| |
| |
| |
| Fundamentals | |
| |
| |
| Sets of Real Numbers | |
| |
| |
| Absolute Value | |
| |
| |
| Solving Equations (Review and Preview) | |
| |
| |
| Rectangular Coordinates | |
| |
| |
| Visualizing Data | |
| |
| |
| Graphs and Graphing Utilities | |
| |
| |
| Equations of Lines | |
| |
| |
| Symmetry and Graphs | |
| |
| |
| Circles | |
| |
| |
| |
| Equations And Inequalities | |
| |
| |
| Quadratic Equations: Theory and Examples | |
| |
| |
| Other Types of Equations | |
| |
| |
| Inequalities | |
| |
| |
| More on Inequalities | |
| |
| |
| |
| Functions | |
| |
| |
| The Definition of a Function | |
| |
| |
| The Graph of a Function | |
| |
| |
| Shapes of Graphs | |
| |
| |
| Average Rate of Change | |
| |
| |
| Techniques in Graphing | |
| |
| |
| Methods of Combining Function | |
| |
| |
| Iteration | |
| |
| |
| Inverse Functions | |
| |
| |
| |
| Polynomial And Rational Functions | |
| |
| |
| Applications to Optimization | |
| |
| |
| Linear Functions | |
| |
| |
| Quadratic Functions | |
| |
| |
| Using Iteration to Model Population Growth (Optional Section) | |
| |
| |
| Setting up Equations That Define Functions | |
| |
| |
| Maximum and Minimum Problems | |
| |
| |
| Polynomial Functions | |
| |
| |
| Rational Functions | |
| |
| |
| |
| Exponential And Logarithmic Functions | |
| |
| |
| Exponential Functions | |
| |
| |
| The Exponential Function y = ex | |
| |
| |
| Logarithmic Functions | |
| |
| |
| Properties of Logarithms | |
| |
| |
| Equations and Inequalities with Logs and Exponents | |
| |
| |
| Compound IntereSt. Exponential Growth and Decay | |
| |
| |
| |
| Trigonometric Functions Of Angles | |
| |
| |
| Trigonometric Functions of Acute Angles | |
| |
| |
| Algebra and the Trigonometric Functions | |
| |
| |
| Right-Triangle Applications | |
| |
| |
| Trigonometric Functions of Angles | |
| |
| |
| Trigonometric Identities | |
| |
| |
| |
| Trigonometric Functions Of Real Numbers | |
| |
| |
| Radian Measure | |
| |
| |
| Radian Measure and Geometry | |
| |
| |
| Trigonometric Functions of Real Numbers | |
| |
| |
| Graphs of the Sine and the Cosine Functions | |
| |
| |
| Graphs of y = A sin(Bx-C) and y = A cos(Bx - C) | |
| |
| |
| Simple Harmonic Motion | |
| |
| |
| Graphs of the Tangent and the Reciprocal Functions | |
| |
| |
| |
| Analytical Trigonometry | |
| |
| |
| The Addition Formulas | |
| |
| |
| The Double-Angle Formulas | |
| |
| |
| The Product-to-Sum and Sum-to-Product Formulas | |
| |
| |
| Trigonometric Equations | |
| |
| |
| The Inverse Trigonometric Functions | |
| |
| |
| |
| Additional Topics In Trigonometry | |
| |
| |
| The Law of Sines and the Law of Cosines | |
| |
| |
| Vectors in the Plane, a Geometric Approach | |
| |
| |
| Vectors in the Plane, an Algebraic Approach | |
| |
| |
| Parametric Equations | |
| |
| |
| Introduction to Polar Coordinates | |
| |
| |
| Curves in Polar Coordinates | |
| |
| |
| |
| Systems Of Equations | |
| |
| |
| Systems of Two Linear Equations in Two Unknowns | |
| |
| |
| Gaussian Elimination | |
| |
| |
| Matrices | |
| |
| |
| The Inverse of a Square Matrix | |
| |
| |
| Determinants and Cramer's Rule | |
| |
| |
| Nonlinear Systems of Equations | |
| |
| |
| Systems of Inequalities | |
| |
| |
| |
| Analytic Geometry | |
| |
| |
| The Basic Equations | |
| |
| |
| The Parabola | |
| |
| |
| Tangents to Parabolas (Optional) | |
| |
| |
| The Ellipse | |
| |
| |
| The Hyperbola | |
| |
| |
| The Focus-Directrix Property of Conics | |
| |
| |
| The Conics in Polar Coordinates | |
| |
| |
| Rotation of Axes | |
| |
| |
| |
| Roots Of Polynomial Equations | |
| |
| |
| The Complex Number System | |
| |
| |
| Division of Polynomials | |
| |
| |
| Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem | |
| |
| |
| The Fundamental Theorem of Algebra | |
| |
| |
| Rational and Irrational Roots | |
| |
| |
| Conjugate Roots and Descartes' Rule of Signs | |
| |
| |
| Introduction to Partial Fractions | |
| |
| |
| More About Partial Fractions | |
| |
| |
| |
| Additional Topics | |
| |
| |
| Mathematical Induction | |
| |
| |
| The Binomial Theorem | |
| |
| |
| Introduction to Sequences and Series | |
| |
| |
| Arithmetic Sequences and Series | |
| |
| |
| Geometric Sequences and Series | |
| |
| |
| DeMoivre's Theorem | |
| |
| |
| |
| Using a Graphing Utility | |
| |
| |
| |
| Significant Digits and Calculators | |
| |
| |
| Tables | |
| |
| |
| Answers to Selected Exercises | |
| |
| |
| Index | |