Precalculus

Preface. To the Student. Prologue: Principles of Problem Solving. 1. FUNDAMENTALS. Chapter Overview. Real Numbers. Exponents and Radicals. Algebraic Expressions. Rational Expressions. Equations. Modeling with Equations. Inequalities. Coordinate Geometry. Graphing Calculators; Solving Equations and Inequalities Graphically. Lines. Making Models Using Variation. Chapter 1 Review. Chapter 1 Test. FOCUS ON MODELING: Fitting Lines to Data. 2. FUNCTIONS. Chapter Overview. What is a Function?. Graphs of Functions. Getting Information from the Graph of a Function. Average Rate of Change of a Function. Transformations of Functions. Combining Functions. One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test. FOCUS ON MODELING: Modeling with Functions. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Chapter Overview. Quadratic Functions and Models. Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Complex Numbers. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Chapter 3 Review. Chapter 3 Test. FOCUS ON MODELING: Fitting Polynomial Curves to Data. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Chapter Overview. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Chapter 4 Review. Chapter 4 Test. FOCUS ON MODELING: Fitting Exponential and Power Curves to Data. Cumulative Review Test: Chapters 2, 3, and 4. 5. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH. Chapter Overview. The Unit Circle. Trigonometric Functions of Real Numbers. Trigonometric Graphs. More Trigonometric Graphs. Inverse Trigonometric Functions and Their Graphs. Modeling Harmonic Motion. Chapter 5 Review. Chapter 5 Test. FOCUS ON MODELING: Fitting Sinusoidal Curves to Data. 6. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH. Chapter Overview. Angle Measure. Trigonometry of Right Triangles. Trigonometric Functions of Angles. Inverse Trigonometric Functions and Triangles. The Law of Sines. The Law of Cosines. Chapter 6 Review. Chapter 6 Test. FOCUS ON MODELING: Surveying. 7. ANALYTIC TRIGONOMETRY. Chapter Overview. Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half-Angle, and Sum-Product Identities. Basic Trigonometric Equations. More Trigonometric Equations. Chapter 7 Review. Chapter 7 Test. FOCUS ON MODELING: Traveling and Standing Waves. Cumulative Review Test: Chapters 5, 6, and 7. 8. POLAR COORDINATES AND PARAMETRIC EQUATIONS. Chapter Overview. Polar Coordinates. Graphs of Polar Equations. Polar Form of Complex Numbers; DeMoivreâs Theorem. Plane Curves and Parametric Equations. Chapter 8 Review. Chapter 8 Test. FOCUS ON MODELING: The Path of a Projectile. 9. VECTORS IN TWO AND THREE DIMENSIONS. Chapter Overview. Vectors in Two Dimensions. The Dot Product. Three â"Dimensional Coordinate Geometry. Vectors in Three Dimensions. The Cross Product. Equations of Lines and Planes. Chapter 9 Review. Chapter 9 Test. FOCUS ON MODELING: Vector Fields. Cumulative Review Test: Chapters 8 and 9. 10. SYSTEMS OF EQUATIONS AND INEQUALITIES. Chapter Overview. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Matrices and Systems of Linear Equations. The Algebra of Matrices. Inverses of Matrices and Matrix Equations. Determinants and Cramerâs Rule. Partial Fractions. Systems of Nonlinear Equations. Systems of Inequalities. Chapter 10 Review. Chapter 10 Test. FOCUS ON MODELING: Linear Programming. 11. CONIC SECTIONS. Chapter Overview. Parabolas. Ellipses. Hyperbolas. Shifted Conics. Rotation of Axes. Polar Equations of Conics. Chapter 11 Review. Chapter 11 Test. FOCUS ON MODELING: Conics in Architecture. Cumulative Review Test: Chapters 10 and 11. 12. SEQUENCES AND SERIES. Chapter Overview. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematics of Finance. Mathematical Induction. The Binomial Theorem. Chapter 12 Review. Chapter 12 Test. FOCUS ON MODELING: Modeling with Recursive Sequences. 13. LIMITS: A PREVIEW OF CALCULUS. Chapter Overview. Finding Limits Numerically and Graphically. Finding Limits Algebraically. Tangent Lines and Derivatives. Limits at Infinity: Limits of Sequences. Areas. Chapter 13 Review. Chapter 13 Test. FOCUS ON MODELING: Interpretations of Area. Cumulative Review Test: Chapters 12 and 13. APPENDIX Calculations and Significant Figures.