequalities
1-1Linear Equations, Formulas, and Problem Solving
1-2Linear Inequalities in One Variable
1-3Absolute Value Equations and Inequalities
1-4Complex Numbers
1-5Solving Quadratic Equations
1-6Solving Other Types of Equations
Chapter 2: Relations, Functions and Graphs
2-1Rectangular Coordinates; Graphing Circles and Relations
2-2Graphs of Linear Equations
2-3Linear Equations and Rates of Change
2-4Functions, Notation, and Graphs of Functions
2-5Analyzing the Graph of a Function
2-6Toolbox Functions and Transformations
2-7Piecewise-Defined Functions
2-8The Algebra and Composition of Functions
Chapter 3: Polynomial and Rational Functions
3-1Quadratic Functions and Applications
3-2Synthetic Division; The Remainder and Factor Theorems
3-3The Zeroes of Polynomial Functions
3-4Graphing Polynomial Functions
3-5Graphing Rational Functions
3-6Additional Insights into Rational Functions
3-7Polynomial and Rational Inequalities
3-8Variation: Function Models in Action
Chapter 4: Exponential and Logarithmic Functions
4-1One-to-One and Inverse Functions
4-2Exponential Functions
4-3Logarithms and Logarithmic Functions
4-4Properties of Logarithms; Solving Exponential and Logarithmic Equations
4-5Applications from Business, Finance, and Science
Chapter 5: Introduction to Trigonometric Functions
5-1Angle Measure, Special Triangles, and Special Angles
5-2Unit Circles and the Trigonometry of Real Numbers
5-3Graphs of Sine and Cosine Functions; Cosecant and Secant Functions
5-4Graphs of Tangent and Cotangent Functions
5-5Transformations and Applications of Trigonometric Graphs
5-6The Trigonometry of Right Triangles
5-7Trigonometry and the Coordinate Plane
Chapter 6: Trigonometric Identities, Inverses, and Equations
6-1Fundamental Identities and Families of Identities
6-2Constructing and Verifying Identities
6-3The Sum and Difference Identities
6-4Double Angle, Half Angle & Product-to-Sum Identities
6-5The Inverse Trigonometric Functions and Their Applications
6-6Solving Basic Trigonometric Equations
6-7General Trigonometric Equations and Applications
Chapter 7: Applications of Trigonometry
7-1Oblique Triangles and the Law of Sines
7-2The Law of Cosines; Area of a Triangle
7-3Vectors and Vector Diagrams
7-4Vector Applications and the Dot Product
7-5Complex Numbers in Trigonometric Form
7-6Demoivre’s Theorem and the Theorem on nth Roots
Chapter 8: Systems of Equations and Inequalities
8-1Linear Systems in Two Variables with Applications
8-2Linear Systems in Three Variables with Applications
8-3Partial Fraction Decomposition
8-4Systems of Inequalities and Linear Programming
8-5Solving Systems Using Matrices and Row Operations
8-6The Algebra of Matrices
8-7Solving Linear Systems Using Matrix Equations
8-8Applications of Matrices and Determinants: Cramer's Rule, Geometry, and More
Chapter 9: Analytical Geometry
9-1Introduction to Analytic Geometry
9-2The Circle and the Ellipse
9-3The Hyperbola
9-4The Analytic Parabola
9-5Nonlinear Systems of Equations and Inequalities
9-6Polar Coordinates, Equations, and Graphs
9-7More on Conic Sections: Rotation of Axes and Polar Form
9-8Parametric Equations and Graphs
Chapter 10: Additional Topics in Algebra
10-1 Sequences and Series
10-2 Arithmetic Sequences
10-3 Geometric Sequences
10-4 Mathematical Induction
10-5 Counting Techniques
10-6 Introduction to Probability
10-7 The Binomial Theorem
Chapter 11: Bridges to Calculus - An Introduction to Limits
11-1 Finding Limits Numerically and Graphically
11-2 Algebraic Methods for Finding Limits; One-Sided Limits and Continuity
11-3 Infinite Limits and Limits at Infinity
11-4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve
APPENDICES
A-1A Review of Basic Concepts and Skills
A-2US Standard Units and the Metric System
A-3Rational Expressions and the Least Common Denominator
A-4Deriving the Equation of a Conic
A-5More on Matrices
A-6Deriving the Equation of a Conic
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