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