Algebra and Trigonometry with Analytic Geometry, Classic Edition

1. FUNDAMENTAL CONCEPTS OF ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Fractional Expressions. Chapter 1 Review Exercises. Chapter 1 Discussion Exercises. 2. EQUATIONS AND INEQUALITIES. Equations. Applied Problems. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. More on Inequalities. Chapter 2 Review Exercises. Chapter 2 Discussion Exercises. 3. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. Chapter 3 Review Exercises. Chapter 3 Discussion Exercises. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions of Degree Greater than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation. Chapter 4 Review Exercises. Chapter 4 Discussion Exercises. 5. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. Chapter 5 Review Exercises. Chapter 5 Discussion Exercises. 6. THE TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. Chapter 6 Review Exercises. Chapter 6 Discussion Exercises. 7. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Addition and Subtraction Formulas. Multiple-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. The Inverse Trigonometric Functions. Chapter 7 Review Exercises. Chapter 7 Discussion Exercises. 8. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Trigonometric Form for Complex Numbers. De Moivre's Theorem and nth Roots of Complex Numbers. Vectors. The Dot Product. Chapter 8 Review Exercises. Chapter 8 Discussion Exercises. 9. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Linear Equations in More than Two Variables. Partial Fractions. Systems of Inequalities. Linear Programming. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Chapter 9 Review Exercises. Chapter 9 Discussion Exercises. 10. SEQUENCES, SERIES, AND PROBABILITY. Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability. Chapter 10 Review Exercises. Chapter 10 Discussion Exercises. 11. TOPICS FROM ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. Chapter 11 Review Exercises. Chapter 11 Discussion Exercises. Appendices. Answers to Selected Exercises. Index of Applications. Index.