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R. Review of Basic Concepts R.1 Sets R.2 Real Numbers and Their Properties R.3 Polynomials R.4 Factoring Polynomials R.5 Rational Expressions R.6 Rational Exponents R.7 Radical Expressions 1. Equations and Inequalities 1.1 Linear Equations 1.2 Applications and Modeling with Linear Equations 1.3 Complex Numbers 1.4 Quadratic Equations 1.5 Applications and Modeling with Quadratic Equations 1.6 Other Types of Equations and Applications 1.7 Inequalities 1.8 Absolute Value Equations and Inequalities 2. Graphs and Functions 2.1 Rectangular Coordinates and Graphs 2.2 Circles 2.3 Functions 2.4 Linear Functions 2.5 Equations of Lines and Linear Models 2.6 Graphs of Basic Functions 2.7 Graphing Techniques 2.8 Function Operations and Composition 3. Polynomial and Rational Functions 3.1 Quadratic Functions and Models 3.2 Synthetic Division 3.3 Zeros of Polynomial Functions 3.4 Polynomial Functions: Graphs, Applications, and Models 3.5 Rational Functions: Graphs, Applications, and Models 3.6 Variation 4. Inverse, Exponential, and Logarithmic Functions 4.1 Inverse Functions 4.2 Exponential Functions 4.3 Logarithmic Functions 4.4 Evaluating Logarithms and the Change-of-Base Theorem 4.5 Exponential and Logarithmic Equations 4.6 Applications and Models of Exponential Growth and Decay 5. Trigonometric Functions 5.1 Angles 5.2 Trigonometric Functions 5.3 Evaluating Trigonometric Functions 5.4 Solving Right Triangles 6. The Circular Functions and Their Graphs 6.1 Radian Measure 6.2 The Unit Circle and Circular Functions 6.3 Graphs of the Sine and Cosine Functions 6.4 Translations of the Graphs of the Sine and Cosine Functions 6.5 Graphs of the Tangent, Cotangent, Secant, and Cosecant 6.6 Harmonic Motion 7. Trigonometric Identities and Equations 7.1 Fundamental Identities 7.2 Verifying Trigonometric Identities 7.3 Sum and Difference Identities 7.4 Double-Angle and Half-Angle Identities 7.5 Inverse Circular Functions 7.6 Trigonometric Equations 7.7 Equations Involving Inverse Trigonometric Functions 8. Applications of Trigonometry 8.1 The Law of Sines 8.2 The Law of Cosines 8.3 Vectors, Operation, and the Dot Product 8.4 Applications of Vectors 8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients 8.6 De Moivre's Theorem; Powers and Roots of Complex Numbers 8.7 Polar Equations and Graphs 8.8 Parametic Equations, Graphs, and Applications 9. Systems and Matrices 9.1 Systems of Linear Equations 9.2 Matrix Solution of Linear Systems 9.3 Determinant Solution of Linear Systems 9.4 Partial Fractions 9.5 Nonlinear Systems of Equations 9.6 Systems of Inequalities and Linear Programming 9.7 Properties of Matrices 9.8 Matrix Inverses 10. Analytic Geometry 10.1 Parabolas 10.2 Ellipses 10.3 Hyperbolas 10.4 Summary of the Conic Sections 11. Further Topics in Algebra 11.1 Sequences and Series 11.2 Arithmetic Sequences and Series 11.3 Geometric Sequences and Series 11.4 The Binomial Theorem 11.5 Mathematical Induction 11.6 Counting Theory 11.7 Basics of Probability Appendices Appendix A. Polar Form of Conic Sections Appendix B. Rotation of Axes Appendix C. Geometry Formulas Glossary Solutions to Selected Exercises Answers to Selected Exercises Index of Applications Index Table of Contents
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