Chapter R: A Review of Basic Concepts and SkillsR-1The Language, Notation, and Numbers of MathematicsR-2Algebraic Expressions and the Properties of Real NumbersR-3Exponents, Scientific Notation, and a Review of PolynomialsR-4Factoring PolynomialsR-5Rational ExpressionsR-6Radicals and Rational ExponentsChapter 1: Equations and Inequalities1-1Linear Equations, Formulas, and Problem Solving1-2Linear Inequalities in One Variable1-3Absolute Value Equations and Inequalities1-4Complex Numbers1-5Solving Quadratic Equations1-6Solving Other Types of EquationsChapter 2: Relations, Functions and Graphs2-1Rectangular Coordinates; Graphing Circles and Relations2-2Graphs of Linear Equations2-3Linear Equations and Rates of Change2-4Functions, Notation, and Graphs of Functions2-5Analyzing the Graph of a Function2-6Toolbox Functions and Transformations2-7Piecewise-Defined Functions2-8The Algebra and Composition of FunctionsChapter 3: Polynomial and Rational Functions3-1Quadratic Functions and Applications3-2Synthetic Division; The Remainder and Factor Theorems3-3The Zeroes of Polynomial Functions3-4Graphing Polynomial Functions3-5Graphing Rational Functions3-6Additional Insights into Rational Functions3-7Polynomial and Rational Inequalities3-8Variation: Function Models in ActionChapter 4: Exponential and Logarithmic Functions4-1One-to-One and Inverse Functions4-2Exponential Functions4-3Logarithms and Logarithmic Functions4-4Properties of Logarithms; Solving Exponential and Logarithmic Equations4-5Applications from Business, Finance, and ScienceChapter 5: Introduction to Trigonometric Functions5-1Angle Measure, Special Triangles, and Special Angles5-2The Trigonometry of Right Triangles 5-3Trigonometry and the Coordinate Plane 5-4Unit Circles and the Trigonometric of Real Numbers5-5Graphs of Sine and Cosine Functions; Cosecant and Secant Functions 5-6Graphs of Tangent and Cotangent Functions 5-7Transformations and Applications of Trigonometric GraphsChapter 6: Trigonometric Identities, Inverses, and Equations6-1Fundamental Identities and Families of Identities 6-2Constructing and Verifying Identities 6-3The Sum and Difference Identities 6-4Double Angle, Half Angle & Product-to-Sum Identities6-5The Inverse Trigonometric Functions and Their Applications6-6Solving Basic Trigonometric Equations6-7General Trigonometric Equations and ApplicationsChapter 7: Applications of Trigonometry7-1Oblique Triangles and the Law of Sines 7-2The Law of Cosines; Area of a Triangle7-3Vectors and Vector Diagrams7-4Vector 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 Inequalities8-1Linear Systems in Two Variables with Applications8-2Linear Systems in Three Variables with Applications8-3Nonlinear Systems of Equations and Inequalities8-4Systems of Inequalities and Linear ProgrammingChapter 9: Matrices and Matrix Applications9-1Solving Systems Using Matrices and Row Operations9-2The Algebra of Matrices9-3Solving Linear Systems Using Matrix Equations9-4Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More Chapter 10: Analytical Geometry and Conic Sections10-1 Introduction to Analytic Geometry10-2 The Circle and the Ellipse10-3 The Hyperbola10-4 The Analytic Parabola10-5 Polar Coordinates, Equations, and Graphs10-6 More on Conic Sections: Rotation of Axes and Polar Form10-7 Parametric Equations and GraphsChapter 11: Additional Topics in Algebra11-1 Sequences and Series11-2 Arithmetic Sequences11-3 Geometric Sequences11-4 Mathematical Induction11-5 Counting Techniques11-6 Introduction to Probability11-7 The Binomial TheoremSummary and Concept Review
APPENDICESA-1More on Synthetic DivisionA-2More on MatricesA-3Deriving the Equation of a ConicA-4Proof Positive - A Selection of Proofs from Algebra and Trigonometry
