Precalculus

<ul> <li>F. <strong>Foundations: A Prelude to Functions</strong> <ul> <li>F.1 The Distance and Midpoint Formulas</li> <li>F.2 Graphs of Equations in Two Variables; Intercepts; Symmetry</li> <li>F.3 Lines</li> <li>F.4 Circles</li> </ul> </li> </ul> <ol> <li><strong>Functions and Their Graphs</strong> <ul> <li>1.1 Functions</li> <li>1.2 The Graph of a Function</li> <li>1.3 Properties of Functions</li> <li>1.4 Library of Functions; Piecewise-defined Functions</li> <li>1.5 Graphing Techniques: Transformations</li> <li>1.6 Mathematical Models: Constructing Functions</li> <li>1.7 Building Mathematical Models Using Variation</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> </ul> </li> <li><strong>Linear and Quadratic Functions</strong> <ul> <li>2.1 Properties of Linear Functions and Linear Models</li> <li>2.2 Building Linear Models from Data</li> <li>2.3 Quadratic Functions and Their Zeros</li> <li>2.4 Properties of Quadratic Functions</li> <li>2.5 Inequalities Involving Quadratic Functions</li> <li>2.6 Building Quadratic Models from Verbal Descriptions and from Data</li> <li>2.7 Complex Zeros of a Quadratic Function</li> <li>2.8 Equations and Inequalities Involving the Absolute Value Function</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Polynomial and Rational Functions</strong> <ul> <li>3.1 Polynomial Functions and Models</li> <li>3.2 The Real Zeros of a Polynomial Function</li> <li>3.3 Complex Zeros; Fundamental Theorem of Algebra</li> <li>3.4 Properties of Rational Functions</li> <li>3.5 The Graph of a Rational Function</li> <li>3.6 Polynomial and Rational Inequalities</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Exponential and Logarithmic Functions</strong> <ul> <li>4.1 Composite Functions</li> <li>4.2 One-to-One Functions; Inverse Functions</li> <li>4.3 Exponential Functions</li> <li>4.4 Logarithmic Functions</li> <li>4.5 Properties of Logarithms</li> <li>4.6 Logarithmic and Exponential Equations</li> <li>4.7 Compound Interest</li> <li>4.8 Exponential Growth and Decay; Newton’s Law; Logistic Growth and Decay</li> <li>4.9 Building Exponential, Logarithmic, and Logistic Functions from Data</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Trigonometric Functions</strong> <ul> <li>5.1 Angles and Their Measure</li> <li>5.2 Right Triangle Trigonometry</li> <li>5.3 Computing the Values of Trigonometric Functions of Acute Angles</li> <li>5.4 Trigonometric Functions of Any Angle</li> <li>5.5 Unit Circle Approach; Properties of the Trigonometric Functions</li> <li>5.6 Graphs of the Sine and Cosine Functions</li> <li>5.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions</li> <li>5.8 Phase Shift; Sinusoidal Curve Fitting</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Analytic Trigonometry</strong> <ul> <li>6.1 The Inverse Sine, Cosine, and Tangent Functions</li> <li>6.2 The Inverse Trigonometric Functions (Continued)</li> <li>6.3 Trigonometric Equations</li> <li>6.4 Trigonometric Identities</li> <li>6.5 Sum and Difference Formulas</li> <li>6.6 Double-angle and Half-angle Formulas</li> <li>6.7 Product-to-Sum and Sum-to-Product Formulas</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Applications of Trigonometric Functions</strong> <ul> <li>7.1 Right Triangle Trigonometry; Applications Involving Right Triangles</li> <li>7.2 The Law of Sines</li> <li>7.3 The Law of Cosines</li> <li>7.4 Area of a Triangle</li> <li>7.5 Simple Harmonic Motion; Damped Motion; Combining Waves</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Polar Coordinates; Vectors</strong> <ul> <li>8.1 Polar Coordinates</li> <li>8.2 Polar Equations and Graphs</li> <li>8.3 The Complex Plane; DeMoivre’s Theorem</li> <li>8.4 Vectors</li> <li>8.5 The Dot Product</li> <li>8.6 Vectors in Space</li> <li>8.7 The Cross Product</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Analytic Geometry</strong> <ul> <li>9.1 Conics</li> <li>9.2 The Parabola</li> <li>9.3 The Ellipse</li> <li>9.4 The Hyperbola</li> <li>9.5 Rotation of Axes; General Form of a Conic</li> <li>9.6 Polar Equations of Conics</li> <li>9.7 Plane Curves and Parametric Equations</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Systems of Equations and Inequalities</strong> <ul> <li>10.1 Systems of Linear Equations: Substitution and Elimination</li> <li>10.2 Systems of Linear Equations: Matrices</li> <li>10.3 Systems of Linear Equations: Determinants</li> <li>10.4 Matrix Algebra</li> <li>10.5 Partial Fraction Decomposition</li> <li>10.6 Systems of Nonlinear Equations</li> <li>10.7 Systems of Inequalities</li> <li>10.8 Linear Programming</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Sequences; Induction; the Binomial Theorem</strong> <ul> <li>11.1 Sequences</li> <li>11.2 Arithmetic Sequences</li> <li>11.3 Geometric Sequences; Geometric Series</li> <li>11.4 Mathematical Induction</li> <li>11.5 The Binomial Theorem</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>Counting and Probability</strong> <ul> <li>12.1 Counting</li> <li>12.2 Permutations and Combinations</li> <li>12.3 Probability</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> <li>Cumulative Review</li> </ul> </li> <li><strong>A Preview of Calculus: The Limit, Derivative, and Integral of a Function</strong> <ul> <li>13.1 Finding Limits Using Tables and Graphs</li> <li>13.2 Algebra Techniques for Finding Limits</li> <li>13.3 One-sided Limits; Continuous Functions</li> <li>13.4 The Tangent Problem; The Derivative</li> <li>13.5 The Area Problem; The Integral</li> <li>Chapter Review</li> <li>Chapter Test</li> <li>Chapter Projects</li> </ul> </li> </ol> <h3>Appendix A. Review</h3> <ul> <li>A.1 Algebra Essentials</li> <li>A.2 Geometry Essentials</li> <li>A.3 Polynomials</li> <li>A.4 Factoring Polynomials</li> <li>A.5 Synthetic Division</li> <li>A.6 Rational Expressions</li> <li>A.7 nth Roots; Rational Exponents</li> <li>A.8 Solving Equations</li> <li>A.9 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Jobs</li> <li>A.10 Interval Notation; Solving Inequalities</li> <li>A.11 Complex Numbers</li> </ul> <h3>Appendix B. Graphing Utilities</h3> <ul> <li>B.1 The Viewing Rectangle</li> <li>B.2 Using a Graphing Utility to Graph Equations</li> <li>B.3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry</li> <li>B.4 Using a Graphing Utility to Solve Equations</li> <li>B.5 Square Screens</li> <li>B.6 Using a Graphing Utility to Graph Inequalities</li> <li>B.7 Using a Graphing Utility to Solve Systems of Linear Equations</li> <li>B.8 Using a Graphing Utility to Graph a Polar Equation</li> <li>B.9 Using a Graphing Utility to Graph Parametric Equations</li> </ul> <ul> <li>Answers</li> <li>Index</li> </ul>